MoG-VQE: Multiobjective genetic variational quantum eigensolver

TL;DR

MoG-VQE introduces a multiobjective genetic algorithm to optimize quantum circuit ansatz, balancing energy accuracy and circuit complexity, significantly reducing gate counts for near-term quantum computing applications.

Contribution

It presents a novel multiobjective genetic approach combining Pareto optimization and CMA-ES to improve VQE ansatz design for low-depth, high-precision quantum computations.

Findings

Nearly ten-fold reduction in two-qubit gate counts.

Achieved chemical precision with only 12 CNOTs for 12-qubit LiH.

Enhanced ground state fidelity for near-term quantum devices.

Abstract

Variational quantum eigensolver (VQE) emerged as a first practical algorithm for near-term quantum computers. Its success largely relies on the chosen variational ansatz, corresponding to a quantum circuit that prepares an approximate ground state of a Hamiltonian. Typically, it either aims to achieve high representation accuracy (at the expense of circuit depth), or uses a shallow circuit sacrificing the convergence to the exact ground state energy. Here, we propose the approach which can combine both low depth and improved precision, capitalizing on a genetically-improved ansatz for hardware-efficient VQE. Our solution, the multiobjective genetic variational quantum eigensolver (MoG-VQE), relies on multiobjective Pareto optimization, where topology of the variational ansatz is optimized using the non-dominated sorting genetic algorithm (NSGA-II). For each circuit topology, we optimize angles of single-qubit rotations using covariance matrix adaptation evolution strategy (CMA-ES) -- a derivative-free approach known to perform well for noisy black-box optimization. Our protocol allows preparing circuits that simultaneously offer high performance in terms of obtained energy precision and the number of two-qubit gates, thus trying to reach Pareto-optimal solutions. Tested for various molecules (H$_2$, H$_4$, H$_6$, BeH$_2$, LiH), we observe nearly ten-fold reduction in the two-qubit gate counts as compared to the standard hardware-efficient ansatz. For 12-qubit LiH Hamiltonian this allows reaching chemical precision already at 12 CNOTs. Consequently, the algorithm shall lead to significant growth of the ground state fidelity for near-term devices.