Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2406.04351

Efficiently Building and Characterizing Electromagnetic Models of Multi-Qubit Superconducting Circuits

Fadi Wassaf

Published May 13, 2024• 0 citations
arXivHTMLPDF

Abstract

In an attempt to better leverage superconducting quantum computers, scaling efforts have become the central concern. These efforts have been further exacerbated by the increased complexity of these circuits. The added complexity can introduce parasitic couplings and resonances, which may hinder the overall performance and scalability of these devices. We explore a method of modeling and characterization based on multiport impedance functions that correspond to multi-qubit circuits. By combining vector fitting techniques with a novel method for interconnecting rational impedance functions, we are able to efficiently construct Hamiltonians for multi-qubit circuits using electromagnetic simulations. Our methods can also be applied to circuits that contain both lumped and distributed element components. The constructed Hamiltonians account for all the interactions within a circuit that are described by the impedance function. We then present characterization methods that allow us to estimate effective qubit coupling rates, state-dependent dispersive shifts of resonant modes, and qubit relaxation times.

DOI
10.48550/arxiv.2406.04351

Related papers

Simple Impedance Response Formulas for the Dispersive Interaction Rates in the Effective Hamiltonians of Low Anharmonicity Superconducting Qubits

Firat Solgun, David Peter Divincenzo, Jay Gambetta

For superconducting quantum processors consisting of low anharmonicity qubits such as transmons, we give a complete microwave description of the system in the qubit subspace. We assume that the qubits are dispersively coupled to a distributed microwave structure such that the detunings of the qubits from the internal modes of the microwave structure are stronger than their couplings. We define "qubit ports" across the terminals of the Josephson junctions and "drive ports" where transmission lines carrying drive signals reach the chip and we obtain the multiport impedance response of the linear passive part of the system between the ports. We then relate interaction parameters in between qubits and between the qubits and the environment to the entries of this multiport impedance function; in particular, we show that the exchange coupling rate J between qubits is related in a simple way to the off-diagonal entry connecting the qubit ports. Similarly, we relate couplings of the qubits to voltage drives and lossy environment to the entries connecting the qubits and the drive ports. Our treatment takes into account all the modes (possibly infinite) that might be present in the distributed electromagnetic structure and provides an efficient method for the modeling and analysis of the circuits.

•Jan 1, 2019•24 citations

Analysis and Synthesis of Multi-Qubit, Multi-Mode Quantum Devices

Firat Solgun, Guido Burkard, David Peter Divincenzo

In this thesis we propose new methods in multi-qubit multi-mode circuit quantum electrodynamics (circuit-QED) architectures. In Chapter 2 we describe a direct parity measurement method for three qubits, which can be realized in 2D circuit-QED with a possible extension to four qubits in a 3D circuit-QED setup for the implementation of the surface code. In Chapter 3 we show how to derive Hamiltonians and compute relaxation rates of the multi-mode superconducting microwave circuits consisting of single Josephson junctions using an exact impedance synthesis technique (the Brune synthesis) and applying previous formalisms for lumped element circuit quantization. In the rest of the thesis we extend our method in Chapter 3 to multi-junction (multi-qubit) multi-mode circuits through the use of state-space descriptions which allows us to quantize any multiport microwave superconducting circuit with a reciprocal lossy impedance response.

•Jan 1, 2015•1 citation

Simple Impedance Response Formulas for the Dispersive Interaction Rates in the Effective Hamiltonians of Low Anharmonicity Superconducting Qubits

Firat Solgun, David Peter Divincenzo, Jay M. Gambetta

For superconducting quantum processors consisting of low anharmonicity qubits such as transmons, we give a complete microwave description of the system in the qubit subspace. We assume that the qubits are dispersively coupled to a distributed microwave structure such that the detunings of the qubits from the internal modes of the microwave structure are stronger than their couplings. We define “qubit ports” across the terminals of the Josephson junctions and “drive ports” where transmission lines carrying drive signals reach the chip and we obtain the multiport impedance response of the linear passive part of the system between the ports. We then relate interaction parameters in between qubits and between the qubits and the environment to the entries of this multiport impedance function; in particular, we show that the exchange coupling rate J between qubits is related in a simple way to the off-diagonal entry connecting the qubit ports. Similarly, we relate couplings of the qubits to voltage drives and lossy environment to the entries connecting the qubits and the drive ports. Our treatment takes into account all the modes (possibly infinite) that might be present in the distributed electromagnetic structure and provides an efficient method for the modeling and analysis of the circuits.

arXiv:1712.08154•IEEE Transactions on Microwave Theory and Techniques•Feb 4, 2019•36 citations

MACROSCOPIC QED FORMALISM FOR EVALUATING TRANSMON EXCHANGE COUPLING RATE IN PRACTICAL DEVICES

Ghazi Khan

Superconducting qubits are one of the leading platforms for creating practical quantum computers. However, these architectures face significant engineering challenges as they scale up and move towards devices capable of error correction. To aid these efforts, three-dimensional (3D) full-wave computational electromagnetics tools are increasingly being utilized to characterize these devices; however, standard approaches relying on eigenmode solvers are often computationally prohibitive and lack the scalability required to analyse devices beyond a few qubits. To overcome these limitations, this thesis introduces an efficient, alternative modeling framework for superconducting circuits, applied specifically to the evaluation of the qubit-qubit exchange coupling rate in transmon architectures. This coupling rate is a key design parameter that governs the entanglement speed for multi-qubit gates and influences error channels such as qubit crosstalk. Leveraging a field-based formalism within the broader context of macroscopic quantum electrodynamics, we establish that the exchange coupling rate is directly related to the electromagnetic dyadic Green’s function. We then map the imaginary part of the Green’s function to the system’s classical impedance response. Since the impedance response can be evaluated quickly and accurately in standard full-wave solvers, this new formulation provides a scalable way to characterize large-scale superconducting devices. We validate this framework by simulating four practical multi-qubit circuits, benchmarking the extracted coupling rates against both 3D numerical diagonalization methods and experimental data. We also demonstrate how the exchange coupling rate impacts qubit crosstalk, and characterize a multi-coupler device to find operational sweet spots, where the crosstalk is minimized while maintaining strong enough qubit-qubit coupling to enable fast multi-qubit gates. We then conclude this thesis and outline some plans for future work.

•Jul 23, 2026•0 citations

Field-based formalism for calculating multiqubit exchange-coupling rates for transmon qubits

Ghazi Khan, Thomas E. Roth

Superconducting qubits are one of the most mature platforms for achieving practical quantum computers, but significant performance improvements are still needed. To improve the engineering of these systems, three-dimensional (3D) full-wave computational electromagnetics analyses are increasingly being turned to. Unfortunately, existing analysis approaches often rely on full-wave simulations using eigenmode solvers that are typically cumbersome, not robust, and computationally prohibitive if devices with more than a few qubits are to be analyzed. To improve the characterization of superconducting circuits while circumventing these drawbacks, this work begins the development of an alternative modeling framework that we illustrate in the context of evaluating the qubit-qubit exchange coupling rate between transmon qubits. This quantity is a key design parameter that determines the entanglement rate for fast multiqubit gate performance and also affects decoherence sources like qubit crosstalk. Our modeling framework uses a field-based formalism in the context of macroscopic quantum electrodynamics, which we use to show that the qubit-qubit exchange coupling rate can be related to the electromagnetic dyadic Green's function linking the qubits together. We further show how the needed quantity involving the dyadic Green's function can be related to the impedance response of the system that can be easily and efficiently computed with classical computational electromagnetics tools. We demonstrate the validity and efficacy of this approach by simulating four practical multiqubit superconducting circuits and evaluating their qubit-qubit exchange coupling rates. We validate our results against a 3D numerical diagonalization method and against experimental data where available. We also demonstrate the impact of the qubit-qubit exchange coupling rate on qubit crosstalk by simulating a multicoupler device and identifying operating points where the qubit crosstalk becomes zero.

arXiv:2406.05473•Physical Review Applied•Dec 23, 2024•6 citations

Incorporating multi-qubit exchange coupling effects between transmon qubits in Maxwell-Schrödinger numerical methods

Ghazi Khan, Thomas E. Roth

Superconducting qubits have emerged as a leading platform for realizing quantum computers. Accurate modeling of these devices is essential for predicting performance, improving design, and optimizing control. Many modeling approaches currently rely on lumped circuit approximations or other simplified treatments that can be limited in resolving the interplay between the qubit dynamics and the electromagnetic circuitry, leading to significant experimental deviations from numerical predictions at times. To address many of these limitations, methods that self-consistently solve the Schrödinger equation for qubit dynamics with the classical Maxwell's equations have been developed and shown to accurately predict a wide range of effects related to superconducting qubit control and readout. Despite these successes, these methods have not been able to consider multi-qubit effects that give rise to qubit-qubit entanglement. Here, we address this by rigorously deriving how multi-qubit coupling effects between transmon qubits can be embedded into Maxwell-Schrödinger methods. To support this, we build on earlier first-principles derivations of Maxwell-Schrödinger methods for the specific case of two transmon qubits coupled together through a common electromagnetic system in the dispersive regime. To aid in validating aspects of the Maxwell-Schrödinger framework, we also provide a new interpretation of Maxwell-Schrödinger methods as an efficient simulation strategy to capture the class of non-Markovian open quantum system dynamics. Our results demonstrate that these effects can give rise to strong classical crosstalk that can significantly alter multi-qubit dynamics, which we demonstrate for the cross-resonance gate. These classical crosstalk effects have been noted in cross-resonance experiments, but previous quantum theory and device analysis could not explain their origin.

quant-pharXiv:2512.24448•Jan 1, 2026•0 citations
In an attempt to better leverage superconducting quantum computers, scaling efforts have become the central concern. These efforts have been further exacerbated by the increased complexity of these circuits. The added complexity can introduce parasitic couplings and resonances, which may hinder the overall performance and scalability of these devices. We explore a method of modeling and characterization based on multiport impedance functions that correspond to multi-qubit circuits. By combining vector fitting techniques with a novel method for interconnecting rational impedance functions, we are able to efficiently construct Hamiltonians for multi-qubit circuits using electromagnetic simulations. Our methods can also be applied to circuits that contain both lumped and distributed element components. The constructed Hamiltonians account for all the interactions within a circuit that are described by the impedance function. We then present characterization methods that allow us to estimate effective qubit coupling rates, state-dependent dispersive shifts of resonant modes, and qubit relaxation times.
For superconducting quantum processors consisting of low anharmonicity qubits such as transmons, we give a complete microwave description of the system in the qubit subspace. We assume that the qubits are dispersively coupled to a distributed microwave structure such that the detunings of the qubits from the internal modes of the microwave structure are stronger than their couplings. We define "qubit ports" across the terminals of the Josephson junctions and "drive ports" where transmission lines carrying drive signals reach the chip and we obtain the multiport impedance response of the linear passive part of the system between the ports. We then relate interaction parameters in between qubits and between the qubits and the environment to the entries of this multiport impedance function; in particular, we show that the exchange coupling rate J between qubits is related in a simple way to the off-diagonal entry connecting the qubit ports. Similarly, we relate couplings of the qubits to voltage drives and lossy environment to the entries connecting the qubits and the drive ports. Our treatment takes into account all the modes (possibly infinite) that might be present in the distributed electromagnetic structure and provides an efficient method for the modeling and analysis of the circuits.
In this thesis we propose new methods in multi-qubit multi-mode circuit quantum electrodynamics (circuit-QED) architectures. In Chapter 2 we describe a direct parity measurement method for three qubits, which can be realized in 2D circuit-QED with a possible extension to four qubits in a 3D circuit-QED setup for the implementation of the surface code. In Chapter 3 we show how to derive Hamiltonians and compute relaxation rates of the multi-mode superconducting microwave circuits consisting of single Josephson junctions using an exact impedance synthesis technique (the Brune synthesis) and applying previous formalisms for lumped element circuit quantization. In the rest of the thesis we extend our method in Chapter 3 to multi-junction (multi-qubit) multi-mode circuits through the use of state-space descriptions which allows us to quantize any multiport microwave superconducting circuit with a reciprocal lossy impedance response.
For superconducting quantum processors consisting of low anharmonicity qubits such as transmons, we give a complete microwave description of the system in the qubit subspace. We assume that the qubits are dispersively coupled to a distributed microwave structure such that the detunings of the qubits from the internal modes of the microwave structure are stronger than their couplings. We define “qubit ports” across the terminals of the Josephson junctions and “drive ports” where transmission lines carrying drive signals reach the chip and we obtain the multiport impedance response of the linear passive part of the system between the ports. We then relate interaction parameters in between qubits and between the qubits and the environment to the entries of this multiport impedance function; in particular, we show that the exchange coupling rate J between qubits is related in a simple way to the off-diagonal entry connecting the qubit ports. Similarly, we relate couplings of the qubits to voltage drives and lossy environment to the entries connecting the qubits and the drive ports. Our treatment takes into account all the modes (possibly infinite) that might be present in the distributed electromagnetic structure and provides an efficient method for the modeling and analysis of the circuits.
Superconducting qubits are one of the leading platforms for creating practical quantum computers. However, these architectures face significant engineering challenges as they scale up and move towards devices capable of error correction. To aid these efforts, three-dimensional (3D) full-wave computational electromagnetics tools are increasingly being utilized to characterize these devices; however, standard approaches relying on eigenmode solvers are often computationally prohibitive and lack the scalability required to analyse devices beyond a few qubits. To overcome these limitations, this thesis introduces an efficient, alternative modeling framework for superconducting circuits, applied specifically to the evaluation of the qubit-qubit exchange coupling rate in transmon architectures. This coupling rate is a key design parameter that governs the entanglement speed for multi-qubit gates and influences error channels such as qubit crosstalk. Leveraging a field-based formalism within the broader context of macroscopic quantum electrodynamics, we establish that the exchange coupling rate is directly related to the electromagnetic dyadic Green’s function. We then map the imaginary part of the Green’s function to the system’s classical impedance response. Since the impedance response can be evaluated quickly and accurately in standard full-wave solvers, this new formulation provides a scalable way to characterize large-scale superconducting devices. We validate this framework by simulating four practical multi-qubit circuits, benchmarking the extracted coupling rates against both 3D numerical diagonalization methods and experimental data. We also demonstrate how the exchange coupling rate impacts qubit crosstalk, and characterize a multi-coupler device to find operational sweet spots, where the crosstalk is minimized while maintaining strong enough qubit-qubit coupling to enable fast multi-qubit gates. We then conclude this thesis and outline some plans for future work.
Superconducting qubits are one of the most mature platforms for achieving practical quantum computers, but significant performance improvements are still needed. To improve the engineering of these systems, three-dimensional (3D) full-wave computational electromagnetics analyses are increasingly being turned to. Unfortunately, existing analysis approaches often rely on full-wave simulations using eigenmode solvers that are typically cumbersome, not robust, and computationally prohibitive if devices with more than a few qubits are to be analyzed. To improve the characterization of superconducting circuits while circumventing these drawbacks, this work begins the development of an alternative modeling framework that we illustrate in the context of evaluating the qubit-qubit exchange coupling rate between transmon qubits. This quantity is a key design parameter that determines the entanglement rate for fast multiqubit gate performance and also affects decoherence sources like qubit crosstalk. Our modeling framework uses a field-based formalism in the context of macroscopic quantum electrodynamics, which we use to show that the qubit-qubit exchange coupling rate can be related to the electromagnetic dyadic Green's function linking the qubits together. We further show how the needed quantity involving the dyadic Green's function can be related to the impedance response of the system that can be easily and efficiently computed with classical computational electromagnetics tools. We demonstrate the validity and efficacy of this approach by simulating four practical multiqubit superconducting circuits and evaluating their qubit-qubit exchange coupling rates. We validate our results against a 3D numerical diagonalization method and against experimental data where available. We also demonstrate the impact of the qubit-qubit exchange coupling rate on qubit crosstalk by simulating a multicoupler device and identifying operating points where the qubit crosstalk becomes zero.
Superconducting qubits have emerged as a leading platform for realizing quantum computers. Accurate modeling of these devices is essential for predicting performance, improving design, and optimizing control. Many modeling approaches currently rely on lumped circuit approximations or other simplified treatments that can be limited in resolving the interplay between the qubit dynamics and the electromagnetic circuitry, leading to significant experimental deviations from numerical predictions at times. To address many of these limitations, methods that self-consistently solve the Schrödinger equation for qubit dynamics with the classical Maxwell's equations have been developed and shown to accurately predict a wide range of effects related to superconducting qubit control and readout. Despite these successes, these methods have not been able to consider multi-qubit effects that give rise to qubit-qubit entanglement. Here, we address this by rigorously deriving how multi-qubit coupling effects between transmon qubits can be embedded into Maxwell-Schrödinger methods. To support this, we build on earlier first-principles derivations of Maxwell-Schrödinger methods for the specific case of two transmon qubits coupled together through a common electromagnetic system in the dispersive regime. To aid in validating aspects of the Maxwell-Schrödinger framework, we also provide a new interpretation of Maxwell-Schrödinger methods as an efficient simulation strategy to capture the class of non-Markovian open quantum system dynamics. Our results demonstrate that these effects can give rise to strong classical crosstalk that can significantly alter multi-qubit dynamics, which we demonstrate for the cross-resonance gate. These classical crosstalk effects have been noted in cross-resonance experiments, but previous quantum theory and device analysis could not explain their origin.