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

Digest - IEEE Antennas and Propagation Society. International Symposium

Derivation of a Semiclassical Model for a Transmon Capacitively Coupled to a Transmission Line

Thomas E. Roth

Published Jul 10, 2022• 3 citations
Publisher

Abstract

Accurately controlling the state of a transmon qubit via applied microwave pulses is essential in successfully running quantum computers that use these qubits. Currently, control pulses are designed using classical simulations of time-dependent quantum systems that neglect any back-action of the transmon on the transmission lines that deliver the microwaves. In this work, we develop a semiclassical model for a transmon capacitively coupled to a transmission line that treats the transmon quantum mechanically and the transmission line classically. This model can be used in the future to study the detailed interactions of microwave control pulses with transmon qubits to better optimize the control pulses. We show results from a classical model of this system to highlight that the back-action of the transmon may not be negligible for common experimental parameters, emphasizing the need for more rigorous models as experimental parameters are changed to accommodate scaling in device density.

DOI
10.1109/ap-s/usnc-ursi47032.2022.9886800

Related papers

Toward a Fully-Coupled Semiclassical Model of Transmon Control Dynamics: Classical Case

Samuel T. Elkin, Thomas E. Roth

In superconducting circuit quantum systems, transmon qubits are typically controlled through applying classical microwave pulses on a transmission line capacitively coupled to the qubit. In order to design a pulse that achieves the desired result, modeling the coupled dynamics of the transmission line and transmon is necessary. Existing models consider the dynamics of both portions of the system, but often fail to account for effects such as the back-action of each subsystem on the other. This work begins to study this effect using a 1-D finite element time-domain solution to the equations governing the transmission line flux and transmon phase in a fully classical treatment, which will be extended to a full-wave semiclassical model in a future work.

Digest - IEEE Antennas and Propagation Society. International Symposium•Jul 10, 2022•0 citations

Maxwell-Schrödinger Modeling of Superconducting Qubits Coupled to Transmission Line Networks

Thomas E. Roth, Samuel T. Elkin

In superconducting circuit quantum information technologies, classical microwave pulses are applied to control and measure the qubit states. Currently, the design of these microwave pulses use simple theoretical or numerical models that do not account for the self-consistent interactions of how the qubit state modifies the applied microwave pulse. In this work, we present the formulation and finite element time domain discretization of a semiclassical Maxwell-Schrödinger method for describing these self-consistent dynamics for the case of a superconducting qubit capacitively coupled to a general transmission line network. We validate the proposed method by characterizing key effects related to common control and measurement approaches for transmon and fluxonium qubits in systems that are amenable to theoretical analysis. Our numerical results also highlight scenarios where including the self-consistent interactions are essential. By treating the microwaves classically, our method is substantially more efficient than fully-quantum methods for the many situations where the quantum statistics of the microwaves are not needed. Further, our approach does not require any reformulations when the transmission line system is modified. In the future, our method can be used to rapidly explore broader design spaces to search for more effective control and measurement protocols for superconducting qubits.

arXiv:2210.07923•Oct 14, 2022•0 citations

Maxwell-Schrödinger Hybrid Simulation for Analyzing Control and Readout of Transmon Qubits

Thomas E. Roth, Samuel T. Elkin

The control and readout of a transmon qubit through applied microwave pulses is a key capability in operating many quantum technologies. Currently, the design of microwave pulses for these purposes is done through simple theoretical or numerical models that do not account for how the transmon modifies the applied microwave field. In this work, we present the formulation and discretization of a self-consistent semiclassical model that solves the Schrödinger equation describing qubit dynamics in tandem with a one-dimensional wave equation describing transmission line dynamics. Numerical results are presented using this Maxwell-Schrödinger method to characterize the control and readout of a transmon qubit. We show that our method matches simple theoretical predictions in relevant operating regimes and also look at situations where simplified models break down. In the future, our method can be used to explore these broader operating regimes to search for more effective control and readout protocols.

European Conference on Antennas and Propagation•Mar 26, 2023•1 citation

Maxwell-Schrödinger Modeling of a Superconducting Qubit Coupled to a Transmission Line Network

Thomas E. Roth, Samuel T. Elkin

In superconducting circuit quantum information technologies, classical microwave pulses are applied to control and measure the qubit states. Currently, the design of these microwave pulses uses simple theoretical or numerical models that do not account for the self-consistent interactions of how the qubit state modifies the applied microwave pulse. In this work, we present the formulation and finite element time domain discretization of a semiclassical Maxwell-Schrödinger method for describing these self-consistent dynamics for the case of a superconducting qubit capacitively coupled to a general transmission line network. We validate the proposed method by characterizing key effects related to common control and measurement approaches for transmon and fluxonium qubits in systems that are amenable to theoretical analysis. Our numerical results also highlight scenarios where including the self-consistent interactions is essential. By treating the microwaves classically, our method is substantially more efficient than fully-quantum methods for the many situations where the quantum statistics of the microwaves are not needed. Further, our approach does not require any reformulations when the transmission line system is modified. In the future, our method can be used to rapidly explore broader design spaces to search for more effective control and measurement protocols for superconducting qubits.

IEEE journal on multiscale and multiphysics computational techniques•Jan 1, 2024•12 citations

Hybrid 1D Maxwell-Schrödinger Modeling of Dispersive Regime Effects of a Transmon Qubit

Thomas E. Roth

Transmon qubits integrated into microwave circuitry are a leading quantum computing architecture. However, significant engineering improvements are still needed. General-purpose numerical methods are becoming of interest to tackle these challenges, but existing fully-quantum methods are highly inefficient. In this work, we formulate a semiclassical Maxwell-Schrödinger model as an alternative approach to efficiently analyze the interactions of transmons capacitively coupled to transmission line networks. Additionally, we present a suitable discretization and time marching strategy. We validate our approach by comparing it to theoretical models relevant to the dispersive operating regime used in most hardware implementations. Our results show that our method can accurately predict effects related to transmon state measurements that are typically derived using fully-quantum models. In the future, our approach can be used to rapidly explore broader design spaces to improve the speed and fidelity of qubit state measurements, which is a key obstacle toward achieving fault-tolerant quantum computation.

URSI International Symposium on Electromagnetic Theory•May 22, 2023•0 citations

Finite Element Time Domain Discretization of a Semiclassical Maxwell-Schrödinger Model of a Transmon Qubit

Thomas E. Roth

In superconducting circuit quantum computers, classical microwave pulses are used to control and measure the state of the qubits. The design of microwave pulses for these purposes typically use simple theoretical or numerical models that do not account for the self-consistent interactions of how the presence of the transmon modifies the applied microwave field. In this work, we present the formulation and finite element time domain discretization of a semiclassical Maxwell-Schrödinger model that can self-consistently characterize the interactions between a transmon and classical microwave pulses. Our numerical results demonstrate the validity of this approach for describing the central effects related to the control and measurement of the state of a transmon. In the future, our numerical method can be used to efficiently investigate a wider range of operating regimes than existing approaches are valid for to search for more effective control and measurement protocols.

IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization•Jun 28, 2023•5 citations
Accurately controlling the state of a transmon qubit via applied microwave pulses is essential in successfully running quantum computers that use these qubits. Currently, control pulses are designed using classical simulations of time-dependent quantum systems that neglect any back-action of the transmon on the transmission lines that deliver the microwaves. In this work, we develop a semiclassical model for a transmon capacitively coupled to a transmission line that treats the transmon quantum mechanically and the transmission line classically. This model can be used in the future to study the detailed interactions of microwave control pulses with transmon qubits to better optimize the control pulses. We show results from a classical model of this system to highlight that the back-action of the transmon may not be negligible for common experimental parameters, emphasizing the need for more rigorous models as experimental parameters are changed to accommodate scaling in device density.
In superconducting circuit quantum systems, transmon qubits are typically controlled through applying classical microwave pulses on a transmission line capacitively coupled to the qubit. In order to design a pulse that achieves the desired result, modeling the coupled dynamics of the transmission line and transmon is necessary. Existing models consider the dynamics of both portions of the system, but often fail to account for effects such as the back-action of each subsystem on the other. This work begins to study this effect using a 1-D finite element time-domain solution to the equations governing the transmission line flux and transmon phase in a fully classical treatment, which will be extended to a full-wave semiclassical model in a future work.
In superconducting circuit quantum information technologies, classical microwave pulses are applied to control and measure the qubit states. Currently, the design of these microwave pulses use simple theoretical or numerical models that do not account for the self-consistent interactions of how the qubit state modifies the applied microwave pulse. In this work, we present the formulation and finite element time domain discretization of a semiclassical Maxwell-Schrödinger method for describing these self-consistent dynamics for the case of a superconducting qubit capacitively coupled to a general transmission line network. We validate the proposed method by characterizing key effects related to common control and measurement approaches for transmon and fluxonium qubits in systems that are amenable to theoretical analysis. Our numerical results also highlight scenarios where including the self-consistent interactions are essential. By treating the microwaves classically, our method is substantially more efficient than fully-quantum methods for the many situations where the quantum statistics of the microwaves are not needed. Further, our approach does not require any reformulations when the transmission line system is modified. In the future, our method can be used to rapidly explore broader design spaces to search for more effective control and measurement protocols for superconducting qubits.
The control and readout of a transmon qubit through applied microwave pulses is a key capability in operating many quantum technologies. Currently, the design of microwave pulses for these purposes is done through simple theoretical or numerical models that do not account for how the transmon modifies the applied microwave field. In this work, we present the formulation and discretization of a self-consistent semiclassical model that solves the Schrödinger equation describing qubit dynamics in tandem with a one-dimensional wave equation describing transmission line dynamics. Numerical results are presented using this Maxwell-Schrödinger method to characterize the control and readout of a transmon qubit. We show that our method matches simple theoretical predictions in relevant operating regimes and also look at situations where simplified models break down. In the future, our method can be used to explore these broader operating regimes to search for more effective control and readout protocols.
In superconducting circuit quantum information technologies, classical microwave pulses are applied to control and measure the qubit states. Currently, the design of these microwave pulses uses simple theoretical or numerical models that do not account for the self-consistent interactions of how the qubit state modifies the applied microwave pulse. In this work, we present the formulation and finite element time domain discretization of a semiclassical Maxwell-Schrödinger method for describing these self-consistent dynamics for the case of a superconducting qubit capacitively coupled to a general transmission line network. We validate the proposed method by characterizing key effects related to common control and measurement approaches for transmon and fluxonium qubits in systems that are amenable to theoretical analysis. Our numerical results also highlight scenarios where including the self-consistent interactions is essential. By treating the microwaves classically, our method is substantially more efficient than fully-quantum methods for the many situations where the quantum statistics of the microwaves are not needed. Further, our approach does not require any reformulations when the transmission line system is modified. In the future, our method can be used to rapidly explore broader design spaces to search for more effective control and measurement protocols for superconducting qubits.
Transmon qubits integrated into microwave circuitry are a leading quantum computing architecture. However, significant engineering improvements are still needed. General-purpose numerical methods are becoming of interest to tackle these challenges, but existing fully-quantum methods are highly inefficient. In this work, we formulate a semiclassical Maxwell-Schrödinger model as an alternative approach to efficiently analyze the interactions of transmons capacitively coupled to transmission line networks. Additionally, we present a suitable discretization and time marching strategy. We validate our approach by comparing it to theoretical models relevant to the dispersive operating regime used in most hardware implementations. Our results show that our method can accurately predict effects related to transmon state measurements that are typically derived using fully-quantum models. In the future, our approach can be used to rapidly explore broader design spaces to improve the speed and fidelity of qubit state measurements, which is a key obstacle toward achieving fault-tolerant quantum computation.
In superconducting circuit quantum computers, classical microwave pulses are used to control and measure the state of the qubits. The design of microwave pulses for these purposes typically use simple theoretical or numerical models that do not account for the self-consistent interactions of how the presence of the transmon modifies the applied microwave field. In this work, we present the formulation and finite element time domain discretization of a semiclassical Maxwell-Schrödinger model that can self-consistently characterize the interactions between a transmon and classical microwave pulses. Our numerical results demonstrate the validity of this approach for describing the central effects related to the control and measurement of the state of a transmon. In the future, our numerical method can be used to efficiently investigate a wider range of operating regimes than existing approaches are valid for to search for more effective control and measurement protocols.