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.