Quantized Low-Rank Quantum State Tomography: Hyperbolic Quantization and Riemannian Least-Squares Recovery

2026-08-27

AI Summary

研究通过HyperQuant量化器和QuantRGD方法解决有限比特Pauli响应下的低秩量子态层析问题，实现了无偏估计和高效恢复。

Abstract

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.

Problem

• Quantum State Tomography
• Low-Rank
• Hyperbolic Quantization
• Finite-bit Pauli Responses
• Bias

Innovation

• Hyperbolic Quantizer
• Low-Rank Quantum State Tomography
• Riemannian Gradient Method