AI 中文总结
针对多量子比特系统密集重建难的问题，提出基于秩一原子坐标的秩自适应无矩阵方法用于低秩量子态层析成像，结合多种操作，通过秩惩罚调整表示大小，模拟显示其在精度、运行时间和内存方面有良好权衡。
AI 中文摘要
量子态层析成像通过测量数据估计未知密度算子。然而，对于多量子比特系统，由于希尔伯特空间维度呈指数增长，密集重建可能不切实际。本文基于秩一原子坐标，开发了一种用于低秩量子态层析成像的秩自适应无矩阵方法。密度算子表示为纯态原子的凸组合，避免了密集的密度、测量和梯度矩阵。算法结合原子更新、单纯形约束系数重加权和周期性谱重构，仅使用预测概率向量、原子向量和描述符级测量操作。这些计算可跨测量结果分解，并允许主从实现。秩惩罚在优化过程中调整表示大小。证明了可行性、预测一致性、惩罚目标的单调下降以及重构步骤的精确谱近端特征。与竞争方法相比，使用泡利测量的模拟显示出良好的精度-运行时间-内存权衡。
英文摘要
Quantum state tomography estimates an unknown density operator from measurement data. Dense reconstruction however, can be impractical for many-qubit systems because the Hilbert-space dimension grows exponentially. This contribution develops a rank-adaptive matrix-free approach to low-rank quantum state tomography based on rank-one atomic coordinates. The density operator is represented as a convex combination of pure-state atoms, which preserves positivity and unit trace while avoiding dense density, measurement, and gradient matrices. The resultant algorithm combines atom updates, simplex-constrained coefficient reweighting, and periodic spectral refactorization using only predicted probability vectors, atom vectors, and descriptor-level measurement actions. These computations decompose across measurement outcomes, and admit a master--worker implementation with the measurements partitioned across workers. A rank penalty adapts the representation size during optimization. Provable feasibility, prediction consistency, monotone descent of the penalized objective, and an exact spectral proximal characterization of the refactorization step are established. Simulations with Pauli measurements show favorable accuracy--runtime--memory tradeoffs relative to competing alternatives.
CommentsAccepted to Allerton 2026
