Quantum Networks in Divergence-free Circuit QED

TL;DR

This paper develops scalable circuit models for superconducting quantum networks coupled to environments, revealing a natural ultraviolet cutoff due to environment dressing, and applies these models to quantum simulation of multi-spin-boson systems.

Contribution

It introduces a systematic analysis of linear coupling configurations in circuit QED, highlighting an intrinsic length scale that ensures proper decoupling at high frequencies.

Findings

Identification of a natural ultraviolet cutoff length in circuit models.

Validation of models through comparison with existing analytical methods.

Application to non-perturbative quantum simulation of multi-spin-boson systems.

Abstract

Superconducting circuits are one of the leading quantum platforms for quantum technologies. With growing system complexity, it is of crucial importance to develop scalable circuit models that contain the minimum information required to predict the behaviour of the physical system. Based on microwave engineering methods, divergent and non-divergent Hamiltonian models in circuit quantum electrodynamics have been proposed to explain the dynamics of superconducting quantum networks coupled to infinite-dimensional systems, such as transmission lines and general impedance environments. Here, we study systematically common linear coupling configurations between networks and infinite-dimensional systems. The main result is that the simple Lagrangian models for these configurations present an intrinsic natural length that provides a natural ultraviolet cutoff. This length is due to the unavoidable dressing of the environment modes by the network. In this manner, the coupling parameters between their components correctly manifest their natural decoupling at high frequencies. Furthermore, we show the requirements to correctly separate infinite-dimensional coupled systems in local bases. We also compare our analytical results with other analytical and approximate methods available in the literature. Finally, we propose several applications of these general methods to analog quantum simulation of multi-spin-boson models in non-perturbative coupling regimes.