Simulating adiabatic evolution of gapped spin systems

Abstract

We show that adiabatic evolution of a low-dimensional lattice of quantum spins with a spectral gap can be simulated efficiently. In particular, we show that as long as the spectral gap ΔE between the ground state and the first excited state is any constant independent of n, the total number of spins, then the ground-state expectation values of local operators, such as correlation functions, can be computed using polynomial space and time resources. Our results also imply that the local ground-state properties of any two spin models in the same quantum phase can be efficiently obtained from each other. A consequence of these results is that adiabatic quantum algorithms can be simulated efficiently if the spectral gap doesn't scale with n. The simulation method we describe takes place in the Heisenberg picture and does not make use of the finitely correlated state/matrix product state formalism.