Efficient Time Evolution of 2D Open-Quantum Lattice Models with Long-Range Interactions using Tensor Networks

TL;DR

This paper introduces a tensor network method called tePEPO for efficiently simulating the time evolution of 2D open quantum systems with long-range interactions, enabling more accurate modeling of complex quantum phenomena.

Contribution

The authors develop a novel tensor network operator, tePEPO, capable of representing long-range interactions in 2D open quantum systems, extending the applicability of tensor networks beyond nearest-neighbor models.

Findings

Efficient representation of long-range interactions with small bond dimension.

Accurate simulation of a Rydberg atom Hamiltonian with dipolar interactions.

Evidence of dipole-dipole blockade effect in dissipative conditions.

Abstract

Simulating many-body open quantum systems is an extremely challenging problem, with methods often restricted to either models with nearest-neighbor interactions or semi-classical approximations. In particular, modeling two-dimensional systems with realistic long-range interactions, in addition to dissipation, is of vital importance to the development of modern quantum computing and simulation platforms. In this paper, we present a construction of the time-evolution operator, as a projected entangled pair operator (denoted tePEPO), that can be used to evolve a tensor network ansatz through time. Interactions beyond nearest-neighbor, including interactions between sites not collinear in the lattice, can be represented efficiently as a tePEPO. Furthermore, we obtain approximations to realistic radial long-range interactions decaying with a power-law, that give accurate results with small tePEPO bond dimension. Finally, we consider a physical example of a Rydberg atom Hamiltonian with long-range dipolar interactions, and show evidence of a dipole-dipole blockading effect in presence of dissipation. This work demonstrates the applicability of tensor networks to two-dimensional systems widely studied in experiments, but previously inaccessible to non-semi-classical methods.