Feedback-Based Quantum Algorithm for Constrained Optimization Problems

TL;DR

This paper extends the FALQON quantum optimization algorithm to handle quadratic constrained binary problems, introducing a new operator and control method that improve efficiency and performance, as demonstrated by simulations.

Contribution

The paper presents a novel generalization of FALQON for constrained problems using Lyapunov control, reducing circuit depth and enhancing optimization performance.

Findings

Reduces quantum circuit depth for constrained problems

Outperforms original FALQON in simulations

Efficiently encodes solutions as ground states

Abstract

The feedback-based algorithm for quantum optimization (FALQON) has recently been proposed to solve quadratic unconstrained binary optimization problems. This paper efficiently generalizes FALQON to tackle quadratic constrained binary optimization (QCBO) problems. For this purpose, we introduce a new operator that encodes the problem's solution as its ground state. Using Lyapunov control theory, we design a quantum control system such that the state converges to the ground state of this operator. When applied to the QCBO problem, we show that our proposed algorithm saves computational resources by reducing the depth of the quantum circuit and can perform better than FALQON. The effectiveness of our proposed algorithm is further illustrated through numerical simulations.