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

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