Simulating quantum transport via collisional models on a digital quantum computer

TL;DR

This paper explores simulating nonequilibrium quantum transport in spin chains using collisional models on digital quantum computers, analyzing accuracy, dynamics regimes, and effects of magnetic fields.

Contribution

It introduces a collisional model approach for simulating open quantum systems on digital quantum computers, focusing on steady states and transport phenomena in spin chains.

Findings

The collisional model accurately reproduces steady states compared to master equations.

Simulation results distinguish diffusive and ballistic regimes in large systems.

Digital simulation effectively captures current rectification under non-uniform magnetic fields.

Abstract

Digital quantum computers have the potential to study the dynamics of complex quantum systems. Nonequilibrium open quantum systems are, however, less straightforward to be implemented. Here we consider a collisional model representation of the nonequilibrium open dynamics for a boundary-driven XXZ spin chain, with a particular focus on its steady states. More specifically, we study the interplay between the accuracy of the result versus the depth of the circuit by comparing the results generated by the corresponding master equations. We study the simulation of a boundary-driven spin chain in regimes of weak and strong interactions, which would lead in large systems to diffusive and ballistic dynamics, considering also possible errors in the implementation of the protocol. Last, we analyze the effectiveness of digital simulation via the collisional model of current rectification when the XXZ spin chains are subject to non-uniform magnetic fields.