Classical verification of a quantum simulator: local relaxation of a 1D Bose gas

In [Nat. Phys. 8, 325-330 (2012)], Trotzky et al. utilize ultracold atoms inan optical lattice to simulate the local relaxation dynamics of a stronglyinteracting Bose gas "for longer times than present classical algorithms cankeep track of". Here, I classically verify the results of this analog quantumsimulator by calculating the evolution of the same quasi-local observables upto the time at which they appear "fully relaxed". Using a parallelimplementation of the time-evolving block decimation (TEBD) algorithm tosimulate the system on a supercomputer, I show that local densities andcurrents can be calculated in a matter of days rather than weeks. The precisionof these numerics allows me to observe deviations from the conjecturedpower-law decay and to determine the effects of the harmonic trappingpotential. As well as providing a robust benchmark for future experimental,theoretical, and numerical methods, this work serves as an example of theindependent verification process.