用张量分解压缩量子态，高效实现量子态重构。
Tensor Train Quantum State Tomography using Compressed Sensing
- 用低秩块张量列车分解参数化量子态，降低复杂度。
- 在纯态、近纯态和哈密顿基态上表现良好。
- 适合需要高效量子态重建的实验与模拟场景。
量子态层析（QST）是从测量数据中估计量子系统状态的基本技术，在评估量子设备性能中至关重要。然而，标准估计方法因状态表示参数呈指数增长而变得不切实际。本文通过使用低秩块张量列车分解参数化量子态，解决了这一挑战，证明该方法在内存和计算上均高效。该框架适用于可被低秩分解良好逼近的广泛量子态类别，包括纯态、近纯态以及哈密顿量的基态。
原文摘要 · Abstract (English)
Quantum state tomography (QST) is a fundamental technique for estimating the state of a quantum system from measured data and plays a crucial role in evaluating the performance of quantum devices. However, standard estimation methods become impractical due to the exponential growth of parameters in the state representation. In this work, we address this challenge by parameterizing the state using a low-rank block tensor train decomposition and demonstrate that our approach is both memory- and computationally efficient. This framework applies to a broad class of quantum states that can be well approximated by low-rank decompositions, including pure states, nearly pure states, and ground states of Hamiltonians.
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