N. Loizeau Quantum many-body simulations with Pauli Strings

I will present numerical methods to simulate quantum many body systems by encoding the Pauli string algebra into low-level logic operations on integers. The efficiency of the technique relies on various truncation methods which allow for systematic extrapolation of the results. We illustrate the effectiveness of our method by (i) performing Heisenberg time evolution through direct numerical integration and (ii) by constructing a Liouvillian Krylov space. We benchmark the results against tensor network methods, and we find our Pauli strings methods perform favorably. In addition, we show that this representation allows for easy encoding of any geometry. We present results for chaotic and integrable spin systems in 1D as well as some examples in 2D. Currently, the main limitations are the inefficiency of representing non-trivial pure states (or other low-rank operators), as well as the need to introduce dissipation to probe long-time dynamics. To make this practical, I am developing the Julia package PauliStrings.jl (https://paulistrings.org/).