Preparing projected entangled pair states on a quantum computer

TL;DR

This paper introduces a quantum algorithm for efficiently preparing injective PEPS, a class of tensor network states, with runtime depending polynomially on key spectral properties.

Contribution

It provides the first quantum algorithm for preparing injective PEPS with runtime scaling polynomially with spectral gap and condition number.

Findings

Algorithm scales polynomially with inverse spectral gap

Runtime depends on the inverse of the PEPS projectors' condition number

Enables efficient quantum state preparation for tensor networks

Abstract

We present a quantum algorithm to prepare injective PEPS on a quantum computer, a class of open tensor networks representing quantum states. The run-time of our algorithm scales polynomially with the inverse of the minimum condition number of the PEPS projectors and, essentially, with the inverse of the spectral gap of the PEPS' parent Hamiltonian.