In the noisy intermediate-scale quantum era, variational quantum algorithms
(VQAs) have emerged as a promising avenue to obtain quantum advantage. However,
the success of VQAs depends on the expressive power of parameterised quantum
circuits, which is constrained by the limited gate number and the presence of
barren plateaus. In this work, we propose and numerically demonstrate a novel
approach for VQAs, utilizing randomised quantum circuits to generate the
variational wavefunction. We parameterize the distribution function of these
random circuits using artificial neural networks and optimize it to find the
solution. This random-circuit approach presents a trade-off between the
expressive power of the variational wavefunction and time cost, in terms of the
sampling cost of quantum circuits. Given a fixed gate number, we can
systematically increase the expressive power by extending the quantum-computing
time. With a sufficiently large permissible time cost, the variational
wavefunction can approximate any quantum state with arbitrary accuracy.
Furthermore, we establish explicit relationships between expressive power, time
cost, and gate number for variational quantum eigensolvers. These results
highlight the promising potential of the random-circuit approach in achieving a
high expressive power in quantum computing.

在嘈杂的中间尺度量子时代，基于变分量子算法（VQA）以提供量子优势而出现为一条有希望的途径。在本研究中，我们提出并数值上证明了一种新颖的 VQA 方法，利用随机量子电路生成变分波函数，并通过人工神经网络对这些随机电路的分布函数进行参数化优化以找到解决方案。这种随机电路的方法在变分波函数的表达能力和量子电路采样成本方面存在着一种权衡关系。在给定的门数量下，我们可以通过扩展量子计算时间来系统地增加表达能力。在足够大的时间成本允许下，变分波函数可以以任意精度近似任意量子态。此外，我们建立了变分量子本征求解器的表达能力、时间成本和门数量之间的明确关系。这些结果突出了随机电路方法在实现量子计算中高表达能力方面的潜在前景。