Rapid adiabatic preparation of injective PEPS and Gibbs 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.