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.

翻译：在含噪中等规模量子时代，变分量子算法已成为获得量子优势的有前景途径。然而，变分量子算法的成功依赖于参数化量子电路的表达能力，而这种能力受到有限门数量和贫瘠高原效应的制约。本文提出并通过数值演示了一种新型变分量子算法方法，利用随机化量子电路生成变分波函数。我们采用人工神经网络参数化这些随机电路的分布函数，并通过优化该分布函数来求解问题。这种随机电路方法在变分波函数的表达能力与时间成本（以量子电路的采样成本衡量）之间实现了权衡。在给定固定门数量的情况下，我们可通过延长量子计算时间系统性地提升表达能力。当允许的时间成本足够大时，变分波函数能以任意精度逼近任意量子态。此外，针对变分量子特征求解器，我们建立了表达能力、时间成本与门数量之间的显式关系。这些结果凸显了随机电路方法在量子计算中实现高度表达能力的巨大潜力。