Neural-network quantum state tomography

• DOI: 10.1038/s41567-018-0048-5
• Publication Date: 2018-02-23T15:50:13Z
• Authors: Giacomo Torlai; Guglielmo Mazzola; Juan Carrasquilla; Matthias Troyer; Roger Melko; Giuseppe Carleo
• Keywords: Quantum Physics; 0303 health sciences; 03 medical and health sciences; Quantum Gases (cond-mat.quant-gas); FOS: Physical sciences; Disordered Systems and Neural Networks (cond-mat.dis-nn); Condensed Matter - Disordered Systems and Neural Networks; Computational Physics (physics.comp-ph); Condensed Matter - Quantum Gases; Quantum Physics (quant-ph); Physics - Computational Physics

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.<br/>Update version and method, now discussing how to reconstruct the complex amplitudes of the wave function<br/>