Meta-Variational Quantum Eigensolver: Learning Energy Profiles of Parameterized Hamiltonians for Quantum Simulation

Abstract

We present the meta-variational quantum eigensolver (VQE), an algorithm capable of learning the ground-state energy profile of a parameterized Hamiltonian. If the meta-VQE is trained with a few data points, it delivers an initial circuit parameterization that can be used to compute the ground-state energy of any parameterization of the Hamiltonian within a certain trust region. We test this algorithm with an XXZ spin chain, an electronic H4 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, it results in improved accuracy in comparison with individual VQE optimization. The meta-VQE algorithm introduces both a gain in efficiency for parameterized Hamiltonians in terms of the number of optimizations and a good starting point for the quantum circuit parameters for individual optimizations. The proposed algorithm 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.