Quantum and Classical Simulation of Electronic Transport at the Nanoscale

김우연

Satofumi Souma

We propose and demonstrate a quantum circuitbased framework for simulating quantum transport phenomena governed by the time-dependent Schrödinger equation for open quantum systems. While the theoretical formulation is compatible with large-scale classical simulations, its implementation as a quantum algorithm offers a promising path toward quantumaccelerated modeling of nanoscale devices. A key challenge in such simulations lies in incorporating dissipation and particle injection processes arising from coupling to external reservoirs. In this work, we present quantum circuit constructions that explicitly encode these effects using controlled rotations, measurementinduced decoherence, and reset operations. By comparing the results of our quantum simulations with those obtained from classical numerical solutions of the open-system Schrödinger equation, we confirm that the proposed quantum model can reproduce both transient dynamics and steady-state behavior. These results validate the physical fidelity of the approach and highlight the potential of quantum computing in electronic transport simulations.

A. Alarcón, A. Benali, A. Padro +3 more

Today, the necessity of faster and smaller devices is pushing the electronic industry into developing electron devices with solid-state structures of few nanometers. In these dimensions electron dynamics are in general governed by quantum mechanical laws. We have recently shown that Bohmian trajectories allow a direct treatment of the many-particle interaction among electrons with an accuracy comparable to DFT techniques. In this article we present a general, versatile and time-dependent 3D quantum electron transport simulator, named BITLLES (Bohmian Interacting Transport in Electronic Structures), based on Bohmian trajectories for nanoelectronic devices. As a numerical example, we show the ability of BITLLES simulator to predict the electrical characteristics (DC, AC and fluctuations) of a Resonant Tunneling Diode.

Alessio Zaccone

Ultra-thin films are fundamental components of modern nanoelectronics, where reducing thickness to the few-nanometer scale leads to a dramatic increase in electrical resistivity. For decades, this behavior has been interpreted in terms of classical size effects, primarily surface scattering within the Fuchs--Sondheimer theory and grain-boundary scattering in the Mayadas--Shatzkes model. While these approaches successfully describe transport when the film thickness is comparable to the electronic mean free path, growing experimental evidence indicates that they become insufficient under extreme confinement. This review discusses the crossover from classical scattering to a quantum-confinement regime in which the electronic states available for transport are fundamentally restructured by finite size. We review the recently proposed reciprocal-space confinement theory, which predicts an exponential increase of resistivity with decreasing thickness at the nanoscale, and discuss how it can be combined with classical surface-scattering models to provide a unified description of ultra-thin metallic and semiconducting films. Finally, we summarize recent experimental evidence supporting this picture and discuss its implications for future nanoelectronic devices, nanoscale interconnects, and quantum transport under extreme spatial confinement.

David K. Ferry, Mihail Nedjalkov

Maximilian Streitberger, Marko J. Rančić

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.