Tensor Train Quantum State Tomography using Compressed Sensing

2025-06-30

AI Summary

Quantum state tomography (QST) suffers from exponential scaling of parameters with system size, severely limiting its scalability. To address this, we propose a novel QST framework that synergistically integrates low-rank block-wise tensor train (TT) decomposition with compressed sensing—the first such combined approach for efficient quantum state reconstruction. Our method represents the quantum state in a low-rank TT format and enables robust recovery from a small number of local measurements, applicable to pure states, nearly pure states, and ground states of local Hamiltonians. Compared to standard QST, it reduces both storage and computational complexity dramatically: memory consumption decreases by several orders of magnitude, and scalability is significantly improved. Extensive experiments on many-body systems demonstrate high-fidelity and computationally efficient reconstruction, overcoming the practical scalability bottleneck of conventional QST methods for large-scale quantum systems.

Technology Category

• Machine Learning: Quantum Machine Learning
• Intelligent Robots: State Estimation
• Search and Optimization: Learning to Search

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

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.

Problem

• Exponential parameter growth in quantum state tomography
• Memory and computational inefficiency in standard methods
• Need for efficient low-rank decomposition for quantum states

Innovation

• Low-rank tensor train decomposition
• Memory-efficient quantum state estimation
• Broad applicability to quantum states