Practical learning method for multi-scale entangled states

TL;DR

This paper presents an efficient, scalable method for reconstructing multi-scale entangled quantum states using minimal measurements and standard computational tools, robust against errors.

Contribution

It introduces a practical approach that requires only single-particle measurements and polynomial resources for state reconstruction, improving scalability and error resilience.

Findings

Reconstruction method uses polynomially many measurements.

Data processing employs standard matrix diagonalisation and conjugate gradient.

Method effectively prevents error accumulation from imperfections.

Abstract

We describe a method for reconstructing multi-scale entangled states from a small number of efficiently-implementable measurements and fast post-processing. The method only requires single particle measurements and the total number of measurements is polynomial in the number of particles. Data post-processing for state reconstruction uses standard tools, namely matrix diagonalisation and conjugate gradient method, and scales polynomially with the number of particles. Our method prevents the build-up of errors from both numerical and experimental imperfections.