Quantum Machine Learning Tensor Network States

Abstract

Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods used to simulate many-body physics and have a further range of applications in machine learning. Finding and contracting tensor network states is a computational task which quantum computers might be used to accelerate. We present a quantum algorithm which returns a classical description of a rank-$r$ tensor network state satisfying an area law and approximating an eigenvector given black-box access to a unitary matrix. Our work creates a bridge between several contemporary approaches, including tensor networks, the variational quantum eigensolver (VQE), quantum approximate optimization (QAOA), and quantum computation.

6 pages, 2 figures, numerics added

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• Generative machine learning with tensor networks: benchmarks on near-term quantum computers
• Tensor networks for interpretable and efficient quantum-inspired machine learning
• Quantum Machine Learning Tensor Network States
• Numerical hardware-efficient variational quantum simulation of a soliton solution
• Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States
• Ion native variational ansatz for quantum approximate optimization
• Quantum tensor network algorithms for evaluation of spectral functions on quantum computers