Tensor renormalization group methods for quantum real-time evolution

For problems in high energy physics, computational time and memory capacity limit what is possible to simulate with classical digital computers. Even for very simple models, exact simulations are only possible for systems with a handful of particles. For example, for a two-state quantum system of N degrees of freedom a computer must keep track of 2^N variables, which in practice limits us to around N = 12. Thus, solving large physical systems exactly is not possible, and we must introduce accurate approximation and truncation schemes to best model a system.

Beginning in the 1950's, Murray Gell-mann, Leo Kadanoff, Ken Wilson and others formulated an idea known as the Renormalization Group (RG). On a high level, it is a method used to describe systems at different scales. In quantum field theory, this was used to justify renormalization of infinite integrals and the ultraviolet cutoff. For models where long range interactions dominate, we can use RG techniques to coarse grain away the short range behavior, leaving us with much less than 2^N variables to account for. The RG has been applied in many ways in computational nuclear and high energy physics. We focus on one application of the RG to models that can be readily represented as tensor networks, known as the tensor renormalization group (TRG). We show that TRG, which was developed for imaginary-time evolution, can be used to accurately real-time evolve wave scattering states of 1D quantum spin systems in the low energy sector.

An alternative approach uses quantum computers, whose computational complexity scales much better than classical computers. Though in their early stages, quantum computers have shown great promise in simulating spin systems on order of tens of sites. Yet, engineering challenges like system noise and qubit decoherence limit both state preparation and time evolution. We develop an efficient approximate fermionic wave packet preparation method for spin systems, simulate on IonQ and IBM quantum hardware, and compare with classical alternatives.