Tensor Train Quantum State Tomography using Compressed Sensing
This addresses the scalability problem in quantum device evaluation, though it appears incremental as it builds on existing tensor train methods.
The paper tackles the exponential parameter growth in quantum state tomography by using a low-rank block tensor train decomposition, achieving memory and computational efficiency for a broad class of quantum states.
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.