Electromagnetic simulation of superconducting qubit–resonator coupling

The precise engineering of electromagnetic couplings is paramount for constructing scalable and high-fidelity 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 ( $\kappa$ ) 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.The precise engineering of electromagnetic couplings is paramount for constructing scalable and high-fidelity 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 ($\kappa$) 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.

arXiv:2405.11426IEEE Transactions on Applied SuperconductivityFeb 17, 20263 citations

Coupling superconducting qubits and resonators

Joel Strand

Bulletin of the American Physical SocietyFeb 29, 20120 citations

Resonator-based superconducting qubit

Ivan N. Zhilyaev

Russian MicroelectronicsNov 1, 20050 citations

Coupling Superconducting Qubits to Electromagnetic and Piezomechanical Resonators

Andrew N. Cleland

Quantum bits have been under intense development since the late 1990s, due to the discovery of a number of potential applications for engineered quantum systems to problems in computation or communication. As superconducting circuits provide a straightforward path to scaling up to large numbers of qubits and are exible in terms of their application to a range of different problems, This chapter focuses on the problem of coupling superconducting qubits to other systems, in particular to microwave frequency electromagnetic resonators as well as mechanical resonators. It begins by introducing the topics of piezoelectricity and its role in solid mechanics, then turns to a description of one flavour of superconducting qubit, the phase qubit. It then describes how the phase qubit can be used to control and measure a superconducting electromagnetic resonator, and concludes by describing how a phase qubit can also be used to control and measure a piezomechanical resonator.Quantum bits have been under intense development since the late 1990s, due to the discovery of a number of potential applications for engineered quantum systems to problems in computation or communication. As superconducting circuits provide a straightforward path to scaling up to large numbers of qubits and are exible in terms of their application to a range of different problems, This chapter focuses on the problem of coupling superconducting qubits to other systems, in particular to microwave frequency electromagnetic resonators as well as mechanical resonators. It begins by introducing the topics of piezoelectricity and its role in solid mechanics, then turns to a description of one flavour of superconducting qubit, the phase qubit. It then describes how the phase qubit can be used to control and measure a superconducting electromagnetic resonator, and concludes by describing how a phase qubit can also be used to control and measure a piezomechanical resonator.

Oxford University Press eBooksMar 5, 20200 citations

Modeling and design of flip-chip packaging in superconducting qubit processors

Liang Zhou, Keqin Chen

This study primarily investigates variations in the radio-frequency (RF) performance characteristics of components within flip-chip packaged superconducting qubit chips. By comparing changes in the lumped-element parameters of identical qubit chip physical structures across different packaging architectures, we analyze the evolving trends in the qubits' energy dissipation models and nonlinear parameters. Simulation and numerical computation results reveal that the metal layers proximal to the chip surface and the microbumps within the flip-chip architecture significantly impact structural parameters such as the resonant frequency and self-capacitance of resonant elements (including the qubits and readout cavities). This influence manifests as an increase in self-capacitance, consequently leading to an overall decrease in resonant frequency. Furthermore, structures such as the XY/Z control lines and the qubit-readout cavity coupling elements exhibit coupling strength of different change trends due to the altered electromagnetic field distribution within the packaging structure. Additionally, the direction of electromagnetic field leakage during coupling undergoes a change.This study primarily investigates variations in the radio-frequency (RF) performance characteristics of components within flip-chip packaged superconducting qubit chips. By comparing changes in the lumped-element parameters of identical qubit chip physical structures across different packaging architectures, we analyze the evolving trends in the qubits' energy dissipation models and nonlinear parameters. Simulation and numerical computation results reveal that the metal layers proximal to the chip surface and the microbumps within the flip-chip architecture significantly impact structural parameters such as the resonant frequency and self-capacitance of resonant elements (including the qubits and readout cavities). This influence manifests as an increase in self-capacitance, consequently leading to an overall decrease in resonant frequency. Furthermore, structures such as the XY/Z control lines and the qubit-readout cavity coupling elements exhibit coupling strength of different change trends due to the altered electromagnetic field distribution within the packaging structure. Additionally, the direction of electromagnetic field leakage during coupling undergoes a change.

Sixth Symposium on Novel Optoelectronic Detection Technology and ApplicationsMay 11, 20260 citations

Phase versus flux coupling between resonator and superconducting flux qubit

Jeffrey Birenbaum, Sean R. O’Kelley, S.M. Anton +11 more

Bulletin of the American Physical SocietyMar 21, 20130 citations

\kappa

) 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.