On the electromagnetic couplings in superconducting qubit circuits

TL;DR

This paper develops a comprehensive theoretical framework for understanding and modeling electromagnetic couplings in superconducting qubit circuits, addressing design challenges and providing tools for improved quantum hardware development.

Contribution

It introduces a unified theoretical approach from first principles for electromagnetic couplings in superconducting circuits, linking formalism to practical parameter extraction methods.

Findings

Formulated equations of motion for coupled resonators and transmission lines.

Reviewed definitions of key parameters like decay rate and coupling coefficient.

Connected theoretical parameters to electromagnetic simulation techniques.

Abstract

The precise engineering of electromagnetic couplings is paramount for constructing scalable and highfidelity superconducting quantum processors. While essential for orchestrating qubit operations, these couplings also present significant design challenges, including the mitigation of crosstalk and the management of environmental decoherence. A clear and unified theoretical framework is therefore crucial for the design, simulation, and analysis of these complex quantum circuits. This paper presents a comprehensive theoretical treatment of the fundamental electromagnetic coupling mechanisms in superconducting devices. Starting from first principles, we formulate the equations of motion and derive the input-output relations for canonical systems, including a single resonator coupled to a multi-port microwave network, interacting resonators, and coupled transmission lines. We review rigorous definitions for key parameters such as the energy decay rate (\k{appa}) and the dimensionless coupling coefficient ({\zeta}) and connect these formalisms to practical methods of parameter extraction from electromagnetic simulations. This work provides a rigorous and pedagogical foundation for understanding and modeling linear electromagnetic interactions, serving as a vital resource for the development of advanced superconducting quantum hardware.