AI 中文总结
提出基于块张量列分解的低秩量子态层析框架，将密度矩阵参数化压缩至线性规模，并开发DMRG算法，实现从有限测量中高效精确重建量子态。
AI 中文摘要
量子态层析是一种从测量数据估计量子系统状态的基本技术，在评估量子器件性能方面起着关键作用。然而，随着系统规模增大，由于描述量子态的密度矩阵随量子比特数呈指数增长，标准估计方法在计算上变得不可行。我们提出了一种基于块张量列（Block-TT）分解的混合态量子态层析低秩张量网络框架。具体而言，密度矩阵被表示为块张量列与其厄米共轭的收缩，从而得到Burer-Monteiro分解的张量列模拟。这种参数化通过构造保证了厄米性和半正定性，同时将优化变量的数量从随量子比特数指数增长压缩为线性增长。基于这一表示，我们开发了单位点和双位点密度矩阵重正化群（DMRG）算法，用于从压缩测量中估计量子态。所得方法直接作用于压缩参数化，支持自适应秩细化，并利用高效的张量网络收缩进行期望值评估。该框架适用于广泛类别的低秩量子态，包括纯态、近纯态以及允许精确张量网络近似的基态。数值实验表明，与传统低秩层析方法相比，该方法能从有限测量中实现精确的状态重建，同时大幅降低内存需求和计算成本。
英文摘要
Quantum state tomography 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 computationally prohibitive as the system size increases due to the exponential growth of the density matrix, describing a quantum state, with the number of qubits. We propose a low-rank tensor-network framework for mixed-state quantum state tomography based on a block tensor train (Block-TT) factorization. Specifically, the density matrix is represented as the contraction of a Block-TT with its Hermitian transpose, yielding a TT analogue of the Burer-Monteiro factorization. This parameterization guarantees Hermiticity and positive semidefiniteness by construction while compressing the number of optimization variables from exponential to linear in the number of qubits. Building on this representation, we develop single-site and two-site density matrix renormalization group (DMRG) algorithms for estimating quantum states from compressed measurements. The resulting methods operate directly on the compressed parameterization, support adaptive rank refinement, and exploit efficient tensor-network contractions for expectation-value evaluation. The framework is applicable to a broad class of low-rank quantum states, including pure states, nearly pure states, and ground states that admit accurate tensor-network approximations. Numerical experiments demonstrate accurate state reconstruction from limited measurements together with substantial reductions in memory requirements and computational cost compared with conventional low-rank tomography methods.
Comments26 pages
