用于受挫伊辛环量子优化的奇偶映射
Parity Mapping for Quantum Optimization on Frustrated Ising Rings
浏览论文内容
中文总结 AI 辅助
本文以受挫伊辛环为基准，研究奇偶映射对QA和QAOA性能的影响，发现奇偶映射可增大QA最小谱隙、使奇偶QAOA层数随尺寸恒定，优于常规QAOA。
中文摘要 AI 辅助
受挫伊辛环是呈现指数闭合谱隙的最简模型之一，是量子退火（QA）的典型且极具挑战性的基准。因此，该模型的基态制备已在连续时间QA和量子近似优化算法（QAOA）等数字化协议中得到广泛研究。本文利用受挫伊辛环研究奇偶映射对QA和QAOA性能的影响。对于QA，有限尺寸计算表明，在本文所用的能量归一化下，奇偶映射会增大最小谱隙，从而实现更快的连续时间基态制备协议。具有单个全局约束的理想奇偶QA（Parity-QA）实现，在可访问的系统尺寸上未表现出指数隙闭合的迹象；而受硬件启发分解为局域约束时，虽拟合指数小于常规QA，但会恢复指数减小。对于数字化协议，我们发现制备精确基态所需的奇偶QAOA层数在模拟尺寸上保持恒定，优于常规QAOA所需的二次缩放。为研究约束在奇偶QAOA中的作用，我们进一步考虑了一个修正伊辛环实例，其中约束项对制备目标基态至关重要，并将其对应的资源需求与常规QAOA进行了比较。
英文摘要
The frustrated Ising ring is one of the simplest models exhibiting exponential closing spectral gaps, making it a paradigmatic and challenging benchmark for quantum annealing (QA). Ground-state preparation for this model has therefore been studied extensively in both continuous-time QA and digitized protocols such as the Quantum Approximate Optimization Algorithm (QAOA). Here, we use the frustrated Ising ring to investigate how the parity mapping affects the performance of both QA and QAOA. For QA, finite-size calculations show that the parity mapping increases the minimum spectral gap under the energy normalization used in this work, thereby enabling faster continuous-time ground state preparation protocols. An ideal implementation of Parity-QA, with a single global constraint, shows no evidence of exponential gap closing over the accessible system sizes, whereas a hardware-motivated decomposition into local constraints restores the exponential decrease, albeit with a smaller fitted exponent than conventional QA. For the digitized protocol, we find that the number of Parity-QAOA layers required to prepare the exact ground state remains constant over the simulated sizes, improving upon the quadratic scaling required by conventional QAOA. To investigate the role of constraints in Parity-QAOA, we further consider a modified Ising ring instance in which the constraint term is essential for preparing the target ground state. We then compare the corresponding resource requirements with those of conventional QAOA.
