Quantum Machine Learning Tensor Network States
This work addresses a computational bottleneck in simulating many-body physics and machine learning by potentially speeding up tensor network contractions, though it appears incremental in integrating existing quantum methods.
The paper tackles the problem of accelerating tensor network state approximation for quantum systems by developing a quantum algorithm that returns a classical description of a rank-r tensor network state approximating an eigenvector, given black-box access to a unitary matrix, bridging tensor networks with quantum computing approaches like VQE and QAOA.
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.