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We propose an efficient algorithm for partitioning Pauli strings intosubgroups, which can be simultaneously measured in a single quantum circuit.Our partitioning algorithm drastically reduces the total number of measurementsin a variational quantum eigensolver for a quantum chemistry, one of the mostpromising applications of quantum computing. The algorithm is based on theIsing model optimization problem, which can be quickly solved using an Isingmachine. We develop an algorithm that is applicable to problems with sizeslarger than the maximum number of variables that an Ising machine can handle($n_\text{bit}$) through its iterative use. The algorithm has much better timecomplexity and solution optimality than other algorithms such asBoppana--Halld\'orsson algorithm and Bron--Kerbosch algorithm, making it usefulfor the quick and effective reduction of the number of quantum circuitsrequired for measuring the expectation values of multiple Pauli strings. Weinvestigate the performance of the algorithm using the second-generationDigital Annealer, a high-performance Ising hardware, for up to $65,535$ Paulistrings using Hamiltonians of molecules and the full tomography of quantumstates. We demonstrate that partitioning problems for quantum chemicalcalculations can be solved with a time complexity of $O(N)$ for $N\leqn_\text{bit}$ and $O(N^2)$ for $N>n_\text{bit}$ for the worst case, where $N$denotes the number of candidate Pauli strings and $n_\text{bit}=8,192$ for thesecond-generation Digital Annealer used in this study. The reduction factor,which is the number of Pauli strings divided by the number of obtainedpartitions, can be $200$ at maximum.

Pauli String Partitioning Algorithm with the Ising Model for Simultaneous Measurement