MoG-VQE: Multiobjective genetic variational quantum eigensolver

• URL: http://arxiv.org/abs/2007.04424v1
• Date: Wed, 8 Jul 2020 20:44:50 GMT
• Title: MoG-VQE: Multiobjective genetic variational quantum eigensolver
• Authors: D. Chivilikhin, A. Samarin, V. Ulyantsev, I. Iorsh, A. R. Oganov, O. Kyriienko
• Abstract summary: Variational quantum eigensolver (VQE) emerged as a first practical algorithm for near-term quantum computers. Here, we propose the approach which can combine both low depth and improved precision. We observe nearly ten-fold reduction in the two-qubit gate counts as compared to the standard hardware-efficient ansatz.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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