Learning to Classify Quantum Phases of Matter with a Few Measurements
This work addresses the challenge of classifying quantum phases in experiments like cold atom simulators, which can prepare complex ground states but have limited measurement capabilities, representing an incremental advance in quantum machine learning applications.
The paper tackles the problem of identifying quantum phases of matter with limited prior knowledge by developing a supervised learning method that constructs an observable for classification, showing that certification of new ground states can be achieved with a polynomial number of measurements in some cases.
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.