Learning to Classify Quantum Phases of Matter with a Few Measurements

Document detail

ID

oai:arXiv.org:2409.05188

Topic

Quantum Physics Condensed Matter - Other Condensed... Condensed Matter - Statistical Mec... Computer Science - Machine Learnin... Statistics - Machine Learning

Author

Khosrojerdi, Mehran Pereira, Jason L. Cuccoli, Alessandro Banchi, Leonardo

Year

2024

listing date

9/11/2024

Keywords

learning matter

Metrics

Abstract

We study the identification of quantum phases of matter, at zero temperature, when only part of the phase diagram is known in advance.

Following a supervised learning approach, we show how to use our previous knowledge to construct an observable capable of classifying the phase even in the unknown region.

By using a combination of classical and quantum techniques, such as tensor networks, kernel methods, generalization bounds, quantum algorithms, and shadow estimators, we show that, in some cases, the certification of new ground states can be obtained with a polynomial number of measurements.

An important application of our findings is the classification of the phases of matter obtained in quantum simulators, e.g., cold atom experiments, capable of efficiently preparing ground states of complex many-particle systems and applying simple measurements, e.g., single qubit measurements, but unable to perform a universal set of gates.

Khosrojerdi, Mehran,Pereira, Jason L.,Cuccoli, Alessandro,Banchi, Leonardo, 2024, Learning to Classify Quantum Phases of Matter with a Few Measurements