  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.
