Comparing Belief-Propagation and Matrix-Product-State Simulations of Quantum Dynamics

For the simulation of non-equilibrium dynamics of spin systems, fault-tolerant quantum computers should provide substantial speed-ups over established classical methods. However, promising classical tensor network methods are being developed whose biggest impediments involve either the lattice structure or the maximum bond dimension required to accurately sim ulate strongly entangled states. We benchmark a recently developed belief propagation (BP) tensor network simulation approach against more established matrix product state (MPS) time evolution by simulating the kicked Ising model on heavy hexagonal lattices of various geometries. Our benchmarks move beyond exact verification and identify bond dimensions at which the methods provide comparable results. In addition to local observables, we use a data processed fidelity measure combined with a Monte Carlo sampling approach to compare the two methods as system size is scaled up. We also benchmark the tensor network methods against noisy simulations to test the impact of noise on comparisons between approximate classical simulations and results from noisy quantum hardware.