Preparing topological PEPS on a quantum computer

TL;DR

This paper introduces an efficient quantum algorithm for preparing topological PEPS, including RVB states, with runtime depending polynomially on key physical parameters, enabling simulation of exotic quantum phases.

Contribution

The authors develop a polynomial-time quantum algorithm for preparing a broad class of topological PEPS, advancing quantum simulation capabilities for complex quantum states.

Findings

Algorithm scales polynomially with condition number

Runtime is inverse-polynomial in spectral gap

Enables efficient simulation of topological quantum states

Abstract

Simulating of exotic phases of matter that are not amenable to classical techniques is one of the most important potential applications of quantum information processing. We present an efficient algorithm for preparing a large class of topological quantum states -- the G-injective Projected Entangled Pair States (PEPS) -- on a quantum computer. Important examples include the resonant valence bond (RVB) states, conjectured to be topological spin liquids. The runtime of the algorithm scales polynomially with the condition number of the PEPS projectors, and inverse-polynomially in the spectral gap of the PEPS parent Hamiltonian.