Reconstructing quantum states efficiently

TL;DR

This paper introduces an efficient quantum state reconstruction method that uses a linear number of measurements and polynomial computational resources, significantly improving over traditional exponential approaches for natural quantum states.

Contribution

The authors develop a novel reconstruction scheme combining singular value thresholding and matrix product states, achieving exponential measurement efficiency for typical quantum states.

Findings

Reconstruction scheme requires only a linear number of measurements.

Postprocessing computational complexity is polynomial in system size.

Method achieves high-fidelity state reconstruction for natural quantum states.

Abstract

Quantum state tomography, the ability to deduce the density matrix of a quantum system from measured data, is of fundamental importance for the verification of present and future quantum devices. It has been realized in systems with few components but for larger systems it becomes rapidly infeasible because the number of quantum measurements and computational resources required to process them grow exponentially in the system size. Here we show that we can gain an exponential advantage over direct state tomography for quantum states typically realized in nature. Based on singular value thresholding and matrix product state methods we introduce a state reconstruction scheme that relies only on a linear number of measurements. The computational resources for the postprocessing required to reconstruct the state with high fidelity from these measurements is polynomial in the system size.