Open Quantum System Dynamics from Infinite Tensor Network Contraction

TL;DR

This paper introduces an efficient tensor network method for simulating long-time dynamics of non-Markovian open quantum systems with Gaussian environments, enabling faster computations and steady-state analysis.

Contribution

It demonstrates that infinite MPO evolution can efficiently contract process tensors for Gaussian environments, automating auxiliary degrees of freedom generation.

Findings

Achieves significant computational speed-up over existing methods.

Enables exploration of steady-state phenomena like phase transitions.

Provides a structurally similar approach to hierarchical or pseudomode methods.

Abstract

Approaching the long-time dynamics of non-Markovian open quantum systems presents a challenging task if the bath is strongly coupled. Recent proposals address this problem through a representation of the so-called process tensor in terms of a tensor network. We show that for Gaussian environments highly efficient contraction to matrix product operator (MPO) form can be achieved with infinite MPO evolution methods, leading to significant computational speed-up over existing proposals. The result structurally resembles open system evolution with carefully designed auxiliary degrees of freedom, as in hierarchical or pseudomode methods. Here, however, these degrees of freedom are generated automatically by the MPO evolution algorithm. Moreover, the semi-group form of the resulting propagator enables us to explore steady-state physics, such as phase transitions.