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

TL;DR

This paper introduces a perturbative Clifford-based method for efficiently benchmarking variational quantum algorithms and providing good initial parameters, demonstrated on large hydrogen chain problems.

Contribution

It presents a novel perturbative approach leveraging Clifford circuit classical simulation for benchmarking and initialization in variational quantum algorithms.

Findings

Effective benchmarking of large-scale variational algorithms.

Approximate optimal parameters can serve as initial guesses for further optimization.

Demonstrated on 48-qubit hydrogen chain systems.

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.