Collective optimization for variational quantum eigensolvers

TL;DR

This paper introduces a collective VQE algorithm that optimizes multiple related Hamiltonians simultaneously, improving convergence efficiency and avoiding local minima in quantum chemistry simulations.

Contribution

The paper presents a novel collective VQE method that leverages relations between related tasks to enhance optimization efficiency on quantum computers.

Findings

cVQE converges faster than traditional VQE.

cVQE reduces the risk of getting trapped in local minima.

Numerical simulations confirm improved performance in molecular bond length problems.

Abstract

Variational quantum eigensolver (VQE) optimizes parameterized eigenstates of a Hamiltonian on a quantum processor by updating parameters with a classical computer. Such a hybrid quantum-classical optimization serves as a practical way to leverage up classical algorithms to exploit the power of near-term quantum computing. Here, we develop a hybrid algorithm for VQE, emphasizing the classical side, that can solve a group of related Hamiltonians simultaneously. The algorithm incorporates a snake algorithm into many VQE tasks to collectively optimize variational parameters of different Hamiltonians. Such so-called collective VQEs~(cVQEs) is applied for solving molecules with varied bond length, which is a standard problem in quantum chemistry. Numeral simulations show that cVQE is not only more efficient in convergence, but also trends to avoid single VQE task to be trapped in local minimums. The collective optimization utilizes intrinsic relations between related tasks and may inspire advanced hybrid quantum-classical algorithms for solving practical problems.