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

• URL: http://arxiv.org/abs/2608.27503v1
• Date: Thu, 27 Aug 2026 04:24:35 GMT
• Title: Quantized Low-Rank Quantum State Tomography: Hyperbolic Quantization and Riemannian Least-Squares Recovery
• Abstract summary: We study low-rank quantum state tomography from finite-bit Pauli batch responses.<n>We propose HyperQuant, a mean-preserving hyperbolic quantizer adapted to the second-moment scale of Pauli responses.<n>We derive nonasymptotic recovery guarantees and an explicit bit--shot tradeoff under which finite-bit responses retain the error order of unquantized batch averages.
• Score: 8.187661034157335
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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