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Fix Pauli-basis expansion normalization #5107

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Fix Pauli-basis expansion normalization #5107

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7 changes: 5 additions & 2 deletions docs/guides/specify-observables-pauli.ipynb
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Expand Up @@ -147,10 +147,13 @@
"We expand the observable $O$ as\n",
"\n",
"$$\n",
"O = \\sum_{P \\in \\{I, X, Y, Z\\}^{\\otimes n}} \\mathrm{Tr}(O P) P,\n",
"O =\n",
"\\frac{1}{2^n}\n",
"\\sum_{P \\in \\{I, X, Y, Z\\}^{\\otimes n}}\n",
"\\mathrm{Tr}(O P) P,\n",
"$$\n",
"\n",
"where the sum runs over all possible $n$-qubit Pauli terms and $\\mathrm{Tr}(\\cdot)$ is the trace of a matrix, which acts as inner product.\n",
"where the sum runs over all possible $n$-qubit Pauli terms and $\\mathrm{Tr}(\\cdot)$ is the trace of a matrix, which acts as an inner product. The factor $1/2^n$ accounts for the Hilbert--Schmidt normalization of $n$-qubit Pauli strings.\n",
"You can implement this decomposition from a matrix to Pauli terms using the `SparsePauliOp.from_operator` method, like so:"
]
},
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