Adiabatic Optimization of Tensor Networks

We present a novel algorithm for building a tensor network ground-state representation using adiabatic optimization. The basic idea follows the so-called s-source framework to construct a quantum circuit that interpolates between the ground state of system size L and 2L. This procedure can then be iterated to reach the thermodynamic limit. In contrast with standard algorithms which rely on the variational principle, our approach is based on the adiabatic theorem and may prove particularly useful for Hamiltonians where variational methods tend to fail. We propose an explicit numerical scheme for optimizing the interpolating quantum circuit and benchmark it against DMRG for several spin chain models; even near a quantum phase transition, where the spectral gap is small, we observe good agreement between the methods.