In quantum information processing, the Josephson parametric amplifier (JPA) has become a crucial tool for fast, high-fidelity readout of superconducting qubits, and for the generation of squeezed microwave radiation. However, research groups worldwide have reported unexpected nonidealities in these devices, leading to poorer than anticipated performance. Using numerical simulations complemented by experiments, the authors pinpoint oft-neglected higher-order circuit nonlinearities as the main source of these nonidealities, and provide simple, concrete steps to improve JPA performance.
In quantum information processing, the Josephson parametric amplifier (JPA) has become a crucial tool for fast, high-fidelity readout of superconducting qubits, and for the generation of squeezed microwave radiation. However, research groups worldwide have reported unexpected nonidealities in these devices, leading to poorer than anticipated performance. Using numerical simulations complemented by experiments, the authors pinpoint oft-neglected higher-order circuit nonlinearities as the main source of these nonidealities, and provide simple, concrete steps to improve JPA performance.
Josephson parametric amplifiers (JPA) are nonlinear devices that are used for quantum sensing and qubit readout in the microwave regime. While JPAs regularly operate near the quantum limit, their gain saturates for very small (few-photon) input power. In a previous work, we showed that the saturation power of JPAs is not limited by pump depletion, but instead by the fourth-order nonlinearity of Josephson junctions, the nonlinear circuit elements that enables amplification in JPAs. Here, we present a systematic study of the nonlinearities in JPAs, show which nonlinearities limit the saturation power, and present a strategy for optimizing the circuit parameters for achieving the best possible JPA. For concreteness, we focus on JPAs that are constructed around a Josephson ring modulator (JRM). We show that by tuning the external and shunt inductors, we should be able to take the best experimentally available JPAs and improve their saturation power by $\ensuremath{\approx}15\phantom{\rule{0.16em}{0ex}}\mathrm{dB}$. Finally, we argue that our methods and qualitative results are applicable to a broad range of cavity-based JPAs.
Circuit quantum-electrodynamics-based quantum information processing relies on low noise amplification for signal readout. In the realm of microwave superconducting circuits, this amplification is often achieved via Josephson parametric amplifiers (JPAs). In the past, these amplifiers exhibited low power added efficiency (PAE), which is roughly the fraction of pump power that is converted to output signal power. This is increasingly relevant because recent attempts to build high saturation power amplifiers achieve this at the cost of very low PAE, which in turn puts a high heat load on the cryostat and limits the number of these devices that a dilution refrigerator can host. Here, we numerically investigate upper bounds on PAE. We focus on a class of parametric amplifiers that consists of a capacitor shunted by a nonlinear inductive block. We first set a benchmark for this class of amplifiers by considering nonlinear blocks described by an arbitrary polynomial current-phase relation. Next, we identify that it is important for amplifiers with inductive blocks composed of repeating elements to have monotonic current-phase relations for each element in order to avoid exciting high-frequency modes. Using this design rule, we propose two circuit implementations for repeating elements in JPA inductive blocks. Finally, we investigate polynomial amplifier chains. We find that while amplifiers with higher gain have a lower PAE, regardless of the gain there is considerable room to improve as compared with state-of-the-art devices. For example, for a degenerate amplifier with a power gain of 20 dB, the PAE is $\ensuremath{\approx}0.1%$ for typical JPAs, 37.9% for our simpler circuit JPAs, 42.6% for our more complex circuit JPAs, 63.3% for our arbitrary polynomial amplifiers, and at least 98% for our amplifier chains.
Superconducting quantum circuits are a leading platform for building a large-scale quantum processor [1]. A crucial component necessary for the high-fidelity readout of qubits in this framework, is an ultra-low-noise microwave amplifier. Thus, over the past two decades, superconducting Josephson parametric amplifiers (JPAs) have been developed that achieve near quantum-limited noise performance, an order of magnitude lower than competing microwave amplifiers based on semiconductor transistors [2]. Nevertheless, JPAs suffer from drawbacks such as limited bandwidth and compression power that makes them difficult to use in an eventual large-scale quantum processor. Thus, an ongoing theme in JPA development is to optimize the circuit to improve these specifications without sacrificing other desirable properties such as the noise performance, ease of construction and operation, etc. Here, we review some results of optimizing a specific JPA circuit called the SNAIL parametric amplifier [3]–[5], shown in Fig. 1, where the acronym SNAIL refers to the Superconducting Nonlinear Asymmetric Inductive eLement. The SNAIL is a composite element made from conventional Al/AlOx/Al Josephson junctions, which has a nonlinear current-phase relation that can be approximated as a nonlinear inductance. By applying a strong microwave frequency pump to modulate the nonlinear inductance, parametric amplification can be realized. By device and circuit engineering we have demonstrated two orders of magnitude improvement in compression power (Fig. 2) in such devices without sacrificing other desirable characteristics.
Josephson Parametric Amplifiers (JPAs) are key components in quantum information processing due to their ability to amplify weak quantum signals with near-quantum-limited noise performance. This is essential for applications such as qubit readout, quantum sensing, and communication, where signal fidelity and coherence preservation are critical. Unlike CMOS and HEMT amplifiers used in conventional RF systems, JPAs are specifically optimized for millikelvin (mK) cryogenic environments. CMOS amplifiers offer good integration but perform poorly at ultra-low temperatures due to high noise. HEMT amplifiers provide better noise performance but are power-intensive and less suited for mK operation. JPAs, by contrast, combine low power consumption with ultra-low noise and excellent cryogenic compatibility, making them ideal for quantum systems. The first part of this study compares these RF amplifier types and explains why JPAs are preferred in cryogenic quantum applications. The second part focuses on the design and analysis of JPAs based on both single Josephson junctions and junction arrays. While single-junction JPAs utilize nonlinear inductance for amplification, they suffer from gain compression, limited dynamic range, and sensitivity to fabrication variations. To overcome these challenges, this work explores JPA designs using Josephson junction arrays. Arrays distribute the nonlinear response, enhancing power handling, linearity, impedance tunability, and coherence while reducing phase noise. Several advanced JPA architectures are proposed, simulated, and compared using quantum theory and CAD tools to assess performance trade-offs and improvements over conventional designs.
Nonlinearity of the current-phase relationship of a Josephson junction is the key resource for a Josephson parametric amplifier (JPA) as well as for a Josephson traveling-wave parametric amplifier, the only devices in which the quantum limit for added noise has so far been approached at microwave frequencies. A standard approach to describe JPA takes into account only the lowest order (cubic) nonlinearity resulting in a Duffing-like oscillator equation of motion or in a Kerr-type nonlinearity term in the Hamiltonian. In this paper we derive the quantum expression for the gain of JPA including all orders of the Josephson junction nonlinearity in the linear response regime. We then analyze gain saturation effect for stronger signals within a semiclassical approach. Our results reveal nonlinear effects of higher orders and their implications for operation of a JPA.
Josephson parametric amplifiers (JPA) have become key devices in quantum science and technology with superconducting circuits. In particular, they can be utilized as quantum-limited amplifiers or as a source of squeezed microwave fields. Here, we report on the detailed measurements of five flux-driven JPAs, three of them exhibiting a hysteretic dependence of the resonant frequency versus the applied magnetic flux. We model the measured characteristics by numerical simulations based on the two-dimensional potential landscape of the dc superconducting quantum interference devices (dc-SQUID), which provide the JPA nonlinearity, for a finite screening parameter βL>0 and demonstrate excellent agreement between the numerical results and the experimental data. Furthermore, we study the nondegenerate response of different JPAs and accurately describe the experimental results with our theory.