Optimizing Parameterized Quantum Circuits with Free-Axis Selection

TL;DR

This paper introduces a novel method for constructing variational quantum circuits by continuously optimizing both rotation angles and axes, enhancing expressibility and effectiveness in quantum optimization tasks.

Contribution

It proposes a continuous parameterization approach for single-qubit rotation axes, improving PQC expressibility and performance over traditional fixed-axis methods.

Findings

Free-axis selection improves expressibility as measured by KL divergence.

PQCs with free-axis selection outperform in finding ground states of Hamiltonians.

Method simplifies PQC design by removing the need to predefine rotation axes.

Abstract

Variational quantum algorithms, which utilize Parametrized Quantum Circuits (PQCs), are promising tools to achieve quantum advantage for optimization problems on near-term quantum devices. Their PQCs have been conventionally constructed from parametrized rotational angles of single-qubit gates around predetermined set of axes, and two-qubit entangling gates, such as CNOT gates. We propose a method to construct a PQC by continuous parametrization of both the angles and the axes of its single-qubit rotation gates. The method is based on the observation that when rotational angles are fixed, optimal axes of rotations can be computed by solving a system of linear equations whose coefficients can be determined from the PQC with small computational overhead. The method can be further simplified to select axes freely from continuous parameters with rotational angles fixed to half rotation or $\pi$. We show the simplified free-axis selection method has better expressibility against other structural optimization methods when measured with Kullback-Leibler (KL) divergence. We also demonstrate PQCs with free-axis selection are more effective to search the ground states of Hamiltonians for quantum chemistry and combinatorial optimization. Because free-axis selection allows designing PQCs without specifying their single-qubit rotational axes, it may significantly improve the handiness of PQCs.