Iterative quantum optimisation with a warm-started quantum state
This work is significant for quantum computing researchers and practitioners, as it offers an incremental improvement to the QAOA algorithm, addressing a known limitation and demonstrating better performance on specific optimization problems.
This paper introduces an iterative framework to enhance the Quantum Approximate Optimization Algorithm (QAOA) by preparing a warm-started quantum state from measurements. The method effectively addresses the 'stuck issue' of standard QAOA, achieving an improved approximation ratio for the 3-regular MaxCut problem that iteratively converges toward the best classical algorithms for p=1 standard QAOA, and shows more favorable scaling for identifying the global minimal in the discrete global minimal variance portfolio (DGMVP) model.
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.