Maximizing quantum-computing expressive power through randomized circuits

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 parametrized quantum circuits, which is constrained by the limited gate number and the presence of barren plateaus. In this paper, we propose and numerically demonstrate an approach for VQAs, utilizing randomized quantum circuits to generate the variational wave function. We parametrize 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 maximizing the expressive power of the variational wave function and minimizing the associated time cost, specifically 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 wave function 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. Published by the American Physical Society 2024