Iterative Quantum Optimization with Adaptive Problem Hamiltonian

TL;DR

This paper introduces an iterative quantum optimization method that adaptively refines the problem Hamiltonian to better approximate solutions for complex discrete optimization problems, demonstrated on the shortest vector problem.

Contribution

The paper presents a novel iterative algorithm that dynamically updates the problem Hamiltonian to improve quantum optimization outcomes.

Findings

Converges to the desired solution in numerical experiments.

Effectively refines the problem Hamiltonian over iterations.

Applicable to complex discrete optimization problems.

Abstract

Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of qubits, however, poses the risk of finding only the optimum within the restricted space supported by this Hamiltonian. We describe an iterative algorithm in which a solution obtained with such a restricted problem Hamiltonian is used to define a new problem Hamiltonian that is better suited than the previous one. In numerical examples of the shortest vector problem, we show that the algorithm with a sequence of improved problem Hamiltonians converges to the desired solution.