Tensor-network simulation of quantum transport in many-quantum-dot systems

TL;DR

This paper introduces a tensor-network based method for simulating quantum transport in large quantum-dot systems, significantly reducing computational resources and enabling modeling of up to fifty dots.

Contribution

The authors extend a tensor-based solver with a jump-counting estimator to directly compute steady-state currents, surpassing classical methods in efficiency and system size.

Findings

Quantitative agreement with master-equation solver QmeQ in benchmark tests.

Reduces memory and time by orders of magnitude compared to classical approaches.

Able to simulate quantum transport in arrays of up to fifty quantum dots.

Abstract

Transport through correlated nanoscale systems underpins the operation of quantum-dot and molecular-scale devices, yet accurate simulations of large open quantum systems remain computationally challenging as system size increases. Tensor-network methods offer a promising route past this scaling barrier by efficiently compressing quantum states. Here we extend a tensor-based solver with a jump-counting estimator that enables direct computation of steady-state electron currents from lead-induced tunneling events. We benchmark the resulting currents against the state-of-the-art master-equation solver QmeQ across a range of lead-dot and inter-dot coupling parameters and find quantitative agreement in the tractable regime. Compared with classical approaches, TJM reduces memory requirements and wall-clock time by orders of magnitude, enabling simulations of interacting quantum-dot arrays far beyond the range accessible to density-matrix-based transport solvers and systematic studies of size-dependent nonequilibrium transport in larger arrays. Our approach allow us to model quantum transport in an array of up to fifty (50) quantum dots.