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Chinese Physics B

Harmonic balance simulation of the influence of component uniformity and reliability on the performance of a Josephson traveling wave parametric amplifier

Yuzhen 煜臻 Zheng 郑, Kanglin Xiong, Jiagui Feng, Hui 辉 Yang 杨

Published Oct 24, 2023• 4 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/ad0624

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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.
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.
Quantum-limited parametric amplifiers have become increasingly interesting and relevant with the progressing field of quantum computing. However, currently it is still challenging to fabricate these complex devices. In this thesis, we developed cross type Josephson junctions (JJs), lumped element LC resonators, lumped element Josephson parametric amplifiers (JPAs) and Josephson traveling wave parametric amplifiers (JTWPAs). We found and resolved several fabrication issues however we suspect that both the JPA and JTWPA suffered from microshorts in the circuits during the cryogenic measurements. Nevertheless, we managed to measure the resonance frequency of the JPA and have noticed the flux focusing effect when we flux tune it. We preformed room temperature measurements on over 300 JJs and calculated the relative standard deviation (RSD) for various JJ sizes. We found the spread of 30 fabricated resonators and a rough estimate of their Q factors. The JTWPAs developed are non-degenerate four wave mixing amplifiers that use the resonant phase matching (RPM) technique to reduce the phase mismatch problem. The transmission through the measured JTWPA showed 50 dB loss probably caused by presumably a short from the transmission line to ground. However, when the JTWPA was driven with a pump we observed 20 dB increase in transmission in some frequency bands.
A comprehensive numerical analysis of the dynamical response of Josephson Traveling Wave Parametric Amplifiers (JTWPA) under varying driving conditions is presented. The primary goal is to examine the effects of a current–phase relation (CPR) incorporating a second-harmonic contribution. The analysis further investigates how parameters such as pump intensity, signal frequency, and DC bias current influence the transition to chaos. The results reveal a wide range of dynamical regimes in JTWPAs, offering insights into optimizing device performance and stability. Notably, the shape of the CPR is shown to have a significant impact on the operational effectiveness and stability of JTWPAs. To obtain results closer to real devices, numerical modeling of JTWPAs implementing Resonant Phase Matching (RPM) circuitry has been performed. We have verified that the introduction of RPM allows a significant increase in the amplifier gain also in the case of non-sinusoidal CPR. These findings may have important implications for the development of next-generation JTWPAs, which are essential components in quantum computing and precision measurement applications.
This work presents the design, fabrication strategy, and numerical modeling of niobium-based Josephson traveling-wave parametric amplifiers (JTWPAs) for quantum microwave readout. These devices are designed as nonlinear transmission lines composed of more than two thousand Josephson junction unit cells, with periodically embedded resonators enabling phase matching. The use of Nb trilayer technology (Nb/AlO[Formula: see text]/Nb) with respect to Al-based devices ensures higher junction uniformity, lower losses, and higher resilience to stray magnetic fields. We developed a multi-scale modeling framework combining harmonic balance methods and time-domain simulations of nonlinear coupled differential equations to describe wave propagation, parametric amplification, and spectral dynamics. Numerical results predict broadband gain up to 20[Formula: see text]dB over multi-GHz bandwidths. These results demonstrate the potential of Nb-based JTWPAs as scalable components for quantum applications.