Quantum Machine Learning Tensor Network States

TL;DR

This paper introduces a quantum algorithm for efficiently approximating tensor network states that satisfy an area law, bridging tensor networks, VQE, QAOA, and quantum computation.

Contribution

It presents a novel quantum algorithm to find classical descriptions of tensor network states from black-box access to unitaries, enhancing simulation of quantum many-body systems.

Findings

Provides a quantum algorithm for tensor network state approximation.

Connects tensor networks with variational quantum algorithms.

Enables potential acceleration of tensor network contractions on quantum computers.

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.