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arXiv:2509.07816 · IEEE International Conference on Quantum Computing and Engineering (QCE)

Nonlinear Co-simulation for Designing Kinetic Inductance Parametric Amplifiers

Likai Yang, Yufeng Wu, Chaofan Wang, Mingrui Xu, Hong Tang, Mohamed A. Hassan, Eric T. Holland

Published Aug 30, 2025• 1 citation
arXivHTMLPDF

Abstract

Kinetic inductance parametric amplifiers (KIPAs) have been widely studied for small-signal detection in superconducting quantum circuits. In this work, we demonstrate the modeling of a niobium nitride nanowire based KIPA using electromagnetic (EM) and circuit co-simulation, and compare the outcomes with experimental results. EM analysis is first performed on the device layout, taking into account the linear part of the kinetic inductance. The results are then integrated into a harmonic balance circuit simulator, in which the currentdependent inductance is modeled by representing the nanowire as a nonlinear inductor. Both linear and nonlinear responses of the device, including temperature-dependent resonance spectra and parametric gain, are extracted and show good agreement with experiments. We further show that when the KIPA operates as a degenerate amplifier, its phase-sensitive behavior can be accurately reproduced by the simulation. Our technique can serve as a valuable enabler for the simulation and design of quantum parametric amplifiers and superconducting kinetic inductance devices.

DOI
10.1109/qce65121.2025.00155

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Kinetic inductance parametric amplifiers (KIPAs) have been widely studied for small-signal detection in superconducting quantum circuits. In this work, we demonstrate the modeling of a niobium nitride nanowire based KIPA using electromagnetic (EM) and circuit co-simulation, and compare the outcomes with experimental results. EM analysis is first performed on the device layout, taking into account the linear part of the kinetic inductance. The results are then integrated into a harmonic balance circuit simulator, in which the currentdependent inductance is modeled by representing the nanowire as a nonlinear inductor. Both linear and nonlinear responses of the device, including temperature-dependent resonance spectra and parametric gain, are extracted and show good agreement with experiments. We further show that when the KIPA operates as a degenerate amplifier, its phase-sensitive behavior can be accurately reproduced by the simulation. Our technique can serve as a valuable enabler for the simulation and design of quantum parametric amplifiers and superconducting kinetic inductance devices.
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.
Abstract Kinetic inductance travelling wave parametric amplifiers (KI-TWPAs) have been simulated using Keysight’s Advanced Design System. A lumped element representation of a superconducting transmission line has been developed using nonlinear inductor elements to represent the current dependency of the intrinsic kinetic inductance. This provides a fast, simple and easily modifiable method for analysing the parametric processes that occur in nonlinear kinetic inductance devices, such as parametric oscillators or amplifiers while also allowing the accompanying RF network to be optimised. This methodology is used to model the behaviour of a select number of KI-TWPA designs operating in the 3-wave mixing (3WM) and 4-wave mixing (4WM) regimes. S-parameters and dispersion properties are extracted from large signal S-parameter simulations, and the gain curve of each amplifier design is generated from harmonic balance simulations. The results are compared to the gain expression from the analytic solutions of the coupled mode equations while making reference to the gain curves of the equivalent KI-TWPAs from literature.
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.
Nonlinear superconducting devices, typically based on Josephson-junction (JJ) nonlinearities, are the basis for superconducting quantum electronics, enabling, e.g., the formation of isolated two-level superconducting qubits and amplifiers. While emerging spin, hybrid spin-superconducting (including Majorana), and nanomagneto-optical quantum systems could benefit tremendously from superconducting nonlinearities, the presence of strong magnetic fields in these systems is incompatible with conventional JJ devices, which are highly sensitive to applied magnetic fields. One potential solution is the use of kinetic inductance (KI) nonlinearity. To date, only linear KI devices have been shown to operate in high magnetic fields, while nonlinear KI device operation in high magnetic fields has received virtually no attention. Here, we study the nonlinearity of superconducting nanowire (NW) KI resonators and their performance as parametric amplifiers for in-plane magnetic fields. We study the Kerr coefficients of NW KI resonators made from 10-nm-thick $\mathrm{Nb}\text{\ensuremath{-}}\mathrm{Ti}\text{\ensuremath{-}}\mathrm{N}$ films with characteristic impedance up to 3 $\mathrm{k}\mathrm{\ensuremath{\Omega}}$, and demonstrate both nondegenerate and degenerate parametric amplification, at magnetic fields up to 2 T. We find that narrow KI resonators of width $0.1\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}$ are robust, in terms of gain, dynamic range and noise, to magnetic fields up to approximately 2T2\phantom{\rule{0.2em}{0ex}}\mathrm{T}2T, for up to 12 dB (16 dB) of phase-insensitive (phase-sensitive) gain. In comparison, wider KI resonators of width $1\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}$ suffer significant suppression in the gain at fields well below 222 T. Around 8-dB deamplification is also observed for coherent states for a 0.1-$\text{\ensuremath{\mu}}\mathrm{m}$ NW KI resonator, implying the capability of noise squeezing. These results open a pathway to developing nonlinear quantum devices that operate in or generate high magnetic fields such as spin, hybrid spin-superconducting, and magneto-optomechanical devices.
Microwave parametric amplifiers operating at the quantum noise limit have become indispensable tools for a range of cryogenic quantum technologies. These amplifiers are typically constructed from nonlinear Josephson junctions, which limit the ability to amplify high-power signals. This study reports a device based instead on the weakly nonlinear kinetic inductance intrinsic to a superconducting film of niobium titanium nitride. The amplifier offers large phase-sensitive gain and high power handling, plus a simple design and fabrication process. As it contains no junctions, it is robust to electrostatic discharge and potentially operable under high temperatures and large magnetic fields.
Parametric amplification is essential for quantum measurement, enabling the amplification of weak microwave signals with minimal added noise. While Josephson-junction-based amplifiers have become standard in superconducting quantum circuits, their magnetic sensitivity, limited saturation power, and sub-kelvin operating requirements motivate the development of alternative nonlinear platforms. Here we demonstrate a two-mode kinetic-inductance parametric amplifier based on a pair of capacitively coupled Kerr-nonlinear resonators fabricated from NbTiN and NbN thin films. The distributed Kerr nonlinearity of these materials enables nondegenerate four-wave-mixing amplification with gains approaching 40 dB, gain-bandwidth products up to 6.9 MHz, and 1-dB compression powers two to three orders of magnitude higher than those of state-of-the-art Josephson amplifiers. A coupled-mode theoretical model accurately captures the pump-induced modification of the hybridized modes and quantitatively reproduces the observed signal and idler responses. The NbN device exhibits a significantly larger Kerr coefficient and superior gain-bandwidth performance, highlighting the advantages of high-kinetic-inductance materials. Our results establish coupled kinetic-inductance resonators as a robust platform for broadband, high-power, and magnetically resilient quantum-limited amplification, offering a scalable route for advanced readout in superconducting qubits, spin ensembles, quantum dots, and other microwave-quantum technologies.