Quantum kernels to learn the phases of quantum matter

Abstract

Classical machine learning has succeeded in the prediction of both classical and quantum phases of matter. Notably, kernel methods stand out for their ability to provide interpretable results, relating the learning process with the physical order parameter explicitly. Here, we exploit quantum kernels instead. They are naturally related to the \emph{fidelity} and thus it is possible to interpret the learning process with the help of quantum information tools. In particular, we use a support vector machine (with a quantum kernel) to predict and characterize second order quantum phase transitions. We explain and understand the process of learning when the fidelity per site (rather than the fidelity) is used. The general theory is tested in the Ising chain in transverse field. We show that for small-sized systems, the algorithm gives accurate results, even when trained away from criticality. Besides, for larger sizes we confirm the success of the technique by extracting the correct critical exponent $\nu$. Finally, we present two algorithms, one based on fidelity and one based on the fidelity per site, to classify the phases of matter in a quantum processor.

Published version. Two quantum algorithms added, one for the fidelity per site

References in corpus (22)

• A Quantum Approximate Optimization Algorithm
• An introduction to quantum machine learning
• Learning phase transitions by confusion
• Power of data in quantum machine learning
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Information-theoretic bounds on quantum advantage in machine learning
• Provably efficient machine learning for quantum many-body problems
• Ground state fidelity from tensor network representations
• Machine learning vortices at the Kosterlitz-Thouless transition
• Supervised quantum machine learning models are kernel methods
• Quantum fidelity and quantum phase transitions in matrix product states
• Generalization in Quantum Machine Learning: a Quantum Information Perspective
• Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory
• Deep Reinforcement Learning for Quantum Gate Control
• Fidelity analysis of topological quantum phase transitions
• Towards understanding the power of quantum kernels in the NISQ era
• Fidelity approach to quantum phase transitions: finite size scaling for quantum Ising model in a transverse field
• Importance of Kernel Bandwidth in Quantum Machine Learning
• Fidelity in topological quantum phases of matter
• Adiabatic Spectroscopy and a Variational Quantum Adiabatic Algorithm
• Higgs analysis with quantum classifiers
• Renormalization group flows and quantum phase transitions: fidelity versus entanglement

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• Circuit Complexity through phase transitions: consequences in quantum state preparation
• Identification of topological phases using classically-optimized variational quantum eigensolver
• Qudit Machine Learning
• Quantum-enhanced neural networks in the neural tangent kernel framework
• Experimental benchmarking of quantum state overlap estimation strategies with photonic systems
• Machine learning the Ising transition: A comparison between discriminative and generative approaches
• Benchmarking of quantum fidelity kernels for Gaussian process regression