Self-consistent mean-field quantum approximate optimization

TL;DR

This paper presents a self-consistent mean-field quantum optimization algorithm that efficiently approximates ground states of classical Ising models by decomposing problems and iteratively updating a shared environment, enabling solutions beyond current hardware limits.

Contribution

The paper introduces a novel self-consistent mean-field quantum algorithm that decomposes complex problems and updates a shared environment, improving scalability and efficiency in quantum optimization.

Findings

Effective in approximating ground states of Ising Hamiltonians.

Successfully applied to molecular docking problems.

Demonstrates potential to solve large-scale problems beyond current hardware capabilities.

Abstract

We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions between them in a mean-field manner. These interactions are captured by a common environment, constructed self-consistently through a variational quantum circuit, and which modifies the subproblems to account for mutual influence while maintaining computational independence. Consequently, subproblems can be solved individually, avoiding the computational cost of the full problem. We explore the properties of the generated environment and assess the algorithm's performance through extensive numerical simulations on Sherrington-Kirkpatrick spin glasses. Furthermore, we apply it experimentally to a weighted maximum clique problem applied to molecular docking. This framework enables the solution of problems that would otherwise exceed the qubit and gate counts of current quantum hardware.