Iterative quantum optimisation with a warm-started quantum state

TL;DR

This paper introduces an iterative method to enhance the quantum approximate optimisation algorithm (QAOA) by warm-starting the quantum state, leading to improved solutions for MaxCut and portfolio optimization problems.

Contribution

The paper presents a novel iterative warm-start technique for QAOA that effectively addresses the 'stuck issue' and improves approximation ratios and scaling in optimization tasks.

Findings

Improved approximation ratio for MaxCut with iterative warm-start QAOA.

Enhanced scaling in global minimal variance portfolio optimization.

Effectiveness demonstrated through numerical simulations.

Abstract

We provide a method to prepare a warm-started quantum state from measurements with an iterative framework to enhance the quantum approximate optimisation algorithm (QAOA). The numerical simulations show the method can effectively address the "stuck issue" of the standard QAOA using a single-string warm-started initial state described in [Cain et al., 2023]. When applied to the $3$-regular MaxCut problem, our approach achieves an improved approximation ratio, with a lower bound that iteratively converges toward the best classical algorithms for $p=1$ standard QAOA. Additionally, in the context of the discrete global minimal variance portfolio (DGMVP) model, simulations reveal a more favourable scaling of identifying the global minimal compared to the QAOA standalone, the single-string warm-started QAOA and a classical constrained sampling approach.