Rapid adiabatic preparation of injective PEPS and Gibbs states

TL;DR

This paper introduces a quantum algorithm that efficiently prepares injective PEPS and Gibbs states with polylogarithmic runtime, significantly outperforming previous methods and classical sampling algorithms.

Contribution

It presents a nearly exponential improvement in quantum state preparation efficiency for certain many-body states using adiabatic evolution.

Findings

Achieves $O( ext{polylog}N)$ adiabatic runtime for $O(N)$ spins.

Total elementary gates scale as $O(N ext{polylog}N)$.

Faster than classical Monte Carlo mixing times for thermal states.

Abstract

We propose a quantum algorithm for many-body state preparation. It is especially suited for injective PEPS and thermal states of local commuting Hamiltonians on a lattice. We show that for a uniform gap and sufficiently smooth paths, an adiabatic runtime and circuit depth of $O(\operatorname{polylog}N)$ can be achieved for $O(N)$ spins. This is an almost exponential improvement over previous bounds. The total number of elementary gates scales as $O(N\operatorname{polylog}N)$. This is also faster than the best known upper bound of $O(N^2)$ on the mixing times of Monte Carlo Markov chain algorithms for sampling classical systems in thermal equilibrium.