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arXiv · 2011.09927

Quadratic Clifford expansion for efficient benchmarking and initialization of variational quantum algorithms

Kosuke Mitarai·Yasunari Suzuki·Wataru Mizukami·Yuya O. Nakagawa·Keisuke Fujii
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Abstract

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 $\mathrm{H}_{24}$, which corresponds to $48$-qubit system, using a standard workstation.

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Kosuke Mitarai, Yasunari Suzuki, Wataru Mizukami, Yuya O. Nakagawa, Keisuke Fujii. 2020-11-19. Quadratic Clifford expansion for efficient benchmarking and initialization of variational quantum algorithms. https://arxiv.org/abs/2011.09927

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