量子增强模因禁忌搜索在LABS问题上的规模优势
Scaling advantage with quantum-enhanced memetic tabu search for LABS
AI总结：
本文提出量子增强模因禁忌搜索（QE-MTS），通过数字化反绝热量子优化生成高质量初始解来初始化经典MTS，在LABS问题上将求解时间规模降至O(1.24^N)，超越经典最优启发式算法并预测在N≥47时实现量子优势。
摘要：
我们提出量子增强模因禁忌搜索（QE-MTS），这是一种非变分混合算法，在低自相关二进制序列（LABS）问题上实现了当前最先进的规模表现。通过利用数字化反绝热量子优化（DCQO）生成的高质量初始状态来初始化经典MTS，我们的方法将序列长度$N \in [27,37]$范围内的经验求解时间规模抑制至$\mathcal{O}(1.24^N)$。这一规模表现超越了已知最优的经典启发式算法$\mathcal{O}(1.34^N)$，并优于量子近似优化算法的$\mathcal{O}(1.46^N)$，同时以电路深度减少$6\times$的代价实现了更优越的性能。两阶段自助法分析证实了这一规模优势，并预测交叉点出现在$N \gtrsim 47$处，超过该规模后QE-MTS将优于其经典对应方法。这些结果提供了证据，表明量子增强可以直接改善经典优化算法在典型LABS问题上的规模表现。
英文摘要：
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.
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