Reducing Circuit Depth with Qubitwise Diagonalization

Abstract

Simultaneous diagonalization of commuting Pauli operators is an important routine in several quantum algorithms. We present the implementation of an algorithm that yields a quantum circuit with depth only $\mathcal{O(n \log r)}$ diagonalizing n-qubit operators generated by r independent Pauli operators. The algorithm is described in detail in Paper.

Gallery

Tutorial

Prepare the commuting Pauli Strings

• Ensure the Pauli strings are writen in the file where each line is a Pauli string (for example XX (on the first line), YY (on the second line))

Run the diagonalization routine and obtain the results

• Call the function main in the file diagonalize.py.
• The Function returns X, Z, S, U
• U is the quantum circuit
• X is the transformed X part of the tableau. It should be a zero matrix.
• Z is the transformed Z part of the tableau.
• S is the sign of the transformed Pauli strings. (0 means +, 1 means -)

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