Tensor renormalization group methods for quantum real-time evolution

In the noisy-intermediate scale (NISQ) era of quantum computing, where system noise and qubit decoherence limit system size and simulation time, there is still a need to develop classical simulation algorithms to benchmark quantum hardware and algorithms. One of the ways we benchmark is by real-time evolving quantum spin systems, which become very expensive very quick on classical hardware. We show that the tensor renormalization group with higher-order singular value decomposition (HOTRG), a coarse graining method originally developed for imaginary time evolution, can be used to efficiently and accurately simulate one and two particle scattering processes in real time. For the 1+1D transverse field Ising model, we find that HOTRG works well in the disordered phase, but struggles as you approach the phase transition and into the ordered phase. For one particle simulations we can go up to 128 sites, while for two particles we can only go up to 16 sites. We discuss possible improvements for 1+1D and extending to higher dimensions.