Minimizing State Preparations in Variational Quantum Eigensolver by Partitioning into Commuting Families

TL;DR

This paper presents a systematic method to reduce the number of state preparations in VQE by partitioning commuting Pauli strings, significantly lowering quantum resource requirements for near-term quantum computing applications.

Contribution

It introduces algorithms for approximating minimal commuting partitions and synthesizing measurement circuits, enabling 8-30x reductions in state preparations with minimal overhead.

Findings

Achieved 8-30x reduction in state preparations for representative problems.

Validated techniques through experimental estimation of deuteron ground state energy on IBM Q.

Developed an adaptive strategy to mitigate covariance issues in simultaneous measurements.

Abstract

Variational quantum eigensolver (VQE) is a promising algorithm suitable for near-term quantum machines. VQE aims to approximate the lowest eigenvalue of an exponentially sized matrix in polynomial time. It minimizes quantum resource requirements both by co-processing with a classical processor and by structuring computation into many subproblems. Each quantum subproblem involves a separate state preparation terminated by the measurement of one Pauli string. However, the number of such Pauli strings scales as $N^4$ for typical problems of interest--a daunting growth rate that poses a serious limitation for emerging applications such as quantum computational chemistry. We introduce a systematic technique for minimizing requisite state preparations by exploiting the simultaneous measurability of partitions of commuting Pauli strings. Our work encompasses algorithms for efficiently approximating a MIN-COMMUTING-PARTITION, as well as a synthesis tool for compiling simultaneous measurement circuits. For representative problems, we achieve 8-30x reductions in state preparations, with minimal overhead in measurement circuit cost. We demonstrate experimental validation of our techniques by estimating the ground state energy of deuteron on an IBM Q 20-qubit machine. We also investigate the underlying statistics of simultaneous measurement and devise an adaptive strategy for mitigating harmful covariance terms.