Simulation of time evolution with multiscale entanglement renormalization ansatz

Abstract

We describe an algorithm to simulate time evolution using the multiscale entanglement renormalization ansatz and test it by studying a critical Ising chain with periodic boundary conditions and with up to $L\approx {10}^6$ quantum spins. The cost of a simulation, which scales as $L{\text{log}}_2\left(L\right)$, is reduced to ${\text{log}}_2\left(L\right)$ when the system is invariant under translations. By simulating an evolution in imaginary time, we compute the ground state of the system. The errors in the ground-state energy display no evident dependence on the system size. The algorithm can be extended to lattice systems in higher spatial dimensions.