Many-body quantum state tomography with neural networks

TL;DR

This paper demonstrates that neural networks can efficiently perform quantum state tomography on complex many-body systems, enabling the reconstruction of entangled states and quantities like entanglement entropy from simple measurements.

Contribution

It introduces a machine learning-based method for quantum state tomography that scales efficiently to large, highly-entangled many-body quantum systems in one and two dimensions.

Findings

Neural networks successfully reconstruct complex quantum states.

The method accurately estimates entanglement entropy from measurements.

Applicable to quantum computers and ultra-cold atom simulators.

Abstract

The experimental realization of increasingly complex synthetic quantum systems calls for the development of general theoretical methods, to validate and fully exploit quantum resources. Quantum-state tomography (QST) aims at reconstructing the full quantum state from simple measurements, and therefore provides a key tool to obtain reliable analytics. Brute-force approaches to QST, however, demand resources growing exponentially with the number of constituents, making it unfeasible except for small systems. Here we show that machine learning techniques can be efficiently used for QST of highly-entangled states, in both one and two dimensions. Remarkably, the resulting approach allows one to reconstruct traditionally challenging many-body quantities - such as the entanglement entropy - from simple, experimentally accessible measurements. This approach can benefit existing and future generations of devices ranging from quantum computers to ultra-cold atom quantum simulators.