Tensor Train Quantum State Tomography using Compressed Sensing

• URL: http://arxiv.org/abs/2506.23560v1
• Date: Mon, 30 Jun 2025 07:06:50 GMT
• Title: Tensor Train Quantum State Tomography using Compressed Sensing
• Authors: Shakir Showkat Sofi, Charlotte Vermeylen, Lieven De Lathauwer,
• Abstract summary: Quantum state tomography (QST) is a fundamental technique for estimating the state of a quantum system from measured data.<n>In this work, we address this challenge by parameterizing the state using a low-rank block tensor train decomposition.<n>This framework applies to a broad class of quantum states that can be well approximated by low-rank decompositions.
• Score: 2.493374942115722
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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