Add Adj functor to AssertQubit

[msoeken]

Describe the bug

Not really a bug, but an inconsistency. AssertQubit does not have an Adj functor, but AssertAllZero, which uses AssertQubit, does have one (adjoint self).

To Reproduce

Consider the following operation:

operation ApplyAnd(control1 : Qubit, control2 : Qubit, target : Qubit) : Unit is Adj {
  AssertQubit(Zero, target);
  CCNOT(control1, control2, target);
}

This does not compile because AssertQubit does not have an Adj functor.

Expected behavior

Operation should compile, and check in the adjoint call to ApplyAnd that target is released in state Zero.

Actual behavior

Operation does not compile, however, I can use the following alternative:

operation ApplyAnd(control1 : Qubit, control2 : Qubit, target : Qubit) : Unit is Adj {
  AssertAllZero([target]);
  CCNOT(control1, control2, target);
}

[bamarsha]

Yes, it seems like all of the Assert* operations should support both adjoint and controlled - @cgranade?

[cgranade]

I agree with Adjoint, but Controlled is a bit more subtle. Assertions work by reasoning about the probability of hypothetical measurements, but then that measurement isn't consistent with Controlled. For example:

/// # Summary
/// Given a qubit in the |0⟩ state, prepares it in the |1⟩ state.
operation PrepareOne(target : Qubit) : Unit is Adj + Ctl {
    X(target);
    AssertQubit(One, target);
}

/// # Summary
/// Prepares a maximally entangled pair on two qubits,
/// given two qubits each initially in the |0⟩ state.
operation PrepareBellPair(left : Qubit, right : Qubit) : Unit is Adj + Ctl {
    H(left);
    // Does this assertion pass or fail?
    Controlled PrepareOne([left], right);
}

[swernli]

@cgranade Given your concern about the controlled functor for assertions, should we remove Ctl from AssertMeasurement and AssertMeasurementProbability? These both define a controlled behavior that just ignores the control qubits...

[swernli]

@bettinaheim, @cgranade, @msoeken, bringing this back up so we can land at a decision for the associated PR. As it stands, AssertMeasurement and AssertMeasurementProbability don't have Adj but do have Ctl and my PR just adds Adj but leaves any existing controlled support as-is. From the sound of the discussion here and in the PR, the controlled behavior (which just ignores the controls) seems wrong. Do we want to open a separate issue to remove the controlled support, since that would technically be a breaking change, or do we want to squeeze that into this same issue + PR?

[bettinaheim]

I believe this is resolved with #450