Josephson Traveling Wave Parametric Amplifiers (JTWPAs) are integral parts of many experiments carried out in quantum technologies. Being composed of hundreds of Josephson junction-basedunit 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 insitu 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 as WRSPICE or PSCAN2, 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 using JosephsonCircuits.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.
Traveling Wave Parametric Amplifiers (TWPAs) are extensively employed in experiments involving weak microwave signals for their highly desirable quantum-limited and broadband characteristics.However, TWPAs‘ broadband nature comes with the disadvantage of admitting the activation of spurious nonlinear processes, such as harmonics generation, that can potentially degrade amplification performance. Here we experimentally investigate a Josephson TWPA device with SNAIL (Superconducting Nonlinear Asymmetric Inductive Element)-based unit cells focusing on the amplification behaviour along with the generation of second and third harmonics of the pump. By comparing experimental results with transient numerical simulations, we demonstrate the influence of Josephson junctions‘ fabrication imperfections on the occurrence of harmonics and on the gain behaviour.
Josephson Traveling Wave Parametric Amplifiers (JTWPAs) are largely exploited in quantum technologies for their broadband and low noise performance in the microwave regime. When oneor 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.
We investigate the dynamics of the bistable regime of the generalized Jaynes-Cummings Hamiltonian (GJC), realised by a circuit quantum electrodynamics (cQED) system consisting of atransmon qubit coupled to a microwave cavity. In this regime we observe critical slowing down in the approach to the steady state. By measuring the response of the cavity to a step function drive pulse we characterize this slowing down as a function of driving frequency and power. We find that the critical slowing down saturates as the driving power is increased. We compare these results with the predictions of analytical and numerical calculations both with and without the Duffing approximation. We find that the Duffing approximation incorrectly predicts that the critical slowing down timescale increases exponentially with the drive, whereas the GJC model accurately predicts the saturation seen in our data, suggesting a different process of quantum activation.
Quantum computation requires the precise control of the evolution of a quantum system, typically through application of discrete quantum logic gates on a set of qubits. Here, we usethe cross-resonance interaction to implement a gate between two superconducting transmon qubits with a direct static dispersive coupling. We demonstrate a practical calibration procedure for the optimization of the gate, combining continuous and repeated-gate Hamiltonian tomography with step-wise reduction of dominant two-qubit coherent errors through mapping to microwave control parameters. We show experimentally that this procedure can enable a ZX^−π/2 gate with a fidelity F=97.0(7)%, measured with interleaved randomized benchmarking. We show this in a architecture with out-of-plane control and readout that is readily extensible to larger scale quantum circuits.