The Meta-Variational Quantum Eigensolver (Meta-VQE): Learning energy profiles of parameterized Hamiltonians for quantum simulation

TL;DR

Meta-VQE is a novel algorithm that efficiently learns energy profiles of parameterized Hamiltonians, providing better initializations and reducing optimization efforts in quantum simulations.

Contribution

It introduces a meta-learning approach for VQE, enabling rapid energy profile estimation with minimal training data for various Hamiltonian parameters.

Findings

Successfully applied to spin chains, electronic Hamiltonians, and quantum simulations.

Achieved improved accuracy over traditional VQE in some cases.

Reduced number of optimizations needed for parameterized Hamiltonians.

Abstract

We present the meta-VQE, an algorithm capable to learn the ground state energy profile of a parametrized Hamiltonian. By training the meta-VQE with a few data points, it delivers an initial circuit parametrization that can be used to compute the ground state energy of any parametrization of the Hamiltonian within a certain trust region. We test this algorithm with a XXZ spin chain, an electronic H$_{4}$ Hamiltonian and a single-transmon quantum simulation. In all cases, the meta-VQE is able to learn the shape of the energy functional and, in some cases, resulted in improved accuracy in comparison to individual VQE optimization. The meta-VQE algorithm introduces both a gain in efficiency for parametrized Hamiltonians, in terms of the number of optimizations, and a good starting point for the quantum circuit parameters for individual optimizations. The proposed algorithm proposal can be readily mixed with other improvements in the field of variational algorithms to shorten the distance between the current state-of-the-art and applications with quantum advantage.