近日，复旦大学李晓鹏团队研究了可编程原子腔系统的自适应量子优化算法。该项研究成果发表在2025年11月25日出版的《物理评论A》杂志上。

开发适应近程量子设备特定约束的量子算法是实现实用量子优势的关键一步。在最近的工作中，研究组已证明光学腔中的冷原子可构建为具有可编程全连接相互作用的通用量子优化器，其有效哈密顿量直接编码了数划分问题（NPP）。

现在，研究组通过数值模拟研究了量子退火（QA）与量子近似优化算法（QAOA）在求解原子量子比特基态编码的NPP中的表现。发现标准QA的成功概率随问题规模增大而急剧下降，优化后的退火路径或非均匀驱动场仅带来轻微改善。类似地，QAOA始终陷入虚假局部极小值，增加量子电路深度也未显著提升性能。

为克服NPP求解困难，研究组提出一种自适应变分量子算法（VQA），其试探态通过释放NPP哈密顿量的参数自由度区别于QAOA。数值模拟表明，该自适应VQA在极浅电路深度即可实现较高成功概率，相比QAOA值得为额外参数优化付出代价。因此，这种自适应VQA为可编程原子-腔系统在量子相干时间内展示竞争力的计算能力提供了有力方案。

附：英文原文

Title: Adaptive quantum optimization algorithms for programmable atom-cavity systems

Author: Yuchen Luo, Xiaopeng Li, Jian Lin

Issue&Volume: 2025/11/25

Abstract: Developing quantum algorithms adaptive to specific constraints of near-term devices is an essential step towards practical quantum advantage. In a recent work [Phys. Rev. Lett. 131, 103601 (2023)], we show cold atoms in an optical cavity can be built as a universal quantum optimizer with programmable all-to-all interactions, and the effective Hamiltonian for atoms directly encodes number partitioning problems (NPPs). Here, we numerically investigate the performance of quantum annealing (QA) and quantum approximate optimization algorithm (QAOA) to find the solution of NPP that is encoded in the ground state of atomic qubits. We find the success probability of the standard QA decays rapidly with the problem size. The optimized annealing path or inhomogeneous driving fields only lead to mild improvement on the success probability. Similarly, the QAOA always gets trapped in a false local minimum, and there is no significant performance improvement as we increase the depth of the quantum circuit. To overcome the difficulty of solving NPPs, we propose an adaptive variational quantum algorithm (VQA) whose ansatz differs from that of the QAOA by releasing the parameter freedom of the NPP Hamiltonian. Through numerical simulations, we find that our adaptive VQA can achieve rather high success probability within very small circuit depth. It is thus worth paying the extra optimization cost of additional parameters for improving performance compared to the QAOA. Therefore, our adaptive VQA provides a promising choice for programmable atom-cavity systems to demonstrate competitive computational power within its quantum coherence time.

DOI: 10.1103/515w-htjp

Source: https://journals.aps.org/pra/abstract/10.1103/515w-htjp