From 0aa971ff81068e4df17eabe456b382768dc47a62 Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Wed, 9 Jun 2021 15:44:04 -0700
Subject: [PATCH 01/19] Update documentation notebook for latest IQ# bugfix.

---
 .../examples/experimental-simulators-from-python.ipynb   | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/documentation/examples/experimental-simulators-from-python.ipynb b/documentation/examples/experimental-simulators-from-python.ipynb
index 164612e243b..feb193c3044 100644
--- a/documentation/examples/experimental-simulators-from-python.ipynb
+++ b/documentation/examples/experimental-simulators-from-python.ipynb
@@ -44,7 +44,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Preparing Q# environment...\n"
+      "Preparing Q# environment...\n",
+      "."
      ]
     }
    ],
@@ -876,7 +877,7 @@
        "\r\n",
        "                        <tr>\r\n",
        "                            <th>State data</th>\r\n",
-       "                            <td>$$\\left\\langle XX𝟙𝟙, ZZ𝟙𝟙, 𝟙𝟙Z𝟙, -𝟙𝟙𝟙Z \\right\\rangle$$</td>\r\n",
+       "                            <td>$$\\left\\langle XX𝟙𝟙, ZZ𝟙𝟙, 𝟙𝟙Z𝟙, 𝟙𝟙𝟙Z \\right\\rangle$$</td>\r\n",
        "                        </tr>\r\n",
        "                    </table>\r\n",
        "                "
@@ -933,7 +934,7 @@
        "\r\n",
        "                        <tr>\r\n",
        "                            <th>State data</th>\r\n",
-       "                            <td>$$\\left\\langle X_{0}X_{1}, Z_{0}Z_{1}, Z_{2}, -Z_{3} \\right\\rangle$$</td>\r\n",
+       "                            <td>$$\\left\\langle X_{0}X_{1}, Z_{0}Z_{1}, Z_{2}, Z_{3} \\right\\rangle$$</td>\r\n",
        "                        </tr>\r\n",
        "                    </table>\r\n",
        "                "
@@ -1030,7 +1031,7 @@
        "\r\n",
        "                        <tr>\r\n",
        "                            <th>State data</th>\r\n",
-       "                            <td>$$\\left\\langle X_{0}X_{1}, Z_{0}Z_{1}, Z_{2}, -Z_{3} \\right\\rangle$$</td>\r\n",
+       "                            <td>$$\\left\\langle X_{0}X_{1}, Z_{0}Z_{1}, Z_{2}, Z_{3} \\right\\rangle$$</td>\r\n",
        "                        </tr>\r\n",
        "                    </table>\r\n",
        "                "

From 554d6a9e617fd33ea29056d5f2283c56fe54be69 Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Fri, 11 Jun 2021 11:04:57 -0700
Subject: [PATCH 02/19] Started work on decompositions.

---
 ...uantum.Experimental.Simulators.Runtime.dll | Bin 0 -> 2488320 bytes
 .../ContinuousTimeOperations.cs               |  76 +++++++++++
 .../Decompositions/ApplyWithLessControls.qs   |  40 ++++++
 .../Decompositions/ControlledH.qs             |  43 ++++++
 .../Decompositions/{CZ.qs => ControlledZ.qs}  |   7 +-
 .../Decompositions/Interface.qs               |  18 ---
 .../Decompositions/Measure.qs                 |  64 +++++++++
 .../OpenSystemsSimulator/Diagnostics.cs       |  60 +++++++++
 .../OpenSystemsSimulator.cs                   | 127 ++----------------
 .../OpenSystemsSimulator/QubitManager.cs      |  49 +++++++
 10 files changed, 344 insertions(+), 140 deletions(-)
 create mode 100644 src/Simulation/Native/win10/Microsoft.Quantum.Experimental.Simulators.Runtime.dll
 create mode 100644 src/Simulation/Simulators/OpenSystemsSimulator/ContinuousTimeOperations.cs
 create mode 100644 src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ApplyWithLessControls.qs
 create mode 100644 src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledH.qs
 rename src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/{CZ.qs => ControlledZ.qs} (53%)
 delete mode 100644 src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Interface.qs
 create mode 100644 src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Measure.qs
 create mode 100644 src/Simulation/Simulators/OpenSystemsSimulator/Diagnostics.cs
 create mode 100644 src/Simulation/Simulators/OpenSystemsSimulator/QubitManager.cs

diff --git a/src/Simulation/Native/win10/Microsoft.Quantum.Experimental.Simulators.Runtime.dll b/src/Simulation/Native/win10/Microsoft.Quantum.Experimental.Simulators.Runtime.dll
new file mode 100644
index 0000000000000000000000000000000000000000..538c495488401688d5f725f076750aeadc802ce8
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HcmV?d00001

diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/ContinuousTimeOperations.cs b/src/Simulation/Simulators/OpenSystemsSimulator/ContinuousTimeOperations.cs
new file mode 100644
index 00000000000..fb604f16fdf
--- /dev/null
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/ContinuousTimeOperations.cs
@@ -0,0 +1,76 @@
+// Copyright (c) Microsoft Corporation.
+// Licensed under the MIT License.
+
+using System;
+using System.Linq;
+using Microsoft.Quantum.Simulation.Core;
+using Microsoft.Quantum.Simulation.Common;
+using System.Runtime.InteropServices;
+using System.Threading;
+using Microsoft.Quantum.Simulation.Simulators.Exceptions;
+using Microsoft.Quantum.Intrinsic.Interfaces;
+using System.Collections.Generic;
+using System.Diagnostics;
+using Newtonsoft.Json.Linq;
+
+namespace Microsoft.Quantum.Experimental
+{
+    public partial class OpenSystemsSimulator
+    {
+        // These gates are not yet supported, pending a design for how to extend
+        // noise models to continuous-time gates (that is, those parameterized
+        // by real numbers, such as angles).
+
+        void IIntrinsicExp.Body(IQArray<Pauli> paulis, double angle, IQArray<Qubit> targets)
+        {
+            throw new NotImplementedException();
+        }
+
+        void IIntrinsicExp.AdjointBody(IQArray<Pauli> paulis, double angle, IQArray<Qubit> targets)
+        {
+            throw new NotImplementedException();
+        }
+
+        void IIntrinsicExp.ControlledBody(IQArray<Qubit> controls, IQArray<Pauli> paulis, double angle, IQArray<Qubit> targets)
+        {
+            throw new NotImplementedException();
+        }
+
+        void IIntrinsicExp.ControlledAdjointBody(IQArray<Qubit> controls, IQArray<Pauli> paulis, double angle, IQArray<Qubit> targets)
+        {
+            throw new NotImplementedException();
+        }
+        void IIntrinsicR.Body(Pauli pauli, double angle, Qubit target)
+        {
+            if (pauli == Pauli.PauliI)
+            {
+                // Don't apply global phases on uncontrolled operations.
+                return;
+            }
+            throw new NotImplementedException("Arbitrary rotation with noise is not yet supported.");
+        }
+
+        void IIntrinsicR.AdjointBody(Pauli pauli, double angle, Qubit target)
+        {
+            (this as IIntrinsicR).Body(pauli, -angle, target);
+        }
+
+        void IIntrinsicR.ControlledBody(IQArray<Qubit> controls, Pauli pauli, double angle, Qubit target)
+        {
+            if (controls is { Count: 0 })
+            {
+                (this as IIntrinsicR).Body(pauli, angle, target);
+            }
+            else
+            {
+                throw new NotImplementedException("Arbitrary controlled rotation with noise is not yet supported.");
+            }
+        }
+
+        void IIntrinsicR.ControlledAdjointBody(IQArray<Qubit> controls, Pauli pauli, double angle, Qubit target)
+        {
+            (this as IIntrinsicR).ControlledBody(controls, pauli, -angle, target);
+        }
+
+    }
+}
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ApplyWithLessControls.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ApplyWithLessControls.qs
new file mode 100644
index 00000000000..0b2281fe4f6
--- /dev/null
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ApplyWithLessControls.qs
@@ -0,0 +1,40 @@
+// Copyright (c) Microsoft Corporation.
+// Licensed under the MIT License.
+
+// NB: Copied from Utils.qs.
+namespace Microsoft.Quantum.Experimental.Decompositions {
+    open Microsoft.Quantum.Intrinsic;
+
+    /// Given a multiply-controlled operation that requires k controls 
+    /// applies it using ceiling(k/2) controls and using floor(k/2) temporary qubits
+    internal operation ApplyWithLessControlsA<'T> (op : ((Qubit[],'T) => Unit is Adj), (controls : Qubit[], arg : 'T)) : Unit is Adj {
+        let numControls = Length(controls);
+        let numControlPairs = numControls / 2;
+        use temps = Qubit[numControlPairs] {
+            within {
+                for numPair in 0 .. numControlPairs - 1 { // constant depth
+                    PhaseCCX(controls[2 * numPair], controls[2 * numPair + 1], temps[numPair]);
+                }
+            }
+            apply {
+                let newControls = numControls % 2 == 0 ? temps | temps + [controls[numControls - 1]];
+                op(newControls, arg);
+            }
+        }
+    }
+
+    internal operation PhaseCCX (control1 : Qubit, control2 : Qubit, target : Qubit) : Unit is Adj {
+        // https://arxiv.org/pdf/1210.0974.pdf#page=2
+        H(target);
+        CNOT(target,control1);
+        CNOT(control1,control2);
+        T(control2);
+        Adjoint T(control1);
+        T(target);
+        CNOT(target,control1);
+        CNOT(control1,control2);
+        Adjoint T(control2);
+        CNOT(target,control2);
+        H(target);
+    }
+}
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledH.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledH.qs
new file mode 100644
index 00000000000..db971a23072
--- /dev/null
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledH.qs
@@ -0,0 +1,43 @@
+// Copyright (c) Microsoft Corporation.
+// Licensed under the MIT License.
+
+namespace Microsoft.Quantum.Experimental.Decompositions {
+    open Microsoft.Quantum.Intrinsic;
+
+    internal operation PauliZFlip(basis : Pauli, target : Qubit) : Unit
+    is Adj {
+        if basis == PauliI {
+            fail $"PauliX cannot be mapped to PauliI using conjugation by Clifford";
+        } elif basis == PauliX {
+            H(target);
+        } elif basis == PauliY {
+            Adjoint S(target);
+            Adjoint H(target);
+        } elif basis != PauliZ {
+            fail $"PauliZ must be the only remaining case";
+        }
+    }
+
+    internal operation Ty(target : Qubit) : Unit
+    is Adj {
+        within {
+            PauliZFlip(PauliY, target);
+        } apply {
+            T(target);
+        }
+    }
+
+    internal operation ApplyControlledH(controls : Qubit[], target : Qubit) : Unit
+    is Adj {
+        if Length(controls) == 1 {
+            within {
+                Adjoint Ty(target);
+            } apply {
+                Controlled Z([controls[0]], target);
+            }
+        } else {
+            ApplyWithLessControlsA(Controlled H, (controls, qubit));
+        }
+    }
+
+}
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/CZ.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledZ.qs
similarity index 53%
rename from src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/CZ.qs
rename to src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledZ.qs
index 7fc5eea3f53..8d0939e5ebd 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/CZ.qs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledZ.qs
@@ -1,13 +1,14 @@
 // Copyright (c) Microsoft Corporation.
 // Licensed under the MIT License.
 
-namespace Microsoft.Quantum.Experimental {
+namespace Microsoft.Quantum.Experimental.Decompositions {
 
     internal operation ApplyCZUsingCNOT(control : Qubit, target : Qubit) : Unit {
         within {
-            ApplyUncontrolledH(target);
+            Microsoft.Quantum.Intrinsic.H(target);
         } apply {
-            ApplySinglyControlledX(control, target);
+            Controlled Microsoft.Quantum.Intrinsic.X([control], target);
         }
     }
+
 }
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Interface.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Interface.qs
deleted file mode 100644
index 31059665b33..00000000000
--- a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Interface.qs
+++ /dev/null
@@ -1,18 +0,0 @@
-// Copyright (c) Microsoft Corporation.
-// Licensed under the MIT License.
-
-namespace Microsoft.Quantum.Experimental {
-    open Microsoft.Quantum.Intrinsic;
-
-    operation ApplyUncontrolledH(target : Qubit) : Unit is Adj {
-        body intrinsic;
-        adjoint self;
-    }
-
-    operation ApplySinglyControlledX(control : Qubit, target : Qubit) : Unit is Adj {
-        body intrinsic;
-        adjoint self;
-    }
-
-}
-
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Measure.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Measure.qs
new file mode 100644
index 00000000000..7307c56b3a3
--- /dev/null
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Measure.qs
@@ -0,0 +1,64 @@
+// Copyright (c) Microsoft Corporation.
+// Licensed under the MIT License.
+
+namespace Microsoft.Quantum.Experimental.Decompositions {
+    open Microsoft.Quantum.Intrinsic as Intrinsic;
+
+    internal function IsAnyPauliI(bases : Pauli[]) : Bool {
+        for basis in bases {
+            if basis == PauliI {
+                return true;
+            }
+        }
+        return false;
+    }
+
+    internal operation Measure(bases : Pauli[], register : Qubit[]) : Result {
+        // If anything is PauliI, strip out and recurse.
+        if IsAnyPauliI(bases) {
+            mutable newBases = [];
+            mutable newQubits = [];
+            // NB: using Zipped would be nice here, but this is built before
+            //     M.Q.Standard...
+            for idxBasis in 0..Length(bases) - 1 {
+                if bases[idxBasis] != PauliI {
+                    set newBases += [bases[idxBasis]];
+                    set newQubits += [register[idxBasis]];
+                }
+            }
+
+            if Length(newBases) == 0 {
+                return Zero;
+            } else {
+                return Measure(newBases, register);
+            }
+        }
+
+        // At this point, we're guaranteed that bases contains no PauliI, and
+        // has length at least one. The simulator implementation likewise
+        // guarantees that in the single-qubit case, the basis is not Z.
+        // Let's check the easy single-qubit case first, then, and handle the
+        // X and Y cases.
+        if Length(bases) == 1 {
+            let basis = bases[0];
+            let target = register[0];
+            mutable result = Zero;
+            within {
+                if basis == PauliX {
+                    H(target);
+                } elif basis == PauliY {
+                    H(target);
+                    S(target);
+                } else {
+                    fail "Single-qubit Z case should have been handled by the simulator.";
+                }
+            } apply {
+                set result = Measure([PauliZ], [target]);
+            }
+            return result;
+        } else {
+            // TODO
+            fail "Multi-qubit measurement is not yet implemented.";
+        }
+    }
+}
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Diagnostics.cs b/src/Simulation/Simulators/OpenSystemsSimulator/Diagnostics.cs
new file mode 100644
index 00000000000..422f2e88395
--- /dev/null
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Diagnostics.cs
@@ -0,0 +1,60 @@
+// Copyright (c) Microsoft Corporation.
+// Licensed under the MIT License.
+
+using System;
+using System.Linq;
+using Microsoft.Quantum.Simulation.Core;
+using Microsoft.Quantum.Simulation.Common;
+using System.Runtime.InteropServices;
+using System.Threading;
+using Microsoft.Quantum.Simulation.Simulators.Exceptions;
+using Microsoft.Quantum.Intrinsic.Interfaces;
+using System.Collections.Generic;
+using System.Diagnostics;
+using Newtonsoft.Json.Linq;
+
+namespace Microsoft.Quantum.Experimental
+{
+    public partial class OpenSystemsSimulator
+    {
+
+        public class OpenSystemsDumpMachine<T> : Quantum.Diagnostics.DumpMachine<T>
+        {
+            private OpenSystemsSimulator Simulator { get; }
+
+            public OpenSystemsDumpMachine(OpenSystemsSimulator m) : base(m)
+            {
+                this.Simulator = m;
+            }
+
+            public override Func<T, QVoid> __Body__ => (location) =>
+            {
+                if (location == null) { throw new ArgumentNullException(nameof(location)); }
+                Simulator.MaybeDisplayDiagnostic(Simulator.CurrentState);
+                return QVoid.Instance;
+            };
+        }
+
+        // TODO: implement this by adding a new PartialTrace trait to the
+        //       Rust side, and then exposing it through the C API.
+        //       Until we have that, there's not a sensible way to interpret
+        //       states on subregisters in general.
+        public class OpenSystemsDumpRegister<T> : Quantum.Diagnostics.DumpRegister<T>
+        {
+            private OpenSystemsSimulator Simulator { get; }
+
+            public OpenSystemsDumpRegister(OpenSystemsSimulator m) : base(m)
+            {
+                this.Simulator = m;
+            }
+
+            public override Func<(T, IQArray<Qubit>), QVoid> __Body__ => (args) =>
+            {
+                var (location, register) = args;
+                if (location == null) { throw new ArgumentNullException(nameof(location)); }
+                this.Simulator.Get<Message, Message>().__Body__?.Invoke("DumpRegister not yet supported on OpenSystemsSimulator; skipping.");
+                return QVoid.Instance;
+            };
+        }
+    }
+}
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/OpenSystemsSimulator.cs b/src/Simulation/Simulators/OpenSystemsSimulator/OpenSystemsSimulator.cs
index dfe8e965f94..b708af3cf99 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/OpenSystemsSimulator.cs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/OpenSystemsSimulator.cs
@@ -41,58 +41,11 @@ public NoiseModel NoiseModel
 
         public State CurrentState => NativeInterface.GetCurrentState(this.Id);
 
-        public class OpenSystemsQubitManager : QubitManager
-        {
-            private readonly OpenSystemsSimulator Parent;
-            public OpenSystemsQubitManager(OpenSystemsSimulator parent, uint capacity)
-                : base(capacity)
-            {
-                this.Parent = parent;
-            }
-
-            protected override void Release(Qubit qubit, bool wasUsedOnlyForBorrowing)
-            {
-                if (qubit != null && qubit.IsMeasured)
-                {
-                    // Try to reset measured qubits.
-                    // TODO: There are better ways to do this; increment on the
-                    //       design and make it customizable.
-                    // FIXME: In particular, this implementation uses a lot of
-                    //        extraneous measurements.
-                    if ((this.Parent as IIntrinsicMeasure).Body(new QArray<Pauli>(Pauli.PauliZ), new QArray<Qubit>(qubit)) == Result.One)
-                    {
-                        (this.Parent as IIntrinsicX).Body(qubit);
-                    }
-                }
-                base.Release(qubit, wasUsedOnlyForBorrowing);
-            }
-        }
-
         public OpenSystemsSimulator(uint capacity = 3, string representation = "mixed") : base(new QubitManager((long)capacity))
         {
             this.Id = NativeInterface.Init(capacity, representation);
         }
 
-        void IIntrinsicExp.Body(IQArray<Pauli> paulis, double angle, IQArray<Qubit> targets)
-        {
-            throw new NotImplementedException();
-        }
-
-        void IIntrinsicExp.AdjointBody(IQArray<Pauli> paulis, double angle, IQArray<Qubit> targets)
-        {
-            throw new NotImplementedException();
-        }
-
-        void IIntrinsicExp.ControlledBody(IQArray<Qubit> controls, IQArray<Pauli> paulis, double angle, IQArray<Qubit> targets)
-        {
-            throw new NotImplementedException();
-        }
-
-        void IIntrinsicExp.ControlledAdjointBody(IQArray<Qubit> controls, IQArray<Pauli> paulis, double angle, IQArray<Qubit> targets)
-        {
-            throw new NotImplementedException();
-        }
-
         void IIntrinsicH.Body(Qubit target)
         {
             NativeInterface.H(this.Id, target);
@@ -100,54 +53,28 @@ void IIntrinsicH.Body(Qubit target)
 
         void IIntrinsicH.ControlledBody(IQArray<Qubit> controls, Qubit target)
         {
-            throw new NotImplementedException();
-        }
-
-        Result IIntrinsicMeasure.Body(IQArray<Pauli> paulis, IQArray<Qubit> targets)
-        {
-            if (targets is { Count: 1 } && paulis is { Count: 1 } && paulis.Single() == Pauli.PauliZ)
+            if (controls is { Count: 0 })
             {
-                return NativeInterface.M(this.Id, targets.Single());
+                (this as IIntrinsicH).Body(target);
             }
             else
             {
-                // FIXME: Pass multiqubit and non-Z cases to decompositions.
-                throw new NotImplementedException();
-            }
-        }
-
-        void IIntrinsicR.Body(Pauli pauli, double angle, Qubit target)
-        {
-            if (pauli == Pauli.PauliI)
-            {
-                // Don't apply global phases on uncontrolled operations.
-                return;
+                Get<Decompositions.ApplyControlledH, Decompositions.ApplyControlledH>().__Body__((controls, target));
             }
-            throw new NotImplementedException("Arbitrary rotation with noise is not yet supported.");
-        }
-
-        void IIntrinsicR.AdjointBody(Pauli pauli, double angle, Qubit target)
-        {
-            (this as IIntrinsicR).Body(pauli, -angle, target);
         }
 
-        void IIntrinsicR.ControlledBody(IQArray<Qubit> controls, Pauli pauli, double angle, Qubit target)
+        Result IIntrinsicMeasure.Body(IQArray<Pauli> paulis, IQArray<Qubit> targets)
         {
-            if (controls is { Count: 0 })
+            if (targets is { Count: 1 } && paulis is { Count: 1 } && paulis.Single() == Pauli.PauliZ)
             {
-                (this as IIntrinsicR).Body(pauli, angle, target);
+                return NativeInterface.M(this.Id, targets.Single());
             }
             else
             {
-                throw new NotImplementedException("Arbitrary controlled rotation with noise is not yet supported.");
+                Get<Decompositions.Measure, Decompositions.Measure>().__Body__((paulis, targets));
             }
         }
 
-        void IIntrinsicR.ControlledAdjointBody(IQArray<Qubit> controls, Pauli pauli, double angle, Qubit target)
-        {
-            (this as IIntrinsicR).ControlledBody(controls, pauli, -angle, target);
-        }
-
         void IIntrinsicS.Body(Qubit target)
         {
             NativeInterface.S(this.Id, target);
@@ -234,7 +161,7 @@ void IIntrinsicZ.ControlledBody(IQArray<Qubit> controls, Qubit target)
             }
             else if (controls is { Count: 1 })
             {
-                Get<ApplyCZUsingCNOT, ApplyCZUsingCNOT>().__Body__((controls[0], target));
+                Get<Decompositions.ApplyCZUsingCNOT, Decompositions.ApplyCZUsingCNOT>().__Body__((controls[0], target));
             }
             else
             {
@@ -247,43 +174,5 @@ public void Dispose()
             NativeInterface.Destroy(this.Id);
         }
 
-        public class OpenSystemsDumpMachine<T> : Quantum.Diagnostics.DumpMachine<T>
-        {
-            private OpenSystemsSimulator Simulator { get; }
-
-            public OpenSystemsDumpMachine(OpenSystemsSimulator m) : base(m)
-            {
-                this.Simulator = m;
-            }
-
-            public override Func<T, QVoid> __Body__ => (location) =>
-            {
-                if (location == null) { throw new ArgumentNullException(nameof(location)); }
-                Simulator.MaybeDisplayDiagnostic(Simulator.CurrentState);
-                return QVoid.Instance;
-            };
-        }
-
-        // TODO: implement this by adding a new PartialTrace trait to the
-        //       Rust side, and then exposing it through the C API.
-        //       Until we have that, there's not a sensible way to interpret
-        //       states on subregisters in general.
-        public class OpenSystemsDumpRegister<T> : Quantum.Diagnostics.DumpRegister<T>
-        {
-            private OpenSystemsSimulator Simulator { get; }
-
-            public OpenSystemsDumpRegister(OpenSystemsSimulator m) : base(m)
-            {
-                this.Simulator = m;
-            }
-
-            public override Func<(T, IQArray<Qubit>), QVoid> __Body__ => (args) =>
-            {
-                var (location, register) = args;
-                if (location == null) { throw new ArgumentNullException(nameof(location)); }
-                this.Simulator.Get<Message, Message>().__Body__?.Invoke("DumpRegister not yet supported on OpenSystemsSimulator; skipping.");
-                return QVoid.Instance;
-            };
-        }
     }
 }
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/QubitManager.cs b/src/Simulation/Simulators/OpenSystemsSimulator/QubitManager.cs
new file mode 100644
index 00000000000..7639b90d3cf
--- /dev/null
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/QubitManager.cs
@@ -0,0 +1,49 @@
+// Copyright (c) Microsoft Corporation.
+// Licensed under the MIT License.
+
+using System;
+using System.Linq;
+using Microsoft.Quantum.Simulation.Core;
+using Microsoft.Quantum.Simulation.Common;
+using System.Runtime.InteropServices;
+using System.Threading;
+using Microsoft.Quantum.Simulation.Simulators.Exceptions;
+using Microsoft.Quantum.Intrinsic.Interfaces;
+using System.Collections.Generic;
+using System.Diagnostics;
+using Newtonsoft.Json.Linq;
+
+namespace Microsoft.Quantum.Experimental
+{
+    public partial class OpenSystemsSimulator
+    {
+
+        public class OpenSystemsQubitManager : QubitManager
+        {
+            private readonly OpenSystemsSimulator Parent;
+            public OpenSystemsQubitManager(OpenSystemsSimulator parent, uint capacity)
+                : base(capacity)
+            {
+                this.Parent = parent;
+            }
+
+            protected override void Release(Qubit qubit, bool wasUsedOnlyForBorrowing)
+            {
+                if (qubit != null && qubit.IsMeasured)
+                {
+                    // Try to reset measured qubits.
+                    // TODO: There are better ways to do this; increment on the
+                    //       design and make it customizable.
+                    // FIXME: In particular, this implementation uses a lot of
+                    //        extraneous measurements.
+                    if ((this.Parent as IIntrinsicMeasure).Body(new QArray<Pauli>(Pauli.PauliZ), new QArray<Qubit>(qubit)) == Result.One)
+                    {
+                        (this.Parent as IIntrinsicX).Body(qubit);
+                    }
+                }
+                base.Release(qubit, wasUsedOnlyForBorrowing);
+            }
+        }
+
+    }
+}

From b1fa50ab5996361dd4b5e3f306c59e22a05bafd0 Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Fri, 11 Jun 2021 11:05:32 -0700
Subject: [PATCH 03/19] Added more detail to documentation notebook.

---
 .../experimental-simulators-from-python.ipynb | 1651 +++++++++++++++--
 1 file changed, 1525 insertions(+), 126 deletions(-)

diff --git a/documentation/examples/experimental-simulators-from-python.ipynb b/documentation/examples/experimental-simulators-from-python.ipynb
index feb193c3044..66585a75a4c 100644
--- a/documentation/examples/experimental-simulators-from-python.ipynb
+++ b/documentation/examples/experimental-simulators-from-python.ipynb
@@ -160,6 +160,111 @@
     "DumpPlus.simulate_noise()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "d1fdf2e3",
+   "metadata": {},
+   "source": [
+    "Looking at the output from the above, we notice two distinct differences with the output from `.simulate()`:\n",
+    "\n",
+    "- The experimental simulators use quantum registers of a fixed size (by default, three qubits), and allocate qubits from that register.\n",
+    "- By default, the experimental simulators represent quantum states as density operators ($\\rho = \\left|\\psi\\right\\rangle\\left\\langle\\psi\\right|$) instead of as state vectors ($\\left|\\psi\\right\\rangle$).\n",
+    "\n",
+    "For example, in the output above, the experimental simulator has output the density operator $\\rho = \\left|+00\\right\\rangle\\left\\langle+00\\right|$, as we can verify by using QuTiP."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "9a5bccc8",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
+      ],
+      "text/plain": [
+       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n",
+       "Qobj data =\n",
+       "[[1.]\n",
+       " [0.]]"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ket_zero = qt.basis(2, 0)\n",
+    "ket_zero"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "cd735ba6",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.707\\\\0.707\\\\\\end{array}\\right)\\end{equation*}"
+      ],
+      "text/plain": [
+       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n",
+       "Qobj data =\n",
+       "[[0.70710678]\n",
+       " [0.70710678]]"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ket_one = qt.basis(2, 1)\n",
+    "ket_plus = (ket_zero + ket_one).unit()\n",
+    "ket_plus"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "02f7f83c",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "Quantum object: dims = [[2, 2, 2], [2, 2, 2]], shape = (8, 8), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.500 & 0.0 & 0.0 & 0.0 & 0.500 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.500 & 0.0 & 0.0 & 0.0 & 0.500 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
+      ],
+      "text/plain": [
+       "Quantum object: dims = [[2, 2, 2], [2, 2, 2]], shape = (8, 8), type = oper, isherm = True\n",
+       "Qobj data =\n",
+       "[[0.5 0.  0.  0.  0.5 0.  0.  0. ]\n",
+       " [0.  0.  0.  0.  0.  0.  0.  0. ]\n",
+       " [0.  0.  0.  0.  0.  0.  0.  0. ]\n",
+       " [0.  0.  0.  0.  0.  0.  0.  0. ]\n",
+       " [0.5 0.  0.  0.  0.5 0.  0.  0. ]\n",
+       " [0.  0.  0.  0.  0.  0.  0.  0. ]\n",
+       " [0.  0.  0.  0.  0.  0.  0.  0. ]\n",
+       " [0.  0.  0.  0.  0.  0.  0.  0. ]]"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ket_psi = qt.tensor(ket_plus, ket_zero, ket_zero)\n",
+    "rho = ket_psi * ket_psi.dag()\n",
+    "rho"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "9e1fd1cd",
@@ -178,7 +283,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 9,
    "id": "865fa045",
    "metadata": {},
    "outputs": [],
@@ -188,7 +293,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 10,
    "id": "ff5b88d7",
    "metadata": {},
    "outputs": [
@@ -233,7 +338,7 @@
        "()"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -252,7 +357,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 11,
    "id": "4cfc0e13",
    "metadata": {},
    "outputs": [],
@@ -271,7 +376,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 12,
    "id": "422a7ee2",
    "metadata": {},
    "outputs": [],
@@ -289,7 +394,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 13,
    "id": "a2774610",
    "metadata": {},
    "outputs": [
@@ -305,7 +410,7 @@
        " [ 0.70710678 -0.70710678]]"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 13,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -324,7 +429,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 14,
    "id": "b0a01d12",
    "metadata": {},
    "outputs": [],
@@ -334,7 +439,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 15,
    "id": "938accec",
    "metadata": {},
    "outputs": [],
@@ -345,7 +450,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 16,
    "id": "3add5aa9",
    "metadata": {},
    "outputs": [
@@ -363,7 +468,7 @@
        " [ 0.5   -0.495 -0.495  0.5  ]]"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 16,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -373,6 +478,89 @@
     "noise_model['h']"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "d2a4a48a",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
+      ],
+      "text/plain": [
+       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n",
+       "Qobj data =\n",
+       "[[1.]\n",
+       " [0.]]"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ket_zero = qt.basis(2, 0)\n",
+    "ket_zero"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "147c70db",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0\\\\0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
+      ],
+      "text/plain": [
+       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
+       "Qobj data =\n",
+       "[[1. 0.]\n",
+       " [0. 0.]]"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "rho_zero = ket_zero * ket_zero.dag()\n",
+    "rho_zero"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "b268e69b",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.500 & 0.495\\\\0.495 & 0.500\\\\\\end{array}\\right)\\end{equation*}"
+      ],
+      "text/plain": [
+       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
+       "Qobj data =\n",
+       "[[0.5   0.495]\n",
+       " [0.495 0.5  ]]"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "noise_model['h'](rho_zero)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "b6dc2da9",
@@ -383,7 +571,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 20,
    "id": "23379c8b",
    "metadata": {},
    "outputs": [],
@@ -401,7 +589,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 21,
    "id": "f791e6f6",
    "metadata": {},
    "outputs": [
@@ -446,7 +634,7 @@
        "()"
       ]
      },
-     "execution_count": 15,
+     "execution_count": 21,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -455,6 +643,42 @@
     "DumpPlus.simulate_noise()"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "c664c0c5",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
+       " Qobj data =\n",
+       " [[ 0.06123724 -0.02041241]\n",
+       "  [-0.02041241  0.02041241]],\n",
+       " Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
+       " Qobj data =\n",
+       " [[ 0.70445014  0.70445014]\n",
+       "  [ 0.70445014 -0.70445014]],\n",
+       " Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False\n",
+       " Qobj data =\n",
+       " [[ 0.05707046 -0.02948997]\n",
+       "  [ 0.00190948  0.02948997]],\n",
+       " Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False\n",
+       " Qobj data =\n",
+       " [[-0.00103545  0.04950143]\n",
+       "  [ 0.00197827  0.05044425]]]"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "qt.to_kraus(noise_model['h'])"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "94c70d54",
@@ -473,7 +697,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 23,
    "id": "a02721e7",
    "metadata": {},
    "outputs": [
@@ -508,7 +732,7 @@
        " 'z_meas': {'ZMeasurement': {'pr_readout_error': 0}}}"
       ]
      },
-     "execution_count": 16,
+     "execution_count": 23,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -520,7 +744,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 24,
    "id": "9f7791f6",
    "metadata": {},
    "outputs": [],
@@ -538,7 +762,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 25,
    "id": "fe0142d8",
    "metadata": {},
    "outputs": [],
@@ -548,7 +772,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 26,
    "id": "4db703f8",
    "metadata": {},
    "outputs": [
@@ -586,7 +810,7 @@
        "()"
       ]
      },
-     "execution_count": 19,
+     "execution_count": 26,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -605,115 +829,55 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 27,
    "id": "5f24b886",
    "metadata": {},
    "outputs": [],
    "source": [
-    "qsharp.config['experimental.simulators.nQubits'] = 40"
+    "qsharp.config['experimental.simulators.nQubits'] = 10"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 28,
    "id": "5f4d45b8",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "application/json": 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        "\r\n",
        "                    <table>\r\n",
        "                        <caption>Stabilizer state</caption>\r\n",
        "                        <tr>\r\n",
        "                            <th># of qubits</th>\r\n",
-       "                            <td>40</td>\r\n",
+       "                            <td>10</td>\r\n",
        "                        </tr>\r\n",
        "\r\n",
        "                        <tr>\r\n",
        "                            <th>State data</th>\r\n",
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-       "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
-       "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\end{array}\\right)$$</td>\r\n",
+       "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
+       "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
+       "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
+       "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
+       "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
+       "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
+       "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n",
+       "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
+       "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
+       "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\end{array}\\right)$$</td>\r\n",
        "                        </tr>\r\n",
        "                    </table>\r\n",
        "                "
@@ -731,7 +895,7 @@
        "()"
       ]
      },
-     "execution_count": 21,
+     "execution_count": 28,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -740,6 +904,1068 @@
     "DumpPlus.simulate_noise()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "b6e4795c",
+   "metadata": {},
+   "source": [
+    "If we turn off visualization, we can get significantly more qubits still!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "id": "138ff19b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%%qsharp\n",
+    "open Microsoft.Quantum.Arrays;\n",
+    "\n",
+    "operation SampleRandomBitstring(nQubits : Int) : Result[] {\n",
+    "    use register = Qubit[nQubits];\n",
+    "    ApplyToEachCA(H, register);\n",
+    "    return ForEach(M, register);\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "id": "2f55cd3b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "qsharp.config['experimental.simulators.nQubits'] = 1000"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "id": "92fc3ab1",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Wall time: 2.85 s\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
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+       " 0,\n",
+       " 0,\n",
+       " 1,\n",
+       " 1,\n",
+       " 0,\n",
+       " 1,\n",
+       " 0,\n",
+       " 1,\n",
+       " 1,\n",
+       " 1,\n",
+       " 1,\n",
+       " 1,\n",
+       " 1,\n",
+       " 1,\n",
+       " 0,\n",
+       " 0,\n",
+       " 1,\n",
+       " 0,\n",
+       " 1,\n",
+       " 0,\n",
+       " 1,\n",
+       " 0,\n",
+       " 0,\n",
+       " 0,\n",
+       " 0,\n",
+       " 0,\n",
+       " 1,\n",
+       " 0,\n",
+       " 1,\n",
+       " 0]"
+      ]
+     },
+     "execution_count": 31,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%time SampleRandomBitstring.simulate_noise(nQubits=1000)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "3534390d",
@@ -750,7 +1976,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 32,
    "id": "f3587f4c",
    "metadata": {},
    "outputs": [],
@@ -768,7 +1994,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 33,
    "id": "2204f4ae",
    "metadata": {},
    "outputs": [],
@@ -789,7 +2015,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 34,
    "id": "70908857",
    "metadata": {},
    "outputs": [],
@@ -799,7 +2025,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 35,
    "id": "89b437a8",
    "metadata": {},
    "outputs": [
@@ -838,7 +2064,7 @@
        "()"
       ]
      },
-     "execution_count": 25,
+     "execution_count": 35,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -849,7 +2075,180 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 36,
+   "id": "4708c2d9",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/json": "{\"div_id\":\"dump-machine-div-2c22aa8a-df12-4fb0-a61b-91284bd88c5c\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":[{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0}]}",
+      "text/html": [
+       "\r\n",
+       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
+       "                        <thead>\r\n",
+       "                            \r\n",
+       "                        <tr>\r\n",
+       "                            <th>Qubit IDs</th>\r\n",
+       "                            <td span=\"3\">0, 1</td>\r\n",
+       "                        </tr>\r\n",
+       "                    \r\n",
+       "                            <tr>\r\n",
+       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
+       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
+       "                            </tr>\r\n",
+       "                        </thead>\r\n",
+       "                        <tbody>\r\n",
+       "                        \r\n",
+       "                            <tr>\r\n",
+       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
+       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
+       "                                \r\n",
+       "                                <td>\r\n",
+       "                                    <progress\r\n",
+       "                                        max=\"100\"\r\n",
+       "                                        value=\"50.000000000000014\"\r\n",
+       "                                        style=\"width: 100%;\"\r\n",
+       "                                    > \r\n",
+       "                                    <td>\r\n",
+       "                                    <p id=\"round-c50f074d-8fea-4197-b864-c396051924b6\"> \r\n",
+       "                                    <script>\r\n",
+       "                                    var num = 50.000000000000014;\r\n",
+       "                                    num = num.toFixed(4);\r\n",
+       "                                    var num_string = num + \"%\";\r\n",
+       "                                     document.getElementById(\"round-c50f074d-8fea-4197-b864-c396051924b6\").innerHTML = num_string;\r\n",
+       "                                    </script> </p>\r\n",
+       "                                    </td>\r\n",
+       "                                </td>\r\n",
+       "                            \r\n",
+       "                                \r\n",
+       "                                <td style=\"transform: rotate(0deg);\r\n",
+       "                   text-align: center;\">\r\n",
+       "                                 ↑\r\n",
+       "                                </td>\r\n",
+       "                            \r\n",
+       "                            </tr>\r\n",
+       "                        \n",
+       "\r\n",
+       "                            <tr>\r\n",
+       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
+       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
+       "                                \r\n",
+       "                                <td>\r\n",
+       "                                    <progress\r\n",
+       "                                        max=\"100\"\r\n",
+       "                                        value=\"0\"\r\n",
+       "                                        style=\"width: 100%;\"\r\n",
+       "                                    > \r\n",
+       "                                    <td>\r\n",
+       "                                    <p id=\"round-12dd8d8c-4a0d-4ae1-ae0f-72e8ac30a516\"> \r\n",
+       "                                    <script>\r\n",
+       "                                    var num = 0;\r\n",
+       "                                    num = num.toFixed(4);\r\n",
+       "                                    var num_string = num + \"%\";\r\n",
+       "                                     document.getElementById(\"round-12dd8d8c-4a0d-4ae1-ae0f-72e8ac30a516\").innerHTML = num_string;\r\n",
+       "                                    </script> </p>\r\n",
+       "                                    </td>\r\n",
+       "                                </td>\r\n",
+       "                            \r\n",
+       "                                \r\n",
+       "                                <td style=\"transform: rotate(0deg);\r\n",
+       "                   text-align: center;\">\r\n",
+       "                                 ↑\r\n",
+       "                                </td>\r\n",
+       "                            \r\n",
+       "                            </tr>\r\n",
+       "                        \n",
+       "\r\n",
+       "                            <tr>\r\n",
+       "                                <td>$\\left|2\\right\\rangle$</td>\r\n",
+       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
+       "                                \r\n",
+       "                                <td>\r\n",
+       "                                    <progress\r\n",
+       "                                        max=\"100\"\r\n",
+       "                                        value=\"0\"\r\n",
+       "                                        style=\"width: 100%;\"\r\n",
+       "                                    > \r\n",
+       "                                    <td>\r\n",
+       "                                    <p id=\"round-d89234c5-a257-4fee-8a4d-dcc417909519\"> \r\n",
+       "                                    <script>\r\n",
+       "                                    var num = 0;\r\n",
+       "                                    num = num.toFixed(4);\r\n",
+       "                                    var num_string = num + \"%\";\r\n",
+       "                                     document.getElementById(\"round-d89234c5-a257-4fee-8a4d-dcc417909519\").innerHTML = num_string;\r\n",
+       "                                    </script> </p>\r\n",
+       "                                    </td>\r\n",
+       "                                </td>\r\n",
+       "                            \r\n",
+       "                                \r\n",
+       "                                <td style=\"transform: rotate(0deg);\r\n",
+       "                   text-align: center;\">\r\n",
+       "                                 ↑\r\n",
+       "                                </td>\r\n",
+       "                            \r\n",
+       "                            </tr>\r\n",
+       "                        \n",
+       "\r\n",
+       "                            <tr>\r\n",
+       "                                <td>$\\left|3\\right\\rangle$</td>\r\n",
+       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
+       "                                \r\n",
+       "                                <td>\r\n",
+       "                                    <progress\r\n",
+       "                                        max=\"100\"\r\n",
+       "                                        value=\"50.000000000000014\"\r\n",
+       "                                        style=\"width: 100%;\"\r\n",
+       "                                    > \r\n",
+       "                                    <td>\r\n",
+       "                                    <p id=\"round-a334accb-a13c-4c7f-8ee2-5147bbde6306\"> \r\n",
+       "                                    <script>\r\n",
+       "                                    var num = 50.000000000000014;\r\n",
+       "                                    num = num.toFixed(4);\r\n",
+       "                                    var num_string = num + \"%\";\r\n",
+       "                                     document.getElementById(\"round-a334accb-a13c-4c7f-8ee2-5147bbde6306\").innerHTML = num_string;\r\n",
+       "                                    </script> </p>\r\n",
+       "                                    </td>\r\n",
+       "                                </td>\r\n",
+       "                            \r\n",
+       "                                \r\n",
+       "                                <td style=\"transform: rotate(0deg);\r\n",
+       "                   text-align: center;\">\r\n",
+       "                                 ↑\r\n",
+       "                                </td>\r\n",
+       "                            \r\n",
+       "                            </tr>\r\n",
+       "                        \r\n",
+       "                        </tbody>\r\n",
+       "                    </table>"
+      ],
+      "text/plain": [
+       "|0⟩\t0.7071067811865476 + 0𝑖\n",
+       "|1⟩\t0 + 0𝑖\n",
+       "|2⟩\t0 + 0𝑖\n",
+       "|3⟩\t0.7071067811865476 + 0𝑖"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "()"
+      ]
+     },
+     "execution_count": 36,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "DumpBellPair.simulate()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
    "id": "40431ed1",
    "metadata": {},
    "outputs": [],
@@ -859,7 +2258,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 38,
    "id": "1cc366e4",
    "metadata": {},
    "outputs": [
@@ -895,7 +2294,7 @@
        "()"
       ]
      },
-     "execution_count": 27,
+     "execution_count": 38,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -906,7 +2305,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 39,
    "id": "07439931",
    "metadata": {},
    "outputs": [],
@@ -916,7 +2315,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 40,
    "id": "7f4560f8",
    "metadata": {},
    "outputs": [
@@ -952,7 +2351,7 @@
        "()"
       ]
      },
-     "execution_count": 29,
+     "execution_count": 40,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -971,7 +2370,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 42,
    "id": "5b80e500",
    "metadata": {},
    "outputs": [
@@ -981,7 +2380,7 @@
        "SequenceProcess(n_qubits=1, processes=[ChpDecompositionProcess(n_qubits=1, operations=[Hadamard(idx_target=0)]), MixedPauliProcess(n_qubits=1, operators=[(0.9, 'I'), (0.1, 'Z')])])"
       ]
      },
-     "execution_count": 30,
+     "execution_count": 42,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1003,7 +2402,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 43,
    "id": "94c8b146",
    "metadata": {},
    "outputs": [],
@@ -1013,13 +2412,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 56,
    "id": "c517bb74",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "application/json": "{\"Table\":{\"SchemaVersion\":1,\"Dimensions\":[8,9],\"Data\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false],\"AsArray\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false]},\"Data\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false],\"NQubits\":4}",
+      "application/json": "{\"Table\":{\"SchemaVersion\":1,\"Dimensions\":[8,9],\"Data\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,true,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false],\"AsArray\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,true,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false]},\"Data\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,true,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false],\"NQubits\":4}",
       "text/html": [
        "\r\n",
        "                    <table>\r\n",
@@ -1031,7 +2430,7 @@
        "\r\n",
        "                        <tr>\r\n",
        "                            <th>State data</th>\r\n",
-       "                            <td>$$\\left\\langle X_{0}X_{1}, Z_{0}Z_{1}, Z_{2}, Z_{3} \\right\\rangle$$</td>\r\n",
+       "                            <td>$$\\left\\langle -X_{0}X_{1}, Z_{0}Z_{1}, Z_{2}, Z_{3} \\right\\rangle$$</td>\r\n",
        "                        </tr>\r\n",
        "                    </table>\r\n",
        "                "
@@ -1049,7 +2448,7 @@
        "()"
       ]
      },
-     "execution_count": 32,
+     "execution_count": 56,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1068,7 +2467,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 57,
    "id": "56168b7e",
    "metadata": {},
    "outputs": [
@@ -1086,7 +2485,7 @@
        "   'version': '0.17.210627752-alpha'}}}"
       ]
      },
-     "execution_count": 33,
+     "execution_count": 57,
      "metadata": {},
      "output_type": "execute_result"
     }

From 0922442fb3553c64a8c5845b4bb7f8d2b890a539 Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Fri, 11 Jun 2021 12:22:00 -0700
Subject: [PATCH 04/19] Moved all decomposition logic to Q# operations.

---
 .../Decompositions/ApplyWithLessControls.qs   |  24 +--
 .../Decompositions/ControlledH.qs             |  15 +-
 .../Decompositions/ControlledZ.qs             |  14 --
 .../Decompositions/IntrinsicInterface.qs      | 152 ++++++++++++++++++
 .../Decompositions/Measure.qs                 |  64 --------
 .../Decompositions/NativeInterface.qs         |  48 ++++++
 .../Decompositions/Utils.qs                   |  16 ++
 .../NativeImplementations.cs                  | 122 ++++++++++++++
 .../OpenSystemsSimulator.cs                   |  80 +++------
 9 files changed, 379 insertions(+), 156 deletions(-)
 delete mode 100644 src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledZ.qs
 create mode 100644 src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
 delete mode 100644 src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Measure.qs
 create mode 100644 src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/NativeInterface.qs
 create mode 100644 src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Utils.qs
 create mode 100644 src/Simulation/Simulators/OpenSystemsSimulator/NativeImplementations.cs

diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ApplyWithLessControls.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ApplyWithLessControls.qs
index 0b2281fe4f6..d8fc2d288ae 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ApplyWithLessControls.qs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ApplyWithLessControls.qs
@@ -3,7 +3,7 @@
 
 // NB: Copied from Utils.qs.
 namespace Microsoft.Quantum.Experimental.Decompositions {
-    open Microsoft.Quantum.Intrinsic;
+    open Microsoft.Quantum.Experimental.Native as Native;
 
     /// Given a multiply-controlled operation that requires k controls 
     /// applies it using ceiling(k/2) controls and using floor(k/2) temporary qubits
@@ -25,16 +25,16 @@ namespace Microsoft.Quantum.Experimental.Decompositions {
 
     internal operation PhaseCCX (control1 : Qubit, control2 : Qubit, target : Qubit) : Unit is Adj {
         // https://arxiv.org/pdf/1210.0974.pdf#page=2
-        H(target);
-        CNOT(target,control1);
-        CNOT(control1,control2);
-        T(control2);
-        Adjoint T(control1);
-        T(target);
-        CNOT(target,control1);
-        CNOT(control1,control2);
-        Adjoint T(control2);
-        CNOT(target,control2);
-        H(target);
+        Native.H(target);
+        Native.CNOT(target,control1);
+        Native.CNOT(control1,control2);
+        Native.T(control2);
+        Adjoint Native.T(control1);
+        Native.T(target);
+        Native.CNOT(target,control1);
+        Native.CNOT(control1,control2);
+        Adjoint Native.T(control2);
+        Native.CNOT(target,control2);
+        Native.H(target);
     }
 }
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledH.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledH.qs
index db971a23072..716a3f20ade 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledH.qs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledH.qs
@@ -2,17 +2,18 @@
 // Licensed under the MIT License.
 
 namespace Microsoft.Quantum.Experimental.Decompositions {
-    open Microsoft.Quantum.Intrinsic;
+    open Microsoft.Quantum.Experimental.Native as Native;
+    open Microsoft.Quantum.Experimental.Intrinsic as Intrinsic;
 
     internal operation PauliZFlip(basis : Pauli, target : Qubit) : Unit
     is Adj {
         if basis == PauliI {
             fail $"PauliX cannot be mapped to PauliI using conjugation by Clifford";
         } elif basis == PauliX {
-            H(target);
+            Native.H(target);
         } elif basis == PauliY {
-            Adjoint S(target);
-            Adjoint H(target);
+            Adjoint Native.S(target);
+            Native.H(target);
         } elif basis != PauliZ {
             fail $"PauliZ must be the only remaining case";
         }
@@ -23,7 +24,7 @@ namespace Microsoft.Quantum.Experimental.Decompositions {
         within {
             PauliZFlip(PauliY, target);
         } apply {
-            T(target);
+            Native.T(target);
         }
     }
 
@@ -33,10 +34,10 @@ namespace Microsoft.Quantum.Experimental.Decompositions {
             within {
                 Adjoint Ty(target);
             } apply {
-                Controlled Z([controls[0]], target);
+                Controlled Intrinsic.Z([controls[0]], target);
             }
         } else {
-            ApplyWithLessControlsA(Controlled H, (controls, qubit));
+            ApplyWithLessControlsA(Controlled Intrinsic.H, (controls, target));
         }
     }
 
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledZ.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledZ.qs
deleted file mode 100644
index 8d0939e5ebd..00000000000
--- a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledZ.qs
+++ /dev/null
@@ -1,14 +0,0 @@
-// Copyright (c) Microsoft Corporation.
-// Licensed under the MIT License.
-
-namespace Microsoft.Quantum.Experimental.Decompositions {
-
-    internal operation ApplyCZUsingCNOT(control : Qubit, target : Qubit) : Unit {
-        within {
-            Microsoft.Quantum.Intrinsic.H(target);
-        } apply {
-            Controlled Microsoft.Quantum.Intrinsic.X([control], target);
-        }
-    }
-
-}
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
new file mode 100644
index 00000000000..4649f09d301
--- /dev/null
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
@@ -0,0 +1,152 @@
+// Copyright (c) Microsoft Corporation.
+// Licensed under the MIT License.
+
+// This namespace contains definitions that parallel each operation in
+// M.Q.Intrinsic, making it easier to forward intrinsic definitions from the
+// simulator.
+
+namespace Microsoft.Quantum.Experimental.Intrinsic {
+    open Microsoft.Quantum.Experimental.Native as Native;
+    open Microsoft.Quantum.Experimental.Decompositions;
+
+    internal operation H(target : Qubit) : Unit is Adj + Ctl {
+        body (...) {
+            Native.H(target);
+        }
+
+        controlled (controls, ...) {
+            if Length(controls) == 0 {
+                H(target);
+            } else {
+                ApplyControlledH(controls, target);
+            }
+        }
+    }
+
+    internal operation X(target : Qubit) : Unit is Adj + Ctl {
+        body (...) {
+            Native.X(target);
+        }
+
+        controlled (controls, ...) {
+            if Length(controls) == 0 {
+                X(target);
+            } elif Length(controls) == 1 {
+                Native.CNOT(controls[0], target);
+            } else {
+                fail "Not yet implemented.";
+            }
+        }
+    }
+
+    internal operation Y(target : Qubit) : Unit is Adj + Ctl {
+        body (...) {
+            Native.Y(target);
+        }
+
+        controlled (controls, ...) {
+            if Length(controls) == 0 {
+                Y(target);
+            } elif Length(controls) == 1 {
+                within {
+                    H(target);
+                    S(target);
+                } apply {
+                    Native.CNOT(controls[0], target);
+                }
+            } else {
+                fail "Not yet implemented.";
+            }
+        }
+    }
+
+    internal operation Z(target : Qubit) : Unit is Adj + Ctl {
+        body (...) {
+            Native.Z(target);
+        }
+
+        controlled (controls, ...) {
+            if Length(controls) == 0 {
+                Z(target);
+            } elif Length(controls) == 1 {
+                within {
+                    H(target);
+                } apply {
+                    Native.CNOT(controls[0], target);
+                }
+            } else {
+                fail "Not yet implemented.";
+            }
+        }
+    }
+
+    internal operation S(target : Qubit) : Unit is Adj + Ctl {
+        body (...) {
+            Native.S(target);
+        }
+
+        controlled (controls, ...) {
+            fail "Not yet implemented.";
+        }
+    }
+
+    internal operation T(target : Qubit) : Unit is Adj + Ctl {
+        body (...) {
+            Native.T(target);
+        }
+
+        controlled (controls, ...) {
+            fail "Not yet implemented.";
+        }
+    }
+
+    internal operation Measure(bases : Pauli[], register : Qubit[]) : Result {
+        // If anything is PauliI, strip out and recurse.
+        if IsAnyPauliI(bases) {
+            mutable newBases = [];
+            mutable newQubits = [];
+            // NB: using Zipped would be nice here, but this is built before
+            //     M.Q.Standard...
+            for idxBasis in 0..Length(bases) - 1 {
+                if bases[idxBasis] != PauliI {
+                    set newBases += [bases[idxBasis]];
+                    set newQubits += [register[idxBasis]];
+                }
+            }
+
+            if Length(newBases) == 0 {
+                return Zero;
+            } else {
+                return Measure(newBases, register);
+            }
+        }
+
+        // At this point, we're guaranteed that bases contains no PauliI, and
+        // has length at least one. The simulator implementation likewise
+        // guarantees that in the single-qubit case, the basis is not Z.
+        // Let's check the easy single-qubit case first, then, and handle the
+        // X and Y cases.
+        if Length(bases) == 1 {
+            let basis = bases[0];
+            let target = register[0];
+            mutable result = Zero;
+            within {
+                if basis == PauliX {
+                    Native.H(target);
+                } elif basis == PauliY {
+                    Native.H(target);
+                    Native.S(target);
+                } else {
+                    fail "Single-qubit Z case should have been handled by the simulator.";
+                }
+            } apply {
+                set result = Measure([PauliZ], [target]);
+            }
+            return result;
+        } else {
+            // TODO
+            fail "Multi-qubit measurement is not yet implemented.";
+        }
+    }
+
+}
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Measure.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Measure.qs
deleted file mode 100644
index 7307c56b3a3..00000000000
--- a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Measure.qs
+++ /dev/null
@@ -1,64 +0,0 @@
-// Copyright (c) Microsoft Corporation.
-// Licensed under the MIT License.
-
-namespace Microsoft.Quantum.Experimental.Decompositions {
-    open Microsoft.Quantum.Intrinsic as Intrinsic;
-
-    internal function IsAnyPauliI(bases : Pauli[]) : Bool {
-        for basis in bases {
-            if basis == PauliI {
-                return true;
-            }
-        }
-        return false;
-    }
-
-    internal operation Measure(bases : Pauli[], register : Qubit[]) : Result {
-        // If anything is PauliI, strip out and recurse.
-        if IsAnyPauliI(bases) {
-            mutable newBases = [];
-            mutable newQubits = [];
-            // NB: using Zipped would be nice here, but this is built before
-            //     M.Q.Standard...
-            for idxBasis in 0..Length(bases) - 1 {
-                if bases[idxBasis] != PauliI {
-                    set newBases += [bases[idxBasis]];
-                    set newQubits += [register[idxBasis]];
-                }
-            }
-
-            if Length(newBases) == 0 {
-                return Zero;
-            } else {
-                return Measure(newBases, register);
-            }
-        }
-
-        // At this point, we're guaranteed that bases contains no PauliI, and
-        // has length at least one. The simulator implementation likewise
-        // guarantees that in the single-qubit case, the basis is not Z.
-        // Let's check the easy single-qubit case first, then, and handle the
-        // X and Y cases.
-        if Length(bases) == 1 {
-            let basis = bases[0];
-            let target = register[0];
-            mutable result = Zero;
-            within {
-                if basis == PauliX {
-                    H(target);
-                } elif basis == PauliY {
-                    H(target);
-                    S(target);
-                } else {
-                    fail "Single-qubit Z case should have been handled by the simulator.";
-                }
-            } apply {
-                set result = Measure([PauliZ], [target]);
-            }
-            return result;
-        } else {
-            // TODO
-            fail "Multi-qubit measurement is not yet implemented.";
-        }
-    }
-}
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/NativeInterface.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/NativeInterface.qs
new file mode 100644
index 00000000000..7166fff1e44
--- /dev/null
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/NativeInterface.qs
@@ -0,0 +1,48 @@
+// Copyright (c) Microsoft Corporation.
+// Licensed under the MIT License.
+
+// This namespace contains those intrinsics supported by the experimental
+// simulators native interface (NativeInterface.cs).
+
+namespace Microsoft.Quantum.Experimental.Native {
+
+    internal operation H(target : Qubit) : Unit {
+        body intrinsic;
+        adjoint self;
+    }
+
+    internal operation X(target : Qubit) : Unit {
+        body intrinsic;
+        adjoint self;
+    }
+
+    internal operation Y(target : Qubit) : Unit {
+        body intrinsic;
+        adjoint self;
+    }
+
+    internal operation Z(target : Qubit) : Unit {
+        body intrinsic;
+        adjoint self;
+    }
+
+    internal operation S(target : Qubit) : Unit {
+        body intrinsic;
+        adjoint intrinsic;
+    }
+
+    internal operation T(target : Qubit) : Unit {
+        body intrinsic;
+        adjoint intrinsic;
+    }
+
+    internal operation CNOT(control : Qubit, target : Qubit) : Unit {
+        body intrinsic;
+        adjoint self;
+    }
+
+    internal operation M(target : Qubit) : Result {
+        body intrinsic;
+    }
+
+}
\ No newline at end of file
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Utils.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Utils.qs
new file mode 100644
index 00000000000..d8a93b40216
--- /dev/null
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Utils.qs
@@ -0,0 +1,16 @@
+// Copyright (c) Microsoft Corporation.
+// Licensed under the MIT License.
+
+namespace Microsoft.Quantum.Experimental.Decompositions {
+    open Microsoft.Quantum.Experimental.Native as Native;
+
+    internal function IsAnyPauliI(bases : Pauli[]) : Bool {
+        for basis in bases {
+            if basis == PauliI {
+                return true;
+            }
+        }
+        return false;
+    }
+
+}
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/NativeImplementations.cs b/src/Simulation/Simulators/OpenSystemsSimulator/NativeImplementations.cs
new file mode 100644
index 00000000000..1334559dfa6
--- /dev/null
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/NativeImplementations.cs
@@ -0,0 +1,122 @@
+// Copyright (c) Microsoft Corporation.
+// Licensed under the MIT License.
+
+using System;
+using System.Linq;
+using Microsoft.Quantum.Simulation.Core;
+using Microsoft.Quantum.Simulation.Common;
+using System.Runtime.InteropServices;
+using System.Threading;
+using Microsoft.Quantum.Simulation.Simulators.Exceptions;
+using Microsoft.Quantum.Intrinsic.Interfaces;
+using System.Collections.Generic;
+using System.Diagnostics;
+using Newtonsoft.Json.Linq;
+
+using Native = Microsoft.Quantum.Experimental.Native;
+
+namespace Microsoft.Quantum.Experimental
+{
+    public partial class OpenSystemsSimulator : SimulatorBase
+    {
+
+        internal class H : Native.H
+        {
+            public H(IOperationFactory m) : base(m) { }
+
+            public override Func<Qubit, QVoid> __Body__ => (target) =>
+            {
+                NativeInterface.H((this.__Factory__ as OpenSystemsSimulator).Id, target);
+                return QVoid.Instance;
+            };
+        }
+
+        internal class X : Native.X
+        {
+            public X(IOperationFactory m) : base(m) { }
+
+            public override Func<Qubit, QVoid> __Body__ => (target) =>
+            {
+                NativeInterface.X((this.__Factory__ as OpenSystemsSimulator).Id, target);
+                return QVoid.Instance;
+            };
+        }
+
+        internal class Y : Native.Y
+        {
+            public Y(IOperationFactory m) : base(m) { }
+
+            public override Func<Qubit, QVoid> __Body__ => (target) =>
+            {
+                NativeInterface.Y((this.__Factory__ as OpenSystemsSimulator).Id, target);
+                return QVoid.Instance;
+            };
+        }
+
+        internal class Z : Native.Z
+        {
+            public Z(IOperationFactory m) : base(m) { }
+
+            public override Func<Qubit, QVoid> __Body__ => (target) =>
+            {
+                NativeInterface.Z((this.__Factory__ as OpenSystemsSimulator).Id, target);
+                return QVoid.Instance;
+            };
+        }
+
+        internal class S : Native.S
+        {
+            public S(IOperationFactory m) : base(m) { }
+
+            public override Func<Qubit, QVoid> __Body__ => (target) =>
+            {
+                NativeInterface.S((this.__Factory__ as OpenSystemsSimulator).Id, target);
+                return QVoid.Instance;
+            };
+
+            public override Func<Qubit, QVoid> __AdjointBody__ => (target) =>
+            {
+                NativeInterface.SAdj((this.__Factory__ as OpenSystemsSimulator).Id, target);
+                return QVoid.Instance;
+            };
+        }
+
+        internal class T : Native.T
+        {
+            public T(IOperationFactory m) : base(m) { }
+
+            public override Func<Qubit, QVoid> __Body__ => (target) =>
+            {
+                NativeInterface.T((this.__Factory__ as OpenSystemsSimulator).Id, target);
+                return QVoid.Instance;
+            };
+
+            public override Func<Qubit, QVoid> __AdjointBody__ => (target) =>
+            {
+                NativeInterface.TAdj((this.__Factory__ as OpenSystemsSimulator).Id, target);
+                return QVoid.Instance;
+            };
+        }
+
+        internal class CNOT : Native.CNOT
+        {
+            public CNOT(IOperationFactory m) : base(m) { }
+
+            public override Func<(Qubit, Qubit), QVoid> __Body__ => (args) =>
+            {
+                NativeInterface.CNOT((this.__Factory__ as OpenSystemsSimulator).Id, args.Item1, args.Item2);
+                return QVoid.Instance;
+            };
+        }
+
+        internal class M : Native.M
+        {
+            public M(IOperationFactory m) : base(m) { }
+
+            public override Func<Qubit, Result> __Body__ => (target) =>
+                NativeInterface.M((this.__Factory__ as OpenSystemsSimulator).Id, target);
+        }
+
+    }
+
+}
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/OpenSystemsSimulator.cs b/src/Simulation/Simulators/OpenSystemsSimulator/OpenSystemsSimulator.cs
index b708af3cf99..0c0af6dda83 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/OpenSystemsSimulator.cs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/OpenSystemsSimulator.cs
@@ -13,6 +13,8 @@
 using System.Diagnostics;
 using Newtonsoft.Json.Linq;
 
+using ExpIntrin = Microsoft.Quantum.Experimental.Intrinsic;
+
 namespace Microsoft.Quantum.Experimental
 {
     // NB: This class should not implement IQSharpCore, but does so temporarily
@@ -46,127 +48,87 @@ public OpenSystemsSimulator(uint capacity = 3, string representation = "mixed")
             this.Id = NativeInterface.Init(capacity, representation);
         }
 
+        Result IIntrinsicMeasure.Body(IQArray<Pauli> paulis, IQArray<Qubit> targets) =>
+            Get<ExpIntrin.Measure, ExpIntrin.Measure>().__Body__((paulis, targets));
+
         void IIntrinsicH.Body(Qubit target)
         {
-            NativeInterface.H(this.Id, target);
+            Get<ExpIntrin.H, ExpIntrin.H>().__Body__(target);
         }
 
         void IIntrinsicH.ControlledBody(IQArray<Qubit> controls, Qubit target)
         {
-            if (controls is { Count: 0 })
-            {
-                (this as IIntrinsicH).Body(target);
-            }
-            else
-            {
-                Get<Decompositions.ApplyControlledH, Decompositions.ApplyControlledH>().__Body__((controls, target));
-            }
-        }
-
-        Result IIntrinsicMeasure.Body(IQArray<Pauli> paulis, IQArray<Qubit> targets)
-        {
-            if (targets is { Count: 1 } && paulis is { Count: 1 } && paulis.Single() == Pauli.PauliZ)
-            {
-                return NativeInterface.M(this.Id, targets.Single());
-            }
-            else
-            {
-                Get<Decompositions.Measure, Decompositions.Measure>().__Body__((paulis, targets));
-            }
+            Get<ExpIntrin.H, ExpIntrin.H>().__ControlledBody__((controls, target));
         }
 
         void IIntrinsicS.Body(Qubit target)
         {
-            NativeInterface.S(this.Id, target);
+            Get<ExpIntrin.S, ExpIntrin.S>().__Body__(target);
         }
 
         void IIntrinsicS.AdjointBody(Qubit target)
         {
-            NativeInterface.SAdj(this.Id, target);
+            Get<ExpIntrin.S, ExpIntrin.S>().__AdjointBody__(target);
         }
 
         void IIntrinsicS.ControlledBody(IQArray<Qubit> controls, Qubit target)
         {
-            throw new NotImplementedException();
+            Get<ExpIntrin.S, ExpIntrin.S>().__ControlledBody__((controls, target));
         }
 
         void IIntrinsicS.ControlledAdjointBody(IQArray<Qubit> controls, Qubit target)
         {
-            throw new NotImplementedException();
+            Get<ExpIntrin.S, ExpIntrin.S>().__ControlledAdjointBody__((controls, target));
         }
 
         void IIntrinsicT.Body(Qubit target)
         {
-            NativeInterface.T(this.Id, target);
+            Get<ExpIntrin.T, ExpIntrin.T>().__Body__(target);
         }
 
         void IIntrinsicT.AdjointBody(Qubit target)
         {
-            NativeInterface.TAdj(this.Id, target);
+            Get<ExpIntrin.T, ExpIntrin.T>().__AdjointBody__(target);
         }
 
         void IIntrinsicT.ControlledBody(IQArray<Qubit> controls, Qubit target)
         {
-            throw new NotImplementedException();
+            Get<ExpIntrin.T, ExpIntrin.T>().__ControlledBody__((controls, target));
         }
 
         void IIntrinsicT.ControlledAdjointBody(IQArray<Qubit> controls, Qubit target)
         {
-            throw new NotImplementedException();
+            Get<ExpIntrin.T, ExpIntrin.T>().__ControlledAdjointBody__((controls, target));
         }
 
         void IIntrinsicX.Body(Qubit target)
         {
-            NativeInterface.X(this.Id, target);
+            Get<ExpIntrin.X, ExpIntrin.X>().__Body__(target);
         }
 
         void IIntrinsicX.ControlledBody(IQArray<Qubit> controls, Qubit target)
         {
-            // TODO: pass off to decompositions for more than one control.
-            if (controls is { Count: 0 })
-            {
-                (this as IIntrinsicX).Body(target);
-            }
-            else if (controls is { Count: 1 })
-            {
-                NativeInterface.CNOT(this.Id, controls[0], target);
-            }
-            else
-            {
-                throw new NotImplementedException();
-            }
+            Get<ExpIntrin.X, ExpIntrin.X>().__ControlledBody__((controls, target));
         }
 
         void IIntrinsicY.Body(Qubit target)
         {
-            NativeInterface.Y(this.Id, target);
+            Get<ExpIntrin.Y, ExpIntrin.Y>().__Body__(target);
         }
 
         void IIntrinsicY.ControlledBody(IQArray<Qubit> controls, Qubit target)
         {
-            throw new NotImplementedException();
+            Get<ExpIntrin.Y, ExpIntrin.Y>().__ControlledBody__((controls, target));
         }
 
         void IIntrinsicZ.Body(Qubit target)
         {
-            NativeInterface.Z(this.Id, target);
+            Get<ExpIntrin.Z, ExpIntrin.Z>().__Body__(target);
         }
 
         void IIntrinsicZ.ControlledBody(IQArray<Qubit> controls, Qubit target)
         {
-            // TODO: pass off to decompositions for more than one control.
-            if (controls is { Count: 0 })
-            {
-                (this as IIntrinsicZ).Body(target);
-            }
-            else if (controls is { Count: 1 })
-            {
-                Get<Decompositions.ApplyCZUsingCNOT, Decompositions.ApplyCZUsingCNOT>().__Body__((controls[0], target));
-            }
-            else
-            {
-                throw new NotImplementedException();
-            }
+            Get<ExpIntrin.Z, ExpIntrin.Z>().__ControlledBody__((controls, target));
         }
 
         public void Dispose()

From 086c018d67f5acd790938b536767f7b9562ea123 Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Fri, 11 Jun 2021 16:46:13 -0700
Subject: [PATCH 05/19] Added more decompositions.

---
 .../Decompositions/IntrinsicInterface.qs      | 64 +++++++++++++++++--
 1 file changed, 58 insertions(+), 6 deletions(-)

diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
index 4649f09d301..dcc6e3f90ea 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
@@ -33,8 +33,15 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
                 X(target);
             } elif Length(controls) == 1 {
                 Native.CNOT(controls[0], target);
+            } elif Length(controls) == 2 {
+                // Forward to decomposition of CCZ.
+                within {
+                    H(target);
+                } apply {
+                    Controlled Z(controls, target);
+                }
             } else {
-                fail "Not yet implemented.";
+                ApplyWithLessControlsA(Controlled X, (controls, target));
             }
         }
     }
@@ -54,8 +61,19 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
                 } apply {
                     Native.CNOT(controls[0], target);
                 }
+            } elif Length(controls) == 2 {
+                within {
+                    // TODO: double-check this one...!
+                    within {
+                        H(target);
+                    } apply {
+                        S(target);
+                    }
+                } apply {
+                    Controlled Z(controls, target);
+                }
             } else {
-                fail "Not yet implemented.";
+                ApplyWithLessControlsA(Controlled Y, (controls, target));
             }
         }
     }
@@ -74,9 +92,24 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
                 } apply {
                     Native.CNOT(controls[0], target);
                 }
+            } elif Length(controls) == 1 {
+                // [Page 15 of arXiv:1206.0758v3](https://arxiv.org/pdf/1206.0758v3.pdf#page=15)
+                Adjoint T(controls[0]);
+                Adjoint T(controls[1]);
+                Controlled X([target], controls[0]);
+                T(controls[0]);
+                Controlled X([controls[1]], target);
+                Controlled X([controls[1]], controls[0]);
+                T(target);
+                Adjoint T(controls[0]);
+                Controlled X([controls[1]], target);
+                Controlled X([target], controls[0]);
+                Adjoint T(target);
+                T(controls[0]);
+                Controlled X([controls[1]], controls[0]);
             } else {
-                fail "Not yet implemented.";
-            }
+                ApplyWithLessControlsA(Controlled Z, (controls, target));
+            } 
         }
     }
 
@@ -86,7 +119,19 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
         }
 
         controlled (controls, ...) {
-            fail "Not yet implemented.";
+            if Length(controls) == 0 {
+                S(target);
+            } elif (Length(controls) == 1) {
+                T(controls[0]);
+                T(target);
+                within {
+                    Controlled X([controls[0]], target);
+                } apply {
+                    Adjoint T(target);
+                }
+            } else {
+                ApplyWithLessControlsA(Controlled S, (controls, target));
+            }
         }
     }
 
@@ -96,7 +141,14 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
         }
 
         controlled (controls, ...) {
-            fail "Not yet implemented.";
+            if Length(controls) == 0 {
+                T(target);
+            } else {
+                // TODO: Decompositions of `Controlled T` currently used in Q#
+                //       target packages rely on R1Frac, which is not yet
+                //       implemented in experimental simulation.
+                fail "Controlled T operations are not yet supported.";
+            }
         }
     }
 

From 22258131586aed98e4ce85dc920c01b2e04d16ff Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Fri, 11 Jun 2021 16:50:42 -0700
Subject: [PATCH 06/19] Make known limitations more explicit in README.md.

---
 .../Simulators/OpenSystemsSimulator/README.md      | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/README.md b/src/Simulation/Simulators/OpenSystemsSimulator/README.md
index 59d2d1a1f4e..92662023450 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/README.md
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/README.md
@@ -13,6 +13,20 @@ cargo +nightly doc --features python --open
 
 For more details on using these simulators from Q# programs called from Python hosts, please see <https://github.com/microsoft/iqsharp>.
 
+## Known limitations
+
+As this feature is currently under development, there are still a number of limitations and missing capabilities.
+
+- Continuous-time rotations (e.g.: `Rx`, `Ry`, `Rz`, and `Exp`) are not yet supported.
+- Fractional rotations (e.g.: `R1Frac`, `ExpFrac`) are not yet supported.
+- The `Controlled Y` operation with more than one control qubit is not yet supported.
+- The `Controlled T` operation is not yet supported.
+- Joint measurement is not yet supported.
+
+Some limitations are inherent to open systems simulation, and may not ever be supported:
+
+- Assertions (e.g.: `AssertMeasurement` and `AssertMeasurementProbability`) are not supported, as these assertions may fail for correct code in the presence of noise. These assertions are no-ops on the experimental simulators.
+
 ## Native interface
 
 The core interoperability boundary between the C# runtime for the Quantum Development Kit and the `qdk_sim` native library is defined in the [`NativeInterface` static class](./NativeInterface.cs). This class provides P/Invoke declarations for each function exposed by the C API for the `qdk_sim` crate, as well as methods that call into these C API methods. The managed methods that correspond to each C API function check error codes reuturned by C API functions and convert them into .NET exceptions, allowing for C API errors to be easily caught by managed code.

From 06f03c2400f9178078507edcaf1b10cd9570d3bf Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Fri, 11 Jun 2021 16:51:20 -0700
Subject: [PATCH 07/19] Move known limitations to Markdown documentation./

---
 documentation/experimental-simulators.md        | 17 ++++++++++++++---
 .../Simulators/OpenSystemsSimulator/README.md   | 14 --------------
 2 files changed, 14 insertions(+), 17 deletions(-)

diff --git a/documentation/experimental-simulators.md b/documentation/experimental-simulators.md
index 1336b286761..2e5b779cb8c 100644
--- a/documentation/experimental-simulators.md
+++ b/documentation/experimental-simulators.md
@@ -15,6 +15,20 @@ The experimental simulators are not yet supported by:
 - Q# standalone command-line programs
 - QIR-based executables
 
+## Known limitations
+
+As this feature is currently under development, there are still a number of limitations and missing capabilities.
+
+- Continuous-time rotations (e.g.: `Rx`, `Ry`, `Rz`, and `Exp`) are not yet supported.
+- Fractional rotations (e.g.: `R1Frac`, `ExpFrac`) are not yet supported.
+- The `Controlled Y` operation with more than one control qubit is not yet supported.
+- The `Controlled T` operation is not yet supported.
+- Joint measurement is not yet supported.
+
+Some limitations are inherent to open systems simulation, and may not ever be supported:
+
+- Assertions (e.g.: `AssertMeasurement` and `AssertMeasurementProbability`) are not supported, as these assertions may fail for correct code in the presence of noise. These assertions are no-ops on the experimental simulators.
+
 ## Using Experimental Simulators from Python
 
 > ### **ⓘ** TIP
@@ -34,6 +48,3 @@ After calling `enable_noisy_simulation()`, Q# operations imported into Python wi
 By default, `.simulate_noise()` will assume an ideal error model (that is, no noise). To configure a particular error model, use the `qsharp.experimental.get_noise_model` and `qsharp.experimental.set_noise_model` functions to get and set the current noise model for the experimental simulators. Each error model is represented as a dictionary from intrinsic operation names to objects representing the errors in those intrinsic operations.
 
 For open systems simulation, error channels can be represented by [QuTiP](https://qutip.org/) `Qobj` objects encoding superoperators.
-
-> **Known limitation**: Currently, error channels for stabilizer simulation must be specified manually by their JSON serialization.
-
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/README.md b/src/Simulation/Simulators/OpenSystemsSimulator/README.md
index 92662023450..59d2d1a1f4e 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/README.md
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/README.md
@@ -13,20 +13,6 @@ cargo +nightly doc --features python --open
 
 For more details on using these simulators from Q# programs called from Python hosts, please see <https://github.com/microsoft/iqsharp>.
 
-## Known limitations
-
-As this feature is currently under development, there are still a number of limitations and missing capabilities.
-
-- Continuous-time rotations (e.g.: `Rx`, `Ry`, `Rz`, and `Exp`) are not yet supported.
-- Fractional rotations (e.g.: `R1Frac`, `ExpFrac`) are not yet supported.
-- The `Controlled Y` operation with more than one control qubit is not yet supported.
-- The `Controlled T` operation is not yet supported.
-- Joint measurement is not yet supported.
-
-Some limitations are inherent to open systems simulation, and may not ever be supported:
-
-- Assertions (e.g.: `AssertMeasurement` and `AssertMeasurementProbability`) are not supported, as these assertions may fail for correct code in the presence of noise. These assertions are no-ops on the experimental simulators.
-
 ## Native interface
 
 The core interoperability boundary between the C# runtime for the Quantum Development Kit and the `qdk_sim` native library is defined in the [`NativeInterface` static class](./NativeInterface.cs). This class provides P/Invoke declarations for each function exposed by the C API for the `qdk_sim` crate, as well as methods that call into these C API methods. The managed methods that correspond to each C API function check error codes reuturned by C API functions and convert them into .NET exceptions, allowing for C API errors to be easily caught by managed code.

From fe89ad60ae9169aa917559f6537eb7f73b3553d7 Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Fri, 11 Jun 2021 17:38:43 -0700
Subject: [PATCH 08/19] Started adding tests of decompositions.

---
 .../TestOperations.qs                         | 181 ++++++++++++++++++
 1 file changed, 181 insertions(+)
 create mode 100644 src/Simulation/Simulators.Tests/OpenSystemsSimulatorTests/TestOperations.qs

diff --git a/src/Simulation/Simulators.Tests/OpenSystemsSimulatorTests/TestOperations.qs b/src/Simulation/Simulators.Tests/OpenSystemsSimulatorTests/TestOperations.qs
new file mode 100644
index 00000000000..5eacb4aa5b5
--- /dev/null
+++ b/src/Simulation/Simulators.Tests/OpenSystemsSimulatorTests/TestOperations.qs
@@ -0,0 +1,181 @@
+// Copyright (c) Microsoft Corporation.
+// Licensed under the MIT License.
+
+// # Design notes
+//
+// In testing the open systems simulator, we can't use the same approach used
+// in testing other simulators. In particular, AssertMeasurement and
+// AssertMeasurementProbability are no-ops on experimental simulators. Thus,
+// we need to be a bit more indirect.
+//
+// Moreover, not all decompositions are supported yet
+// (see documentation/experimental-simulators.md), such that we need to avoid
+// unsupported cases.
+//
+// In this file, we list a bunch of operations that are unlikely to work
+// correctly in the presence of decomposition bugs. This is not a guarantee,
+// as we may have in the case of testing Choi–Jamilkowski states with
+// assertions, but it should help build confidence in experimental simulator
+// decompositions.
+//
+// In the future, consolidating these decompositions with those used in other
+// targeting packages will allow using assertions on the full-state simulator
+// to help build confidence in shared decompositions, further improving test
+// coverage.
+
+namespace Microsoft.Quantum.Experimental.Tests {
+    open Microsoft.Quantum.Intrinsic;
+
+    internal function Fact(expected : Bool, message : String) : Unit {
+        if not expected {
+            fail "Fact was false: {message}.";
+        }
+    }
+
+    internal operation MX(target : Qubit) : Result {
+        return Measure([PauliX], [target]);
+    }
+
+    @Test("Microsoft.Quantum.Experimental.OpenSystemsSimulator")
+    operation CheckBellBasisParitiesWithSingleQubitMeasurements() : Unit {
+        use (left, right) = (Qubit(), Qubit()) {
+            H(left);
+            CNOT(left, right);
+
+            Fact(M(left) == M(right), "Z parity in 00 case was wrong.");
+        }
+
+        use (left, right) = (Qubit(), Qubit()) {
+            H(left);
+            CNOT(left, right);
+
+            Fact(MX(left) == MX(right), "X parity in 00 case was wrong.");
+        }
+
+        use (left, right) = (Qubit(), Qubit()) {
+            H(left);
+            CNOT(left, right);
+
+            X(left);
+
+            Fact(M(left) != M(right), "Z parity in 10 case was wrong.");
+        }
+
+        use (left, right) = (Qubit(), Qubit()) {
+            H(left);
+            CNOT(left, right);
+
+            X(left);
+
+            Fact(MX(left) == MX(right), "X parity in 10 case was wrong.");
+        }
+
+        use (left, right) = (Qubit(), Qubit()) {
+            H(left);
+            CNOT(left, right);
+
+            Z(left);
+
+            Fact(M(left) == M(right), "Z parity in 01 case was wrong.");
+        }
+
+        use (left, right) = (Qubit(), Qubit()) {
+            H(left);
+            CNOT(left, right);
+
+            Z(left);
+
+            Fact(MX(left) != MX(right), "X parity in 01 case was wrong.");
+        }
+
+        use (left, right) = (Qubit(), Qubit()) {
+            H(left);
+            CNOT(left, right);
+
+            X(left);
+            Z(left);
+
+            Fact(M(left) != M(right), "Z parity in 11 case was wrong.");
+        }
+
+        use (left, right) = (Qubit(), Qubit()) {
+            H(left);
+            CNOT(left, right);
+
+            X(left);
+            Z(left);
+
+            Fact(MX(left) != MX(right), "X parity in 11 case was wrong.");
+        }
+    }
+
+    internal function Xor(a : Bool, b : Bool) : Bool {
+        return (a or b) and ((not a) or (not b));
+    }
+
+    @Test("Microsoft.Quantum.Experimental.OpenSystemsSimulator")
+    operation CheckToffoliOnComputationalBasisStates() : Unit {
+        for in0 in [false, true] {
+            for in1 in [false, true] {
+                for output in [false, true] {
+                    for useCcz in [false, true] {
+                        use qs = Qubit[3];
+                        if in0 { X(qs[0]); }
+                        if in1 { X(qs[1]); }
+                        if output { X(qs[2]); }
+
+                        let expected = Xor(output, in0 and in1);
+
+                        if useCcz {
+                            within {
+                                H(qs[2]);
+                            } apply {
+                                Controlled Z([qs[0], qs[1]], qs[2]);
+                            }
+                        } else {
+                            Controlled X([qs[0], qs[1]], qs[2]);
+                        }
+                        Fact(M(qs[0]) == (in0 ? One | Zero), "in0 was incorrect.");
+                        Fact(M(qs[1]) == (in1 ? One | Zero), "in1 was incorrect.");
+                        Fact(M(qs[2]) == (expected ? One | Zero), "expected was incorrect.");
+                    }
+                }
+            }
+        }
+    }
+
+    @Test("Microsoft.Quantum.Experimental.OpenSystemsSimulator")
+    operation CheckXHSZSHIsNoOp() : Unit {
+        use q = Qubit();
+
+        X(q);
+        within {
+            H(q);
+            S(q);
+        } apply {
+            Z(q);
+        }
+
+        Fact(M(q) == Zero, "XHSZSH was not a no-op.");
+    }
+
+    @Test("Microsoft.Quantum.Experimental.OpenSystemsSimulator")
+    operation CheckControlledHWorks() : Unit {
+        use control = Qubit();
+        use target = Qubit();
+
+
+        Controlled H([control], target);
+        within {
+            X(control);
+        } apply {
+            Controlled H([control], target);
+        }
+        H(target);
+
+        Fact(M(control) == Zero, "Controlled H did not work correctly.");
+        Fact(M(target) == Zero, "Controlled H did not work correctly.");
+
+    }
+
+}

From 8de35ba552e66078acfd1426252b6dce285845dd Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Fri, 11 Jun 2021 18:09:28 -0700
Subject: [PATCH 09/19] Added missing `open` statement.

---
 .../Simulators.Tests/OpenSystemsSimulatorTests/TestOperations.qs | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/Simulation/Simulators.Tests/OpenSystemsSimulatorTests/TestOperations.qs b/src/Simulation/Simulators.Tests/OpenSystemsSimulatorTests/TestOperations.qs
index 5eacb4aa5b5..4ca42d85f38 100644
--- a/src/Simulation/Simulators.Tests/OpenSystemsSimulatorTests/TestOperations.qs
+++ b/src/Simulation/Simulators.Tests/OpenSystemsSimulatorTests/TestOperations.qs
@@ -25,6 +25,7 @@
 
 namespace Microsoft.Quantum.Experimental.Tests {
     open Microsoft.Quantum.Intrinsic;
+    open Microsoft.Quantum.Diagnostics;
 
     internal function Fact(expected : Bool, message : String) : Unit {
         if not expected {

From 80839879280adc761074ef02b58c8becb418fc8b Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Fri, 11 Jun 2021 18:09:41 -0700
Subject: [PATCH 10/19] Don't mark decompositions as internal.

---
 .../Decompositions/ApplyWithLessControls.qs      |  4 ++--
 .../Decompositions/ControlledH.qs                |  6 +++---
 .../Decompositions/IntrinsicInterface.qs         | 14 +++++++-------
 .../Decompositions/NativeInterface.qs            | 16 ++++++++--------
 .../OpenSystemsSimulator/Decompositions/Utils.qs |  2 +-
 5 files changed, 21 insertions(+), 21 deletions(-)

diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ApplyWithLessControls.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ApplyWithLessControls.qs
index d8fc2d288ae..115ea5744f4 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ApplyWithLessControls.qs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ApplyWithLessControls.qs
@@ -7,7 +7,7 @@ namespace Microsoft.Quantum.Experimental.Decompositions {
 
     /// Given a multiply-controlled operation that requires k controls 
     /// applies it using ceiling(k/2) controls and using floor(k/2) temporary qubits
-    internal operation ApplyWithLessControlsA<'T> (op : ((Qubit[],'T) => Unit is Adj), (controls : Qubit[], arg : 'T)) : Unit is Adj {
+    operation ApplyWithLessControlsA<'T> (op : ((Qubit[],'T) => Unit is Adj), (controls : Qubit[], arg : 'T)) : Unit is Adj {
         let numControls = Length(controls);
         let numControlPairs = numControls / 2;
         use temps = Qubit[numControlPairs] {
@@ -23,7 +23,7 @@ namespace Microsoft.Quantum.Experimental.Decompositions {
         }
     }
 
-    internal operation PhaseCCX (control1 : Qubit, control2 : Qubit, target : Qubit) : Unit is Adj {
+    operation PhaseCCX (control1 : Qubit, control2 : Qubit, target : Qubit) : Unit is Adj {
         // https://arxiv.org/pdf/1210.0974.pdf#page=2
         Native.H(target);
         Native.CNOT(target,control1);
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledH.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledH.qs
index 716a3f20ade..147e496c0e8 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledH.qs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/ControlledH.qs
@@ -5,7 +5,7 @@ namespace Microsoft.Quantum.Experimental.Decompositions {
     open Microsoft.Quantum.Experimental.Native as Native;
     open Microsoft.Quantum.Experimental.Intrinsic as Intrinsic;
 
-    internal operation PauliZFlip(basis : Pauli, target : Qubit) : Unit
+    operation PauliZFlip(basis : Pauli, target : Qubit) : Unit
     is Adj {
         if basis == PauliI {
             fail $"PauliX cannot be mapped to PauliI using conjugation by Clifford";
@@ -19,7 +19,7 @@ namespace Microsoft.Quantum.Experimental.Decompositions {
         }
     }
 
-    internal operation Ty(target : Qubit) : Unit
+    operation Ty(target : Qubit) : Unit
     is Adj {
         within {
             PauliZFlip(PauliY, target);
@@ -28,7 +28,7 @@ namespace Microsoft.Quantum.Experimental.Decompositions {
         }
     }
 
-    internal operation ApplyControlledH(controls : Qubit[], target : Qubit) : Unit
+    operation ApplyControlledH(controls : Qubit[], target : Qubit) : Unit
     is Adj {
         if Length(controls) == 1 {
             within {
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
index dcc6e3f90ea..3dd81752558 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
@@ -9,7 +9,7 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
     open Microsoft.Quantum.Experimental.Native as Native;
     open Microsoft.Quantum.Experimental.Decompositions;
 
-    internal operation H(target : Qubit) : Unit is Adj + Ctl {
+    operation H(target : Qubit) : Unit is Adj + Ctl {
         body (...) {
             Native.H(target);
         }
@@ -23,7 +23,7 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
         }
     }
 
-    internal operation X(target : Qubit) : Unit is Adj + Ctl {
+    operation X(target : Qubit) : Unit is Adj + Ctl {
         body (...) {
             Native.X(target);
         }
@@ -46,7 +46,7 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
         }
     }
 
-    internal operation Y(target : Qubit) : Unit is Adj + Ctl {
+    operation Y(target : Qubit) : Unit is Adj + Ctl {
         body (...) {
             Native.Y(target);
         }
@@ -78,7 +78,7 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
         }
     }
 
-    internal operation Z(target : Qubit) : Unit is Adj + Ctl {
+    operation Z(target : Qubit) : Unit is Adj + Ctl {
         body (...) {
             Native.Z(target);
         }
@@ -113,7 +113,7 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
         }
     }
 
-    internal operation S(target : Qubit) : Unit is Adj + Ctl {
+    operation S(target : Qubit) : Unit is Adj + Ctl {
         body (...) {
             Native.S(target);
         }
@@ -135,7 +135,7 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
         }
     }
 
-    internal operation T(target : Qubit) : Unit is Adj + Ctl {
+    operation T(target : Qubit) : Unit is Adj + Ctl {
         body (...) {
             Native.T(target);
         }
@@ -152,7 +152,7 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
         }
     }
 
-    internal operation Measure(bases : Pauli[], register : Qubit[]) : Result {
+    operation Measure(bases : Pauli[], register : Qubit[]) : Result {
         // If anything is PauliI, strip out and recurse.
         if IsAnyPauliI(bases) {
             mutable newBases = [];
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/NativeInterface.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/NativeInterface.qs
index 7166fff1e44..18d702db908 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/NativeInterface.qs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/NativeInterface.qs
@@ -6,42 +6,42 @@
 
 namespace Microsoft.Quantum.Experimental.Native {
 
-    internal operation H(target : Qubit) : Unit {
+    operation H(target : Qubit) : Unit {
         body intrinsic;
         adjoint self;
     }
 
-    internal operation X(target : Qubit) : Unit {
+    operation X(target : Qubit) : Unit {
         body intrinsic;
         adjoint self;
     }
 
-    internal operation Y(target : Qubit) : Unit {
+    operation Y(target : Qubit) : Unit {
         body intrinsic;
         adjoint self;
     }
 
-    internal operation Z(target : Qubit) : Unit {
+    operation Z(target : Qubit) : Unit {
         body intrinsic;
         adjoint self;
     }
 
-    internal operation S(target : Qubit) : Unit {
+    operation S(target : Qubit) : Unit {
         body intrinsic;
         adjoint intrinsic;
     }
 
-    internal operation T(target : Qubit) : Unit {
+    operation T(target : Qubit) : Unit {
         body intrinsic;
         adjoint intrinsic;
     }
 
-    internal operation CNOT(control : Qubit, target : Qubit) : Unit {
+    operation CNOT(control : Qubit, target : Qubit) : Unit {
         body intrinsic;
         adjoint self;
     }
 
-    internal operation M(target : Qubit) : Result {
+    operation M(target : Qubit) : Result {
         body intrinsic;
     }
 
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Utils.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Utils.qs
index d8a93b40216..b06e781dba2 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Utils.qs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/Utils.qs
@@ -4,7 +4,7 @@
 namespace Microsoft.Quantum.Experimental.Decompositions {
     open Microsoft.Quantum.Experimental.Native as Native;
 
-    internal function IsAnyPauliI(bases : Pauli[]) : Bool {
+    function IsAnyPauliI(bases : Pauli[]) : Bool {
         for basis in bases {
             if basis == PauliI {
                 return true;

From a65a853f8beab1dcd298e3b9fdff35f6b29ee4cf Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Fri, 11 Jun 2021 18:31:33 -0700
Subject: [PATCH 11/19] =?UTF-8?q?Fixed=20build=20issue=20(=F0=9F=92=95=20t?=
 =?UTF-8?q?o=20@swernli=20for=20all=20the=20help!)?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 .../Decompositions/IntrinsicInterface.qs      | 39 +++++++++++--------
 1 file changed, 23 insertions(+), 16 deletions(-)

diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
index 3dd81752558..315a057fd9a 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
@@ -152,25 +152,32 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
         }
     }
 
+    // NB: We separate out this operation to avoid hardware targeting rewrite
+    //     steps from trying to lift this operation and modifying the C#
+    //     code gen in the process.
+    internal operation MeasureWithoutPauliI(bases : Pauli[], register : Qubit[]) : Result {
+        mutable newBases = [];
+        mutable newQubits = [];
+        // NB: using Zipped would be nice here, but this is built before
+        //     M.Q.Standard...
+        for idxBasis in 0..Length(bases) - 1 {
+            if bases[idxBasis] != PauliI {
+                set newBases += [bases[idxBasis]];
+                set newQubits += [register[idxBasis]];
+            }
+        }
+
+        if Length(newBases) == 0 {
+            return Zero;
+        } else {
+            return Measure(newBases, register);
+        }
+    }
+
     operation Measure(bases : Pauli[], register : Qubit[]) : Result {
         // If anything is PauliI, strip out and recurse.
         if IsAnyPauliI(bases) {
-            mutable newBases = [];
-            mutable newQubits = [];
-            // NB: using Zipped would be nice here, but this is built before
-            //     M.Q.Standard...
-            for idxBasis in 0..Length(bases) - 1 {
-                if bases[idxBasis] != PauliI {
-                    set newBases += [bases[idxBasis]];
-                    set newQubits += [register[idxBasis]];
-                }
-            }
-
-            if Length(newBases) == 0 {
-                return Zero;
-            } else {
-                return Measure(newBases, register);
-            }
+            return MeasureWithoutPauliI(bases, register);
         }
 
         // At this point, we're guaranteed that bases contains no PauliI, and

From fda2e11187475deb136288d7b4ff60286e38bb3e Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Fri, 11 Jun 2021 19:04:26 -0700
Subject: [PATCH 12/19] Unit tests now pass.

---
 documentation/experimental-simulators.md      |  3 ++-
 .../TestOperations.qs                         | 25 +++++++++++++++----
 .../Decompositions/IntrinsicInterface.qs      |  3 +--
 .../OpenSystemsSimulator.cs                   |  2 +-
 4 files changed, 24 insertions(+), 9 deletions(-)

diff --git a/documentation/experimental-simulators.md b/documentation/experimental-simulators.md
index 2e5b779cb8c..944cbcb9a8b 100644
--- a/documentation/experimental-simulators.md
+++ b/documentation/experimental-simulators.md
@@ -15,7 +15,7 @@ The experimental simulators are not yet supported by:
 - Q# standalone command-line programs
 - QIR-based executables
 
-## Known limitations
+## Known issues and limitations
 
 As this feature is currently under development, there are still a number of limitations and missing capabilities.
 
@@ -24,6 +24,7 @@ As this feature is currently under development, there are still a number of limi
 - The `Controlled Y` operation with more than one control qubit is not yet supported.
 - The `Controlled T` operation is not yet supported.
 - Joint measurement is not yet supported.
+- In some cases, qubits may need to be manually `Reset` before releasing, even if they have been measured.
 
 Some limitations are inherent to open systems simulation, and may not ever be supported:
 
diff --git a/src/Simulation/Simulators.Tests/OpenSystemsSimulatorTests/TestOperations.qs b/src/Simulation/Simulators.Tests/OpenSystemsSimulatorTests/TestOperations.qs
index 4ca42d85f38..447a1a497b0 100644
--- a/src/Simulation/Simulators.Tests/OpenSystemsSimulatorTests/TestOperations.qs
+++ b/src/Simulation/Simulators.Tests/OpenSystemsSimulatorTests/TestOperations.qs
@@ -29,7 +29,7 @@ namespace Microsoft.Quantum.Experimental.Tests {
 
     internal function Fact(expected : Bool, message : String) : Unit {
         if not expected {
-            fail "Fact was false: {message}.";
+            fail $"Fact was false: {message}";
         }
     }
 
@@ -44,6 +44,7 @@ namespace Microsoft.Quantum.Experimental.Tests {
             CNOT(left, right);
 
             Fact(M(left) == M(right), "Z parity in 00 case was wrong.");
+            ResetAll([left, right]);
         }
 
         use (left, right) = (Qubit(), Qubit()) {
@@ -51,6 +52,7 @@ namespace Microsoft.Quantum.Experimental.Tests {
             CNOT(left, right);
 
             Fact(MX(left) == MX(right), "X parity in 00 case was wrong.");
+            ResetAll([left, right]);
         }
 
         use (left, right) = (Qubit(), Qubit()) {
@@ -60,6 +62,7 @@ namespace Microsoft.Quantum.Experimental.Tests {
             X(left);
 
             Fact(M(left) != M(right), "Z parity in 10 case was wrong.");
+            ResetAll([left, right]);
         }
 
         use (left, right) = (Qubit(), Qubit()) {
@@ -69,6 +72,7 @@ namespace Microsoft.Quantum.Experimental.Tests {
             X(left);
 
             Fact(MX(left) == MX(right), "X parity in 10 case was wrong.");
+            ResetAll([left, right]);
         }
 
         use (left, right) = (Qubit(), Qubit()) {
@@ -78,6 +82,7 @@ namespace Microsoft.Quantum.Experimental.Tests {
             Z(left);
 
             Fact(M(left) == M(right), "Z parity in 01 case was wrong.");
+            ResetAll([left, right]);
         }
 
         use (left, right) = (Qubit(), Qubit()) {
@@ -87,6 +92,7 @@ namespace Microsoft.Quantum.Experimental.Tests {
             Z(left);
 
             Fact(MX(left) != MX(right), "X parity in 01 case was wrong.");
+            ResetAll([left, right]);
         }
 
         use (left, right) = (Qubit(), Qubit()) {
@@ -97,6 +103,7 @@ namespace Microsoft.Quantum.Experimental.Tests {
             Z(left);
 
             Fact(M(left) != M(right), "Z parity in 11 case was wrong.");
+            ResetAll([left, right]);
         }
 
         use (left, right) = (Qubit(), Qubit()) {
@@ -107,6 +114,7 @@ namespace Microsoft.Quantum.Experimental.Tests {
             Z(left);
 
             Fact(MX(left) != MX(right), "X parity in 11 case was wrong.");
+            ResetAll([left, right]);
         }
     }
 
@@ -115,6 +123,7 @@ namespace Microsoft.Quantum.Experimental.Tests {
     }
 
     @Test("Microsoft.Quantum.Experimental.OpenSystemsSimulator")
+    @Test("QuantumSimulator") // validate against full-state simulator.
     operation CheckToffoliOnComputationalBasisStates() : Unit {
         for in0 in [false, true] {
             for in1 in [false, true] {
@@ -125,7 +134,7 @@ namespace Microsoft.Quantum.Experimental.Tests {
                         if in1 { X(qs[1]); }
                         if output { X(qs[2]); }
 
-                        let expected = Xor(output, in0 and in1);
+                        let expectedOut = Xor(output, in0 and in1);
 
                         if useCcz {
                             within {
@@ -136,9 +145,15 @@ namespace Microsoft.Quantum.Experimental.Tests {
                         } else {
                             Controlled X([qs[0], qs[1]], qs[2]);
                         }
-                        Fact(M(qs[0]) == (in0 ? One | Zero), "in0 was incorrect.");
-                        Fact(M(qs[1]) == (in1 ? One | Zero), "in1 was incorrect.");
-                        Fact(M(qs[2]) == (expected ? One | Zero), "expected was incorrect.");
+
+                        let results = [M(qs[0]), M(qs[1]), M(qs[2])];
+                        let expected = [in0 ? One | Zero, in1 ? One | Zero, expectedOut ? One | Zero];
+
+                        Fact(results[0] == expected[0], $"in0 was incorrect in case: {in0} {in1} {output}. Got {results[0]}, expected {expected[0]}.");
+                        Fact(results[1] == expected[1], $"in1 was incorrect in case: {in0} {in1} {output}. Got {results[1]}, expected {expected[1]}.");
+                        Fact(results[2] == expected[2], $"expected was incorrect in case: {in0} {in1} {output}. Got {results[2]}, expected {expected[2]}.");
+
+                        ResetAll(qs);
                     }
                 }
             }
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
index 315a057fd9a..fccc9d27084 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
@@ -196,10 +196,9 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
                     Native.H(target);
                     Native.S(target);
                 } else {
-                    fail "Single-qubit Z case should have been handled by the simulator.";
                 }
             } apply {
-                set result = Measure([PauliZ], [target]);
+                set result = Native.M(target);
             }
             return result;
         } else {
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/OpenSystemsSimulator.cs b/src/Simulation/Simulators/OpenSystemsSimulator/OpenSystemsSimulator.cs
index 0c0af6dda83..9c957cc4c97 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/OpenSystemsSimulator.cs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/OpenSystemsSimulator.cs
@@ -43,7 +43,7 @@ public NoiseModel NoiseModel
 
         public State CurrentState => NativeInterface.GetCurrentState(this.Id);
 
-        public OpenSystemsSimulator(uint capacity = 3, string representation = "mixed") : base(new QubitManager((long)capacity))
+        public OpenSystemsSimulator(uint capacity = 4, string representation = "mixed") : base(new QubitManager((long)capacity))
         {
             this.Id = NativeInterface.Init(capacity, representation);
         }

From d29c99efc6c7fd79b2b8790c6b4048b9c84001bd Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Mon, 14 Jun 2021 15:41:56 -0700
Subject: [PATCH 13/19] Address feedback.

---
 .../TestOperations.qs                         |  2 +
 .../Decompositions/IntrinsicInterface.qs      | 54 ++++++++++---------
 .../Decompositions/NativeInterface.qs         | 14 ++---
 3 files changed, 37 insertions(+), 33 deletions(-)

diff --git a/src/Simulation/Simulators.Tests/OpenSystemsSimulatorTests/TestOperations.qs b/src/Simulation/Simulators.Tests/OpenSystemsSimulatorTests/TestOperations.qs
index 447a1a497b0..db149453199 100644
--- a/src/Simulation/Simulators.Tests/OpenSystemsSimulatorTests/TestOperations.qs
+++ b/src/Simulation/Simulators.Tests/OpenSystemsSimulatorTests/TestOperations.qs
@@ -161,6 +161,7 @@ namespace Microsoft.Quantum.Experimental.Tests {
     }
 
     @Test("Microsoft.Quantum.Experimental.OpenSystemsSimulator")
+    @Test("QuantumSimulator") // validate against full-state simulator.
     operation CheckXHSZSHIsNoOp() : Unit {
         use q = Qubit();
 
@@ -176,6 +177,7 @@ namespace Microsoft.Quantum.Experimental.Tests {
     }
 
     @Test("Microsoft.Quantum.Experimental.OpenSystemsSimulator")
+    @Test("QuantumSimulator") // validate against full-state simulator.
     operation CheckControlledHWorks() : Unit {
         use control = Qubit();
         use target = Qubit();
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
index fccc9d27084..0afda865df2 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
@@ -56,18 +56,17 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
                 Y(target);
             } elif Length(controls) == 1 {
                 within {
-                    H(target);
-                    S(target);
+                    Native.H(target);
+                    Native.S(target);
                 } apply {
                     Native.CNOT(controls[0], target);
                 }
             } elif Length(controls) == 2 {
                 within {
-                    // TODO: double-check this one...!
                     within {
-                        H(target);
+                        Native.H(target);
                     } apply {
-                        S(target);
+                        Native.S(target);
                     }
                 } apply {
                     Controlled Z(controls, target);
@@ -85,28 +84,28 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
 
         controlled (controls, ...) {
             if Length(controls) == 0 {
-                Z(target);
+                Native.Z(target);
             } elif Length(controls) == 1 {
                 within {
                     H(target);
                 } apply {
                     Native.CNOT(controls[0], target);
                 }
-            } elif Length(controls) == 1 {
+            } elif Length(controls) == 2 {
                 // [Page 15 of arXiv:1206.0758v3](https://arxiv.org/pdf/1206.0758v3.pdf#page=15)
-                Adjoint T(controls[0]);
-                Adjoint T(controls[1]);
-                Controlled X([target], controls[0]);
-                T(controls[0]);
-                Controlled X([controls[1]], target);
-                Controlled X([controls[1]], controls[0]);
-                T(target);
-                Adjoint T(controls[0]);
-                Controlled X([controls[1]], target);
-                Controlled X([target], controls[0]);
-                Adjoint T(target);
-                T(controls[0]);
-                Controlled X([controls[1]], controls[0]);
+                Adjoint Native.T(controls[0]);
+                Adjoint Native.T(controls[1]);
+                Controlled Native.X([target], controls[0]);
+                Native.T(controls[0]);
+                Native.CNOT(controls[1], target);
+                Native.CNOT(controls[1], controls[0]);
+                Native.T(target);
+                Adjoint Native.T(controls[0]);
+                Native.CNOT(controls[1], target);
+                Native.CNOT(target, controls[0]);
+                Adjoint Native.T(target);
+                Native.T(controls[0]);
+                Native.CNOT(controls[1], controls[0]);
             } else {
                 ApplyWithLessControlsA(Controlled Z, (controls, target));
             } 
@@ -120,14 +119,14 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
 
         controlled (controls, ...) {
             if Length(controls) == 0 {
-                S(target);
+                Native.S(target);
             } elif (Length(controls) == 1) {
-                T(controls[0]);
-                T(target);
+                Native.T(controls[0]);
+                Native.T(target);
                 within {
                     Controlled X([controls[0]], target);
                 } apply {
-                    Adjoint T(target);
+                    Adjoint Native.T(target);
                 }
             } else {
                 ApplyWithLessControlsA(Controlled S, (controls, target));
@@ -142,7 +141,7 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
 
         controlled (controls, ...) {
             if Length(controls) == 0 {
-                T(target);
+                Native.T(target);
             } else {
                 // TODO: Decompositions of `Controlled T` currently used in Q#
                 //       target packages rely on R1Frac, which is not yet
@@ -155,6 +154,7 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
     // NB: We separate out this operation to avoid hardware targeting rewrite
     //     steps from trying to lift this operation and modifying the C#
     //     code gen in the process.
+    //     See https://github.com/microsoft/qsharp-compiler/issues/768.
     internal operation MeasureWithoutPauliI(bases : Pauli[], register : Qubit[]) : Result {
         mutable newBases = [];
         mutable newQubits = [];
@@ -170,7 +170,7 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
         if Length(newBases) == 0 {
             return Zero;
         } else {
-            return Measure(newBases, register);
+            return Measure(newBases, newQubits);
         }
     }
 
@@ -196,6 +196,8 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
                     Native.H(target);
                     Native.S(target);
                 } else {
+                    // In the PauliZ case, we don't need to do anything here
+                    // since Native.M is already in the Z basis by definition.
                 }
             } apply {
                 set result = Native.M(target);
diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/NativeInterface.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/NativeInterface.qs
index 18d702db908..7fb4695bf16 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/NativeInterface.qs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/NativeInterface.qs
@@ -6,37 +6,37 @@
 
 namespace Microsoft.Quantum.Experimental.Native {
 
-    operation H(target : Qubit) : Unit {
+    operation H(target : Qubit) : Unit is Adj {
         body intrinsic;
         adjoint self;
     }
 
-    operation X(target : Qubit) : Unit {
+    operation X(target : Qubit) : Unit is Adj {
         body intrinsic;
         adjoint self;
     }
 
-    operation Y(target : Qubit) : Unit {
+    operation Y(target : Qubit) : Unit is Adj {
         body intrinsic;
         adjoint self;
     }
 
-    operation Z(target : Qubit) : Unit {
+    operation Z(target : Qubit) : Unit is Adj {
         body intrinsic;
         adjoint self;
     }
 
-    operation S(target : Qubit) : Unit {
+    operation S(target : Qubit) : Unit is Adj {
         body intrinsic;
         adjoint intrinsic;
     }
 
-    operation T(target : Qubit) : Unit {
+    operation T(target : Qubit) : Unit is Adj {
         body intrinsic;
         adjoint intrinsic;
     }
 
-    operation CNOT(control : Qubit, target : Qubit) : Unit {
+    operation CNOT(control : Qubit, target : Qubit) : Unit is Adj {
         body intrinsic;
         adjoint self;
     }

From 3591151c7c3ba48ec98ffbdd6ecfde9a254e4f33 Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Mon, 14 Jun 2021 15:50:03 -0700
Subject: [PATCH 14/19] Fix two small build issues.

---
 .../OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
index 0afda865df2..e21ec2a5f46 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/Decompositions/IntrinsicInterface.qs
@@ -95,7 +95,7 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
                 // [Page 15 of arXiv:1206.0758v3](https://arxiv.org/pdf/1206.0758v3.pdf#page=15)
                 Adjoint Native.T(controls[0]);
                 Adjoint Native.T(controls[1]);
-                Controlled Native.X([target], controls[0]);
+                Native.CNOT(target, controls[0]);
                 Native.T(controls[0]);
                 Native.CNOT(controls[1], target);
                 Native.CNOT(controls[1], controls[0]);
@@ -124,7 +124,7 @@ namespace Microsoft.Quantum.Experimental.Intrinsic {
                 Native.T(controls[0]);
                 Native.T(target);
                 within {
-                    Controlled X([controls[0]], target);
+                    Native.CNOT(controls[0], target);
                 } apply {
                     Adjoint Native.T(target);
                 }

From a950f16c71ed4d33491c3d70054baa8fe59292b2 Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Mon, 14 Jun 2021 15:56:43 -0700
Subject: [PATCH 15/19] Added comment explaining reset / release.

---
 .../OpenSystemsSimulator/QubitManager.cs        | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)

diff --git a/src/Simulation/Simulators/OpenSystemsSimulator/QubitManager.cs b/src/Simulation/Simulators/OpenSystemsSimulator/QubitManager.cs
index 7639b90d3cf..80c0b3062d2 100644
--- a/src/Simulation/Simulators/OpenSystemsSimulator/QubitManager.cs
+++ b/src/Simulation/Simulators/OpenSystemsSimulator/QubitManager.cs
@@ -29,6 +29,23 @@ public OpenSystemsQubitManager(OpenSystemsSimulator parent, uint capacity)
 
             protected override void Release(Qubit qubit, bool wasUsedOnlyForBorrowing)
             {
+                // When a qubit is released, the developer has promised that
+                // either of the following two conditions holds:
+                //
+                //     1. The qubit has been measured immediately before
+                //        releasing, such that its state is known
+                //        determinstically at this point in the program.
+                //     2. The qubit has been coherently unprepared, such that
+                //        the the qubit is known determistically to be in the
+                //        |0⟩ state at this point in the program.
+                //
+                // In either case, noise can cause a correct Q# program to fail
+                // to meet the conditions for releasing a qubit, such that we
+                // want to track the effects of that noise without failing.
+                //
+                // Thus, our strategy will be to always allow the release to
+                // proceed, doing any resets needed to deal with case (1)
+                // above.
                 if (qubit != null && qubit.IsMeasured)
                 {
                     // Try to reset measured qubits.

From ad610f8ad06d556936330e06acc5804a165738d6 Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Mon, 14 Jun 2021 16:03:45 -0700
Subject: [PATCH 16/19] Remove DLL added by accident.

---
 ...uantum.Experimental.Simulators.Runtime.dll | Bin 2488320 -> 0 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 src/Simulation/Native/win10/Microsoft.Quantum.Experimental.Simulators.Runtime.dll

diff --git a/src/Simulation/Native/win10/Microsoft.Quantum.Experimental.Simulators.Runtime.dll b/src/Simulation/Native/win10/Microsoft.Quantum.Experimental.Simulators.Runtime.dll
deleted file mode 100644
index 538c495488401688d5f725f076750aeadc802ce8..0000000000000000000000000000000000000000
GIT binary patch
literal 0
HcmV?d00001

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From 1cc67a37a3fd669f3723e0dcff9f0bb0472a9a7c Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Mon, 14 Jun 2021 16:08:09 -0700
Subject: [PATCH 17/19] Removed one more file added by accident.

---
 src/Simulation/Native/win10/vcomp140.dll | Bin 155296 -> 0 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 src/Simulation/Native/win10/vcomp140.dll

diff --git a/src/Simulation/Native/win10/vcomp140.dll b/src/Simulation/Native/win10/vcomp140.dll
deleted file mode 100644
index 872663e58d4e89f42a2c7f9c3e3977b5751d5d32..0000000000000000000000000000000000000000
GIT binary patch
literal 0
HcmV?d00001

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From a369efed1a2babb2e1dcd2b8e9243dcf2e87e645 Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Mon, 14 Jun 2021 16:13:33 -0700
Subject: [PATCH 18/19] Revert "Removed one more file added by accident."

This reverts commit 1cc67a37a3fd669f3723e0dcff9f0bb0472a9a7c.
---
 src/Simulation/Native/win10/vcomp140.dll | Bin 0 -> 155296 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 src/Simulation/Native/win10/vcomp140.dll

diff --git a/src/Simulation/Native/win10/vcomp140.dll b/src/Simulation/Native/win10/vcomp140.dll
new file mode 100644
index 0000000000000000000000000000000000000000..872663e58d4e89f42a2c7f9c3e3977b5751d5d32
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From 8c617a3bc4bc5f866c3b990c519126648e759374 Mon Sep 17 00:00:00 2001
From: Christopher Granade <cgranade@cgranade.com>
Date: Mon, 14 Jun 2021 16:21:02 -0700
Subject: [PATCH 19/19] Added comment explaining vcomp140.dll.

---
 src/Simulation/Native/.gitignore | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/src/Simulation/Native/.gitignore b/src/Simulation/Native/.gitignore
index 8f1fc6e9a01..aa51796222b 100644
--- a/src/Simulation/Native/.gitignore
+++ b/src/Simulation/Native/.gitignore
@@ -10,3 +10,14 @@ foo*
 CMakeFiles/
 CMakeCache.txt
 *.so
+
+# Ignore build artifacts...
+win10
+# ...except for vcomp140, which isn't actually a build
+# artifact, but provides the Visual C/C++ OpenMP runtime
+# needed by the full-state simulator.
+#
+# Making sure that this file is in the repo will make
+# sure it ends up in our final NuGet packages, as needed
+# for the full-state simulator to work correctly.
+!win10/vcomp140.dll