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Digest - IEEE Antennas and Propagation Society. International Symposium

Hybrid Numerical Modeling Method for Josephson Traveling Wave Parametric Amplifiers

Samuel T. Elkin, Michael Haider, Thomas E. Roth

Published Jul 14, 2024• 2 citations
Publisher

Abstract

Josephson traveling wave parametric amplifiers are a leading tool for enabling readout of superconducting qubits. However, existing design tools for these devices struggle to effectively model variations in amplifier parameters, leading to inconsistencies between theoretical predictions and manufactured devices. This work develops a 1D hybrid numerical modeling approach for these devices that can easily incorporate amplifier property variations, allowing their impact to be considered in the design process. Here, the formulation of the method is introduced and validated against analytical results for a simple architecture. Future work will extend the technique to more advanced amplifier architectures, as well as develop similar methods for 3D full-wave modeling of these systems.

DOI
10.1109/ap-s/inc-usnc-ursi52054.2024.10687127

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Josephson traveling wave parametric amplifiers are a leading tool for enabling readout of superconducting qubits. However, existing design tools for these devices struggle to effectively model variations in amplifier parameters, leading to inconsistencies between theoretical predictions and manufactured devices. This work develops a 1D hybrid numerical modeling approach for these devices that can easily incorporate amplifier property variations, allowing their impact to be considered in the design process. Here, the formulation of the method is introduced and validated against analytical results for a simple architecture. Future work will extend the technique to more advanced amplifier architectures, as well as develop similar methods for 3D full-wave modeling of these systems.
Josephson traveling-wave parametric amplifiers (JTWPAs) are wideband, ultralow-noise amplifiers used to enable the readout of superconducting qubits. While individual JTWPAs have achieved high performance, behavior between devices is inconsistent due to wide manufacturing tolerances. Amplifier designs could be modified to improve resilience towards variations in amplifier components; however, existing device models often rely on analytical techniques that typically fail to incorporate component variations. To begin addressing this issue, a 1D numerical method for modeling JTWPAs is introduced in this work. The method treats the Josephson junctions and transmission lines in an amplifier as coupled subsystems and can easily incorporate arbitrary parameter variations. We discretize the transmission line subsystem with a finite element time domain method and the Josephson junction subsystem with a finite difference method, with leap-frog time marching used to evolve the system in time. We validate our method by comparing the computed gain to an analytical model for a traditional JTWPA architecture and one with resonant phase matching. We then use our method to demonstrate the impact of variations in Josephson junctions and phase-matching resonators on amplification. In future work, the method will be adjusted to incorporate additional amplifier architectures and extended to a 3D full-wave approach.
The development of large-scale superconducting quantum computers critically depends on the accurate readout of qubit states. To enable this, cryogenic parametric amplifiers have been proposed and developed, and have since found widespread use in small-signal detection applications. Among various amplifier architectures, Josephson traveling-wave parametric amplifiers (JTWPAs) are widely adopted due to their broad bandwidth, high saturation power, and compatibility with superconducting qubits. In this work, we present a design workflow of JTWPAs based on a co-simulation approach combining electromagnetic (EM) and circuit-level simulation. We apply this method to a uniform JTWPA, comparing our simulation results with experimental data. To mitigate the challenge of constructing lumped element circuit models usually used in conventional simulation method, we directly perform full EM analysis of the device to accurately determine its linear response. The extracted S parameters are then fed into a nonlinear harmonic balance simulator with Josephson junctions modeled as circuit elements. By doing so, the linear and gain properties of the JTWPA are extracted. Different factors that impact device performance including gain compression, phase matching, and fabrication imperfections are further investigated and modeled. A good agreement between simulation and measurements is identified, establishing the effectiveness of our approach in designing quantum parametric amplifiers.
Josephson traveling-wave parametric amplifiers (JTWPAs) are critical for superconducting quantum computers in enabling simultaneous high-fidelity measurements of many qubits. Despite their importance, translating designs to working hardware remains a significant obstacle, with numerical modeling increasingly being used to help close this gap. Unfortunately, existing time-domain (TD) circuit modeling methods struggle to close this gap due to their inability to model the physical layout of a device. In principle, finite-element time-domain (FETD) methods can model the JTWPA physical layout, but these simulations are complicated by the wide bandwidths and multiscale features involved. Here, we develop an unconditionally stable 1-D FETD model for JTWPAs that can model dispersive losses over wide bandwidths to begin overcoming these challenges. We validate our method against harmonic balance (HB) simulations of a Floquet-mode JTWPA before simulating a realistic multiplexed qubit readout scenario where HB is impractical.
Superconducting parametric amplifiers have great promise for quantum-limited readout of superconducting qubits and detectors. Until recently, most superconducting parametric amplifiers had been based on resonant structures, limiting their bandwidth and dynamic range. Broadband traveling-wave parametric amplifiers based both on the nonlinear kinetic inductance of superconducting thin films and on Josephson junctions are in development. By modifying the dispersion property of the amplifier circuit, referred to as dispersion engineering, the gain can be greatly enhanced and the size can be reduced. We present two theoretical frameworks for analyzing and understanding such parametric amplifiers: 1) generalized coupled-mode equations and 2) a finite difference time domain (FDTD) model combined with a small signal analysis. We show how these analytical and numerical tools may be used to understand device performance.
Superconducting traveling-wave parametric amplifiers are a key technology for high-fidelity qubit readout.Due to their quantum-limited noise performance and the ultra-lowpower signals in quantum circuits, field quantization needs to be taken into account for accurate modeling of these devices.We present a symbolic-numeric modeling approach for the analysis of Josephson traveling-wave parametric amplifiers, including resonant phase matchers.We demonstrate the capabilities of our approach by comparing the results to existing analytical models from the literature and present first results beyond the stiff pump approximation.