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arXiv:2408.17293 · IEEE Transactions on Applied Superconductivity

Modeling Flux Tunability in Josephson Traveling Wave Parameteric Amplifiers With an Open-Source Frequency-Domain Simulator

Anna Levochkina, I. Chatterjee, Pegah Darvehi, Halima Giovanna Ahmad, P. Mastrovito, D. Massarotti, Domenico Montemurro, Francesco Tafuri, Giovanni Piero Pepe, Kevin P. O’Brien, Martina Esposito

Published Mar 18, 2025• 3 citations
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Abstract

Josephson traveling wave parameteric amplifiers (JTWPAs) are integral parts of many experiments carried out in quantum technologies. Being composed of hundreds of Josephson junction-based unit cells, such devices exhibit complex nonlinear behavior that typically cannot be fully explained with simple analytical models, thus necessitating the use of numerical simulators. A very useful characteristic of JTWPAs is the possibility of being biased by an external magnetic flux, allowing in-situ control of the nonlinearity. It is, therefore, very desirable for numerical simulators to support this feature. Open-source numerical tools that allow to model JTWPA flux biasing, such asWRSPICEorPSCAN2, are based on time-domain approaches, which typically require long simulation times to get accurate results. In this work, we model the gain performance in a prototypical flux-tunable JTWPA by usingJosephsonCircuits.jl, a recently developed frequency-domain open-source numerical simulator, which has the benefit of simulation times about 10 000 faster than time-domain methods. By comparing the numerical and experimental results, we validate this approach for modeling the flux dependent behavior of JTWPAs.

DOI
10.1109/tasc.2025.3552432

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Josephson traveling wave parameteric amplifiers (JTWPAs) are integral parts of many experiments carried out in quantum technologies. Being composed of hundreds of Josephson junction-based unit cells, such devices exhibit complex nonlinear behavior that typically cannot be fully explained with simple analytical models, thus necessitating the use of numerical simulators. A very useful characteristic of JTWPAs is the possibility of being biased by an external magnetic flux, allowing in-situ control of the nonlinearity. It is, therefore, very desirable for numerical simulators to support this feature. Open-source numerical tools that allow to model JTWPA flux biasing, such asWRSPICEorPSCAN2, are based on time-domain approaches, which typically require long simulation times to get accurate results. In this work, we model the gain performance in a prototypical flux-tunable JTWPA by usingJosephsonCircuits.jl, a recently developed frequency-domain open-source numerical simulator, which has the benefit of simulation times about 10 000 faster than time-domain methods. By comparing the numerical and experimental results, we validate this approach for modeling the flux dependent behavior of JTWPAs.
Josephson Traveling Wave Parametric Amplifiers (JTWPAs) are largely exploited in quantum technologies for their broadband and low noise performance in the microwave regime. When one or more microwave tones are applied at the input, such devices show a complex wave-mixing response due to their intrinsic nonlinear nature. Numerical simulations of the JTWPAs nonlinear behaviour provide useful insights not only for the design of such devices, but also for the interpretation and validation of the experimental results. Here we present and discuss a comparative analysis of different open-source tools which can be used for JTWPAs numerical simulations. We focus on two tools for transient simulations, WRSPICE and PSCAN2, and on one tool for direct simulation of the frequency domain behaviour, JosephsonCircuit.jl. We describe the working principle of these three tools and test them considering as a benchmark a JTWPA based on SNAILs (Superconducting Nonlinear Asymmetric Inductive eLement) with realistic experimental parameters. Our results can serve as a guide for numerical simulations of JTWPAs with open-source tools, highlighting advantages and disadvantages depending on the simulation tasks.
Abstract A Josephson traveling-wave parametric amplifier (JTWPA) is indispensable for the high-fidelity readout of superconducting qubits, owing to its broadband gain and near-quantum-limited noise performance. Conventional JTWPAs implemented with 0-Josephson junctions (0-JTWPAs) avoid magnetic-flux bias but rely on Kerr nonlinearity, which leads to pump-power-dependent phase mismatch, gain ripple, and a limited dynamic range. More recently, three-wave-mixing (3WM) JTWPAs employing flux-biased rf-SQUIDs have been proposed to suppress Kerr effects. However, these designs require a significant external flux bias per unit cell, which complicates cryogenic hardware, introduces sensitivity to flux noise, and limits scalability in large arrays. In this study, we propose and analyze a π -junction-based JTWPA ( π -JTWPA) in which the intrinsic π phase shift of the junction effectively displaces the operating point of the current–phase relation. This approach aims to realize 3WM-type nonlinearity with reduced flux bias while preserving broadband amplification, thereby simplifying flux-bias distribution, enhancing robustness against flux noise, and providing a pathway toward scalable, multiplexed quantum readout architectures. In addition, we examine the potential applicability of the π -JTWPA in four-wave-mixing (4WM) operation.
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.
Optimizing the performance of cryogenic quantum amplifiers is a key step toward achieving high-fidelity and scalable qubit readout. In this work, we present efficient and accurate modeling of a Josephson traveling-wave parametric amplifier (JTWPA) based on electromagnetic (EM) and circuit co-simulation. In contrast to conventional simulation methods where an equivalent lumped-element circuit model of the JTWPA is required, we directly perform full EM analysis of the device to faithfully determine the linear response. The extracted S-parameters are then fed into a nonlinear harmonic balance simulator with Josephson junctions represented as circuit elements. The simulated linear and gain properties are compared with experimental results and show good agreement.