Tensor Train Quantum State Tomography using Compressed Sensing

TL;DR

This paper introduces a memory- and computationally-efficient quantum state tomography method using tensor train decompositions and compressed sensing, enabling scalable estimation of complex quantum states.

Contribution

It proposes a novel low-rank tensor train parameterization for quantum states, improving efficiency over traditional methods.

Findings

Applicable to various quantum states including pure and ground states

Reduces memory and computational requirements

Demonstrates effectiveness on simulated quantum data

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.