Quantum Phase Recognition via Quantum Kernel Methods

Abstract

The application of quantum computation to accelerate machine learning algorithms is one of the most promising areas of research in quantum algorithms. In this paper, we explore the power of quantum learning algorithms in solving an important class of Quantum Phase Recognition (QPR) problems, which are crucially important in understanding many-particle quantum systems. We prove that, under widely believed complexity theory assumptions, there exists a wide range of QPR problems that cannot be efficiently solved by classical learning algorithms with classical resources. Whereas using a quantum computer, we prove the efficiency and robustness of quantum kernel methods in solving QPR problems through Linear order parameter Observables. We numerically benchmark our algorithm for a variety of problems, including recognizing symmetry-protected topological phases and symmetry-broken phases. Our results highlight the capability of quantum machine learning in predicting such quantum phase transitions in many-particle systems.

References in corpus (23)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum computational advantage using photons
• The power of quantum neural networks
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• Power of data in quantum machine learning
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Quantum advantage in learning from experiments
• A rigorous and robust quantum speed-up in supervised machine learning
• Information-theoretic bounds on quantum advantage in machine learning
• Provably efficient machine learning for quantum many-body problems
• Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
• Quantum machine learning beyond kernel methods
• Linear growth of quantum circuit complexity
• Training Quantum Embedding Kernels on Near-Term Quantum Computers
• Efficient measure for the expressivity of variational quantum algorithms
• Towards understanding the power of quantum kernels in the NISQ era
• Representation Learning via Quantum Neural Tangent Kernels
• Towards a Larger Molecular Simulation on the Quantum Computer: Up to 28 Qubits Systems Accelerated by Point Group Symmetry
• Toward Practical Quantum Embedding Simulation of Realistic Chemical Systems on Near-term Quantum Computers
• Importance of Kernel Bandwidth in Quantum Machine Learning
• Quantum kernels to learn the phases of quantum matter
• Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry
• Quantum evolution kernel : Machine learning on graphs with programmable arrays of qubits

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• Identification of topological phases using classically-optimized variational quantum eigensolver
• Quantum-enhanced neural networks in the neural tangent kernel framework
• Unveiling quantum phase transitions from traps in variational quantum algorithms
• Orbital Expansion Variational Quantum Eigensolver: Enabling Efficient Simulation of Molecules with Shallow Quantum Circuit
• Learning out-of-time-ordered correlators with classical kernel methods
• Learning complexity gradually in quantum machine learning models