Shuffle-QUDIO: accelerate distributed VQE with trainability enhancement and measurement reduction

TL;DR

Shuffle-QUDIO enhances distributed VQE by reducing communication and improving trainability, leading to faster convergence and lower errors in quantum chemistry problems on NISQ devices.

Contribution

It introduces shuffle operations into QUDIO, significantly reducing communication and accelerating convergence in distributed VQE.

Findings

Achieves wall-clock time speedup in ground state energy estimation

Reduces communication frequency among quantum processors

Improves trainability and convergence rate of distributed VQE

Abstract

The variational quantum eigensolver (VQE) is a leading strategy that exploits noisy intermediate-scale quantum (NISQ) machines to tackle chemical problems outperforming classical approaches. To gain such computational advantages on large-scale problems, a feasible solution is the QUantum DIstributed Optimization (QUDIO) scheme, which partitions the original problem into $K$ subproblems and allocates them to $K$ quantum machines followed by the parallel optimization. Despite the provable acceleration ratio, the efficiency of QUDIO may heavily degrade by the synchronization operation. To conquer this issue, here we propose Shuffle-QUDIO to involve shuffle operations into local Hamiltonians during the quantum distributed optimization. Compared with QUDIO, Shuffle-QUDIO significantly reduces the communication frequency among quantum processors and simultaneously achieves better trainability. Particularly, we prove that Shuffle-QUDIO enables a faster convergence rate over QUDIO. Extensive numerical experiments are conducted to verify that Shuffle-QUDIO allows both a wall-clock time speedup and low approximation error in the tasks of estimating the ground state energy of molecule. We empirically demonstrate that our proposal can be seamlessly integrated with other acceleration techniques, such as operator grouping, to further improve the efficacy of VQE.