Constrained Quantum Optimization meets Model Reduction

TL;DR

This paper introduces a model reduction technique for constrained quantum optimization, leveraging quantum measurements as projections to enable lower-dimensional simulations, demonstrated on 3-SAT and graph coordination problems.

Contribution

It proposes a novel model reduction approach for constrained quantum optimization using quantum Zeno dynamics, reducing simulation complexity.

Findings

Exponential state-space reduction achieved for random 3-SAT problems.

Effective reduction demonstrated in agent coordination over graphs.

Abstract

Quantum optimization algorithms promise advantages for difficult problems but are costly to simulate and analyze on classical machines. Recently, constrained quantum optimization has been investigated through the lens of Quantum Zeno dynamics, an approach which constrains the search to a subspace by means of quantum measurements. Exploiting that quantum measurements are projections, we propose a model reduction approach and show that simulations can be conducted in a lower-dimensional space. As possible applications, we demonstrate exponential state-space reduction of constrained quantum optimization in case of random 3-SAT and agent coordination problems over graphs.