Many-body quantum state tomography with neural networks

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.

Update version and method, now discussing how to reconstruct the complex amplitudes of the wave function

References in corpus (9)

• Many-Body Physics with Ultracold Gases
• Scalable multi-particle entanglement of trapped ions
• Learning phase transitions by confusion
• Efficient quantum state tomography
• Experimental entanglement of six photons in graph states
• Demonstration of Entanglement of Electrostatically Coupled Singlet-Triplet Qubits
• Efficient Representation of Quantum Many-body States with Deep Neural Networks
• Efficient tomography of a quantum many-body system
• Permutationally invariant quantum tomography

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