AI 中文总结
该研究针对有限比特泡利批量响应的低秩量子态层析问题，提出HyperQuant量化器与QuantRGD方法，建立相关恢复保证与比特- shots权衡，通过实验验证其有效性。
AI 中文摘要
我们研究基于有限比特泡利批量响应的低秩量子态层析。为避免通用量化引入的偏差，我们提出HyperQuant，一种适配泡利响应二阶矩尺度的保均值双曲量化器。我们建立极小极大失真保证，证明精确均值保留可实现直接的秩约束最小二乘恢复，且不改变总体目标。我们推导非渐近恢复保证及显式的比特- shots权衡关系，在此权衡下，有限比特响应用更少的响应比特即可保持未量化批量均值的误差阶。为实现高效计算，我们开发QuantRGD，一种黎曼梯度方法，在显式资源条件下可证明线性收敛至相应统计邻域。数值实验验证了预测的量化、恢复及收敛行为。
英文摘要
We study low-rank quantum state tomography from finite-bit Pauli batch responses. To avoid bias introduced by generic quantization, we propose HyperQuant, a mean-preserving hyperbolic quantizer adapted to the second-moment scale of Pauli responses. We establish minimax distortion guarantees and show that exact mean preservation enables direct rank-constrained least-squares recovery without altering the population target. We derive nonasymptotic recovery guarantees and an explicit bit--shot tradeoff under which finite-bit responses retain the error order of unquantized batch averages using fewer response bits. For efficient computation, we develop QuantRGD, a Riemannian gradient method with provable linear convergence to the corresponding statistical neighborhood under explicit resource conditions. Numerical experiments validate the predicted quantization, recovery, and convergence behavior.
