Scaling advantage with quantum-enhanced memetic tabu search for LABS

TL;DR

This paper presents a quantum-enhanced memetic tabu search algorithm that significantly improves the scaling performance for the LABS problem by integrating quantum optimization techniques, outperforming classical heuristics and other quantum algorithms.

Contribution

The authors introduce QE-MTS, a hybrid quantum-classical algorithm that achieves superior scaling for LABS by seeding classical search with quantum solutions, surpassing previous methods.

Findings

QE-MTS achieves a scaling of O(1.24^N) for LABS, better than classical and other quantum algorithms.

The method reduces circuit depth by a factor of 6 compared to previous quantum approaches.

Projected crossover point where QE-MTS outperforms classical methods is at N ≈ 47.

Abstract

We introduce quantum-enhanced memetic tabu search (QE-MTS), a non-variational hybrid algorithm that achieves state-of-the-art scaling for the low-autocorrelation binary sequence (LABS) problem. By seeding the classical MTS with high-quality initial states from digitized counterdiabatic quantum optimization (DCQO), our method suppresses the empirical time-to-solution scaling to $\mathcal{O}(1.24^N)$ for sequence length $N \in [27,37]$. This scaling surpasses the best-known classical heuristic $\mathcal{O}(1.34^N)$ and improves upon the $\mathcal{O}(1.46^N)$ of the quantum approximate optimization algorithm, achieving superior performance with a $6\times$ reduction in circuit depth. A two-stage bootstrap analysis confirms the scaling advantage and projects a crossover point at $N \gtrsim 47$, beyond which QE-MTS outperforms its classical counterpart. These results provide evidence that quantum enhancement can directly improve the scaling of classical optimization algorithms for the paradigmatic LABS problem.