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arXiv:2306.05177

Modeling and Harmonic Balance Analysis of Parametric Amplifiers for Qubit Read-out

Daryoush Shiri, Hampus Renberg Nilsson, Pavan Telluri, Anita Fadavi Roudsari, Vitaly S. Shumeiko, Christian Fager, Per Delsing

Published Jun 8, 2023• 1 citation
arXivHTMLPDF

Abstract

Predicting the performance of traveling-wave parametric amplifiers (TWPAs) based on nonlinear elements like superconducting Josephson junctions (JJs) is vital for qubit read-out in quantum computers. The purpose of this article is twofold: (a) to demonstrate how nonlinear inductors based on combinations of JJs can be modeled in commercial circuit simulators, and (b) to show how the harmonic balance (HB) is used in the reliable prediction of the amplifier performance e.g., gain and pump harmonic power conversion. Experimental characterization of two types of TWPA architectures is compared with simulations to showcase the reliability of the HB method. We disseminate the modeling know-how and techniques to new designers of parametric amplifiers.

DOI
10.48550/arxiv.2306.05177

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Predicting the performance of traveling-wave parametric amplifiers (TWPAs) based on nonlinear elements like superconducting Josephson junctions (JJs) is vital for qubit read-out in quantum computers. The purpose of this article is twofold: (a) to demonstrate how nonlinear inductors based on combinations of JJs can be modeled in commercial circuit simulators, and (b) to show how the harmonic balance (HB) is used in the reliable prediction of the amplifier performance e.g., gain and pump harmonic power conversion. Experimental characterization of two types of TWPA architectures is compared with simulations to showcase the reliability of the HB method. We disseminate the modeling know-how and techniques to new designers of parametric amplifiers.
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.
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.
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 traveling-wave parametric amplifiers (TWPAs) are essential elements for enhancing the signal-to-noise ratio (SNR) and thus the read-out fidelity of superconducting qubits because of their high gain and near quantum-limited noise. However, the impact of the pump source, e.g., phase noise on these amplifiers, has not yet been studied. In this work, we show that among the two amplification processes in JTWPAs, the three-wave mixing (3WM) process is more sensitive to the pump phase noise than the four-wave mixing (4WM) process. We show that the even-order nonlinearity of 4th order and above in three-wave mixing is responsible for more than 10 dB increase of phase noise at high frequency offsets within the phase noise mask as the power of the pump increases. A polynomial model of the amplifier and cyclo-stationary property of phase noise also corroborate with the simulations. The Harmonic Balance (HB) periodic noise analysis tool and Leeson phase noise model in Keysight Advanced Design System (ADS) simulator were used in this study.
A Josephson traveling wave parametric amplifier (JTWPA), which is a quantum-limited amplifier with high gain and large bandwidth, is the core device of large-scale measurement and control systems for quantum computing. A typical JTWPA consists of thousands of Josephson junctions connected in series to form a transmission line and hundreds of shunt LC resonators periodically loaded along the line for phase matching. Because the variation of these capacitors and inductors can be detrimental to their high-frequency characteristics, the fabrication of a JTWPA typically necessitates precise processing equipment. To guide the fabrication process and further improve the design for manufacturability, it is necessary to understand how each electronic component affects the amplifier. In this paper, we use the harmonic balance method to conduct a comprehensive study on the impact of nonuniformity and fabrication yield of the electronic components on the performance of a JTWPA. The results provide insightful and scientific guidance for device design and fabrication processes.
Josephson junction based parametric amplifiers are used to read out the state of superconducting qubits with high fidelity. These amplifiers are themselves superconducting circuits operating at temperatures of tens of millikelvin. A version of this type of amplifier which has exhibited large bandwidth and saturation power is the Josephson traveling wave parametric amplifier (JTWPA). One particular JTWPA topology consists of hundreds to thousands of Josephson junctions in a transmission line configuration along with periodic phase matching resonators to increase gain. Here, we look at using a superconducting qubit fabrication process to realize this circuit To analyze the sensitivity of the JTWPA to fabrication process variation, we discuss a linear model for the circuit which takes into account unit cell to unit cell variation. To extract the measured circuit values, we use in-situ measurements of a JTWPA to compare the designed values to the realized values. Finally we discuss preliminary results realizing an example JTWPA design using a fabrication process designed for superconducting qubits.