MoG-VQE: Multiobjective genetic variational quantum eigensolver

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 achie...

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Bibliographic Details
Published in:arXiv.org 2020-07
Main Authors: Chivilikhin, D, Samarin, A, Ulyantsev, V, Iorsh, I, Oganov, A R, Kyriienko, O
Format: Article
Language:English
Subjects:
Algorithms
Covariance matrix
Gate counting
Gates (circuits)
Genetic algorithms
Ground state
Hardware
Multiple objective analysis
Pareto optimization
Pareto optimum
Quantum computers
Qubits (quantum computing)
Sorting algorithms
Topology optimization
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Summary: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.
ISSN:2331-8422