Quantum many-body simulations with PauliStrings.jl

TL;DR

PauliStrings.jl is a Julia package that enables efficient quantum many-body simulations by encoding Pauli strings in binary, allowing for fast algebraic operations and benchmarking against tensor network methods.

Contribution

The paper introduces PauliStrings.jl, a novel Julia package that performs fast Pauli string operations using binary encoding, facilitating scalable quantum simulations.

Findings

Package performs favorably compared to tensor network methods.

Efficient encoding allows for simulations of 1D and 2D spin systems.

Systematic extrapolation enabled by truncation methods.

Abstract

We present the Julia package PauliStrings ( https://github.com/nicolasloizeau/PauliStrings.jl ) for quantum many-body simulations, which performs fast operations on the Pauli group by encoding Pauli strings in binary. All of the Pauli string algebra is encoded into low-level logic operations on integers, and is made efficient by various truncation methods which allow for systematic extrapolation of the results. We illustrate the effectiveness of our package 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 package performs 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.