Predictive simulations of the dynamical response of mesoscopic devices

TL;DR

This paper presents a comprehensive simulation framework for the quantum dynamics of complex mesoscopic devices, specifically applied to quantum dots coupled with topological superconductors, incorporating noise, disorder, and Coulomb interactions.

Contribution

It introduces a novel approach combining tensor network and quantum chemistry techniques to efficiently simulate low-energy quantum dynamics in complex mesoscopic systems.

Findings

Successfully modeled dispersive gate sensing response of quantum dots with topological superconductors.

Demonstrated controlled approximations reduce computational complexity while maintaining accuracy.

Applied the framework to a realistic fermion parity readout setup.

Abstract

As the complexity of mesoscopic quantum devices increases, simulations are becoming an invaluable tool for understanding their behavior. This is especially true for the superconductor-semiconductor heterostructures used to build Majorana-based topological qubits, where quantitatively understanding the interplay of topological superconductivity, disorder, semiconductor quantum dots, Coulomb blockade and noise has been essential for progress on device design and interpretation of measurements. In this paper, we describe a general framework to simulate the low-energy quantum dynamics of such complex systems. We illustrate our approach by computing the dispersive gate sensing (DGS) response of quantum dots coupled to topological superconductors. We start by formulating the DGS response as an open-system quantum dynamics problem, which allows a consistent treatment of drive backaction as well as quantum and classical noise. For microscopic quantum problems subject to Coulomb-blockade, where a direct solution in the exponentially large many-body Hilbert space would be prohibitive, we introduce a series of controlled approximations that incorporate ideas from tensor network theory and quantum chemistry to reduce this Hilbert space to a few low-energy degrees of freedom that accurately capture the low-energy quantum dynamics. We demonstrate the methods introduced in this paper on the example of a single quantum dot coupled to a topological superconductor and a microscopic realization of the fermion parity readout setup of Aghaee et al. arXiv:2401.09549 (2024).