Variational quantum algorithms are considered to be appealing applications of near-term quantum computers. However, it has been unclear whether they can outperform classical algorithms or not. To reveal their limitations, we must seek a technique to benchmark them on large scale problems. Here, we propose a perturbative approach for efficient benchmarking of variational quantum algorithms. The proposed technique performs perturbative expansion of a circuit consisting of Clifford and Pauli rotation gates, which is enabled by exploiting the classical simulatability of Clifford circuits. Our method can be applied to a wide family of parameterized quantum circuits consisting of Clifford gates and single-qubit rotation gates. The approximate optimal parameter obtained by the method can also serve as an initial guess for further optimizations on a quantum device, which can potentially solve the so-called ``barren-plateau'' problem. As the first application of the method, we perform a benchmark of so-called hardware-efficient-type ansatzes when they are applied to the VQE of one-dimensional hydrogen chains up to H24, which corresponds to 48-qubit system, using a standard workstation.
@article{arxiv.2011.09927,
title = {Quadratic Clifford expansion for efficient benchmarking and initialization of variational quantum algorithms},
author = {Kosuke Mitarai and Yasunari Suzuki and Wataru Mizukami and Yuya O. Nakagawa and Keisuke Fujii},
journal= {arXiv preprint arXiv:2011.09927},
year = {2020}
}