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Register a new userCalibration of the cross-resonance two-qubit gate between directly-coupled transmons
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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 use the 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 $hat{ZX}_{-pi/2}$ 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.
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Implementation of high-fidelity swapping operations is of vital importance to execute quantum algorithms on a quantum processor with limited connectivity. We present an efficient pulse control technique, cross-cross resonance (CCR) gate, to implement iSWAP and SWAP operations with dispersively-coupled fixed-frequency transmon qubits. The key ingredient of the CCR gate is simultaneously driving both of the coupled qubits at the frequency of another qubit, wherein the fast two-qubit interaction roughly equivalent to the XY entangling gates is realized without strongly driving the qubits. We develop the calibration technique for the CCR gate and evaluate the performance of iSWAP and SWAP gates The CCR gate shows roughly two-fold improvement in the average gate error and more than 10~% reduction in gate times from the conventional decomposition based on the cross resonance gate.
We present a comprehensive theoretical study of the cross-resonance gate operation covering estimates for gate parameters and gate error as well as analyzing spectator qubits and multi-qubit frequency collisions. We start by revisiting the derivation of effective Hamiltonian models following Magesan et al. (arXiv:1804.04073). Transmon qubits are commonly modeled as a weakly anharmonic Kerr oscillator. Kerr theory only accounts for qubit frequency renormalization, while adopting number states as the eigenstates of the bare qubit Hamiltonian. Starting from the Josephson nonlinearity and by accounting for the eigenstates renormalization, due to counter-rotating terms, we derive a new starting model for the cross-resonance gate with modified qubit-qubit interaction and drive matrix elements. Employing time-dependent Schrieffer-Wolff perturbation theory, we derive an effective Hamiltonian for the cross-resonance gate with estimates for the gate parameters calculated up to the fourth order in drive amplitude. The new model with renormalized eigenstates lead to 10-15 percent relative correction of the effective gate parameters compared to Kerr theory. We find that gate operation is strongly dependent on the ratio of qubit-qubit detuning and anharmonicity. In particular, we characterize five distinct regions of operation, and propose candidate parameter choices for achieving high gate speed and low coherent gate error when the cross-resonance tone is equipped with an echo pulse sequence. Furthermore, we generalize our method to include a third spectator qubit and characterize possible detrimental multi-qubit frequency collisions.
Off-resonant error for a driven quantum system refers to interactions due to the input drives having non-zero spectral overlap with unwanted system transitions. For the cross-resonance gate, this includes leakage as well as off-diagonal computational interactions that lead to bit-flip error on the control qubit. In this work, we quantify off-resonant error, with more focus on the less studied off-diagonal control interactions, for a direct CNOT gate implementation. Our results are based on numerical simulation of the dynamics, while we demonstrate the connection to time-dependent Schrieffer-Wolff and Magnus perturbation theories. We present two methods for suppressing such error terms. First, pulse parameters need to be optimized so that off-resonant transition frequencies coincide with the local minima due to the pulse spectrum sidebands. Second, we show the advantage of a $Y$-DRAG pulse on the control qubit in mitigating off-resonant error. Depending on qubit-qubit detuning, the proposed methods can improve the average off-resonant error from approximately $10^{-3}$ closer to the $10^{-4}$ level for a direct CNOT calibration.
We have demonstrated a novel type of superconducting transmon qubit in which a Josephson junction has been engineered to act as its own parallel shunt capacitor. This merged-element transmon (MET) potentially offers a smaller footprint and simpler fabrication than conventional transmons. Because it concentrates the electromagnetic energy inside the junction, it reduces relative electric field participation from other interfaces. By combining micrometer-scale Al/AlOx/Al junctions with long oxidations and novel processing, we have produced functional devices with $E_{J}$/$E_{C}$ in the low transmon regime ($E_{J}$/$E_{C}$ $lesssim$30). Cryogenic I-V measurements show sharp dI/dV structure with low sub-gap conduction. Qubit spectroscopy of tunab
Circuit quantum electrodynamics systems are typically built from resonators and two-level artificial atoms, but the use of multi-level artificial atoms instead can enable promising applications in quantum technology. Here we present an implementation of a Josephson junction circuit dedicated to operate as a V-shape artificial atom. Based on a concept of two internal degrees of freedom, the device consists of two transmon qubits coupled by an inductance. The Josephson nonlinearity introduces a strong diagonal coupling between the two degrees of freedom that finds applications in quantum non-demolition readout schemes, and in the realization of microwave cross-Kerr media based on superconducting circuits.
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