Pauli String Partitioning Algorithm with the Ising Model for Simultaneous Measurements

Abstract

We propose an efficient algorithm for partitioning Pauli strings into subgroups, which can be simultaneously measured in a single quantum circuit. Our partitioning algorithm drastically reduces the total number of measurements in a variational quantum eigensolver for a quantum chemistry, one of the most promising applications of quantum computing. The algorithm is based on the Ising model optimization problem, which can be quickly solved using an Ising machine. We develop an algorithm that is applicable to problems with sizes larger than the maximum number of variables that an Ising machine can handle (nbit) through its iterative use. The algorithm has much better time complexity and solution optimality than other existing algorithms. We investigate the performance of the algorithm using the second-generation Digital Annealer, a high-performance Ising hardware, for up to 65535 Pauli strings using Hamiltonians of molecules and the full tomography of quantum states. We demonstrate a time complexity of O(N) for N ≤ nbit and O(N2) for N > nbit for the worst case, where N denotes the number of candidate Pauli strings and nbit = 8,192 in this study. The reduction factor, which is the number of Pauli strings divided by the number of obtained partitions, can be 200 at maximum.