发表机构
Research Institute for Advanced Computer Science; USRA（先进计算机科学研究所; 大学研究协会）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明量子随机访问优化（QRAO）的压缩编码可将问题复杂性放大至NP、StoqMA和QMA完全，且该难度在实际编译器中依然存在，揭示量子压缩的最坏情况复杂性障碍。
AI 中文摘要
压缩量子编码旨在克服硬件限制，以应对大规模挑战性问题，将许多经典变量映射到更少量子比特的非对易可观测量上。经典上，诸如MaxCut的半定规划公式等松弛方法以解质量为代价换取计算效率。相比之下，基于压缩的量子松弛可以放大所求解问题的最坏情况复杂性。我们研究量子随机访问优化（QRAO），这是泡利关联编码（PCE）框架的一个特例，该框架将最多三个二元变量分配给每个量子比特的泡利$X$、$Y$和$Z$可观测量，其中打包选择决定了待优化的压缩哈密顿量。我们确定了明确的QRAO最优能量承诺问题，这些问题对NP、StoqMA和QMA是完全的，其中后两者具有逆多项式承诺间隙。我们的问题归约在不需要辅助比特或辅助门的情况下保持逆多项式承诺间隙。对于任何规定的打包，我们证明加权MaxCut实例在已知平移和重新缩放下，可压缩为打包所允许的任意非负权重成对泡利耦合。对于QRAO，使用一个对齐轴给出NP完全能量问题。使用两个或三个正对齐泡利轴通常给出QMA完全问题，而它们的二分限制属于StoqMA。我们表明这种计算难度在编译后依然存在且具有实际相关性。值得注意的是，这一结果直接适用于Qiskit Optimization 0.7.0中当前的QRAO编译器实现，证实我们的难度结果并非人为或牵强打包规则的产物。总之，我们的结果识别了由量子压缩产生的最坏情况复杂性障碍，同时不对典型情况或使用它的算法流水线的性能和可训练性做出广泛声明。
英文摘要
Compressed quantum encodings aim to overcome hardware limitations towards tackling challenging problems at scale, with many classical variables mapped onto noncommuting observables of fewer qubits. Classically, relaxations such as the semidefinite program formulation of MaxCut trade solution quality for computational efficiency. By contrast, quantum relaxations based on compression can amplify the worst-case complexity of the problem being solved. We study quantum random access optimization (QRAO), a special case of the Pauli correlation encoding (PCE) framework that assigns up to three binary variables to the Pauli $X$, $Y$, and $Z$ observables of each qubit, with the packing choices determining the compressed Hamiltonian to be optimized. We identify explicit QRAO optimal energy promise problems complete for NP, StoqMA, and QMA, with inverse-polynomial promise gaps for the latter two. Our problem reductions preserve inverse-polynomial promise gaps without requiring gadgets or ancillas. For any prescribed packing, we show that weighted MaxCut instances compress, up to a known shift and rescaling, to arbitrary nonnegative-weight pairwise Pauli couplings allowed by the packing. For QRAO, using one aligned axis gives an NP-complete energy problem. Using two or three positive aligned Pauli axes generally gives QMA-complete problems, with bipartite restrictions in BQP $\cap$ StoqMA. We show that this computational hardness survives compilation and is practically relevant. Notably, this result applies directly to the current QRAO compiler implementation in Qiskit Optimization 0.7.0, confirming our hardness results are not artifacts of artificial or contrived packing rules. Altogether our results identify worst-case complexity barriers arising from quantum compression, while making no broad claims about typical cases or the performance and trainability of algorithm pipelines that use it.
CommentsAbstract shortened for arxiv submission
