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arXiv:2110.00632 · Physical Review Applied

Fast Flux Entangling Gate for Fluxonium Circuits

Yinqi Chen, Konstantin Nesterov, Vladimir Manucharyan, Maxim Vavilov

Published Sep 12, 2022• 12 citations
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Abstract

We analyze a high-fidelity two-qubit gate using fast flux pulses on superconducting fluxonium qubits. The gate is realized by temporarily detuning the magnetic flux through the fluxonium loop away from the half flux quantum sweet spot. We simulate dynamics of two capacitively coupled fluxoniums during the flux pulses and optimize the pulse parameters to obtain a highly accurate $\sqrt{i\mathrm{SWAP}}$-like entangling gate. We also evaluate the effect of the flux noise and qubit relaxation on the gate fidelity. Our results demonstrate that the gate error remains below ${10}^{\ensuremath{-}4}$ for a currently achievable magnitude of the flux noise and qubit relaxation time.

DOI
10.1103/physrevapplied.18.034027

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We analyze a high-fidelity two-qubit gate using fast flux pulses on superconducting fluxonium qubits. The gate is realized by temporarily detuning the magnetic flux through the fluxonium loop away from the half flux quantum sweet spot. We simulate dynamics of two capacitively coupled fluxoniums during the flux pulses and optimize the pulse parameters to obtain a highly accurate iSWAP\sqrt{i\mathrm{SWAP}}iSWAP​-like entangling gate. We also evaluate the effect of the flux noise and qubit relaxation on the gate fidelity. Our results demonstrate that the gate error remains below 10\ensuremath−4{10}^{\ensuremath{-}4}10\ensuremath−4 for a currently achievable magnitude of the flux noise and qubit relaxation time.
The superconducting fluxonium qubit has a great potential for high-fidelity quantum gates with its long coherence times and strong anharmonicity at the half flux quantum sweet spot. However, current implementations of two-qubit gates compromise fluxonium's coherence properties by requiring either a temporary population of the non-computational states or tuning the magnetic flux off the sweet spot. Here we realize a fast all-microwave cross-resonance gate between two capacitively-coupled fluxoniums with the qubit dynamics well confined to the computational space. We demonstrate a direct CNOT gate in 70 ns with fidelity up to F=0.9949(6)\mathcal{F}=0.9949(6)F=0.9949(6) despite the limitations of a sub-optimal measurement setup and device coherence. Our results project a possible pathway towards reducing the two-qubit error rate below 10−410^{-4}10−4 with present-day technologies.
The superconducting fluxonium qubit has a great potential for high-fidelity quantum gates with its long coherence times and strong anharmonicity at the half-flux-quantum sweet spot. However, current implementations of two-qubit gates compromise fluxonium's coherence properties by requiring either a temporary population of the noncomputational states or tuning the magnetic flux off the sweet spot. Here we realize a fast all-microwave cross-resonance gate between two capacitively coupled fluxoniums with the qubit dynamics well confined to the computational space. We demonstrate a direct controlled not (cnot) gate in 70 ns with fidelity up to F=0.9949(6)\mathcal{F}=0.9949(6)F=0.9949(6) despite the limitations of a suboptimal measurement setup and device coherence. Our results project a possible pathway towards reducing the two-qubit error rate near to or below ${10}^{\ensuremath{-}4}$ with present-day technologies.
Hybrid superconducting architectures combining different types of qubits offer a promising platform for exploiting their complementary advantages, yet high-fidelity entangling gates remain challenging because of strong nonlinearities and residual qubit-qubit interactions. Here, we propose a high-fidelity controlled-Z (CZ) gate for a hybrid circuit comprising a fluxonium qubit, a fixed-frequency transmon qubit, and a flux-tunable transmon coupler. By modulating only the external magnetic flux applied to the coupler, the qubit-qubit interaction is dynamically engineered for conditional-phase accumulation while the residual interaction is suppressed at idle, mitigating spectator-induced errors. We employ a low-dimensional Fourier-cosine pulse parameterization and a physically motivated cost function to independently suppress conditional-phase errors and leakage from the computational subspace. Numerical simulations demonstrate that a microwave-free CZ gate can be realized within 25ns25 \mathrm{ns}25ns, with an average gate fidelity exceeding 99.99%99.99\%99.99% and leakage below 10−510^{-5}10−5. Using experimentally relevant superconducting-qubit parameters and accounting for decoherence, the proposed scheme maintains a CZ-gate fidelity of approximately 99.9%99.9\%99.9%. We further extend the analysis to larger coupled architectures and find that the CZ-gate infidelity remains below 10−410^{-4}10−4 in the presence of spectator qubits. These results establish single-parameter flux control as a simple and robust approach for realizing high-fidelity entangling gates in heterogeneous superconducting quantum architectures.
Two qubit gates constitute fundamental building blocks in the realization of large-scale quantum devices. Using superconducting circuits, two-qubit gates have previously been implemented in different ways with each method aiming to maximize gate fidelity. Another important goal of a new gate scheme is to minimize the complexity of gate calibration. In this work, we demonstrate a high-fidelity two-qubit gate between two fluxonium qubits enabled by an intermediate capacitively coupled transmon. The coupling strengths between the qubits and the coupler are designed to minimize residual crosstalk while still allowing for fast gate operations. The gate is based on frequency selectively exciting the coupler using a microwave drive to complete a 2πππ rotation, conditional on the state of the fluxonium qubits. When successful, this drive scheme implements a conditional phase gate. Using analytically derived pulse shapes, we minimize unwanted excitations of the coupler and obtain gate errors of 10−210^{-2}10−2 for gate times below 60~ns. At longer durations, our gate is limited by relaxation of the coupler. Our results show how carefully designed control pulses can speed up frequency selective entangling gates.
We propose a family of microwave-activated entangling gates on two capacitively coupled fluxonium qubits.A microwave pulse applied to either qubit at a frequency near the half-frequency of the |00 -|11 transition induces two-photon Rabi oscillations with a negligible leakage outside the computational subspace, owing to the strong anharmonicity of fluxoniums.By adjusting the drive frequency, amplitude, and duration, we obtain the gate family that is locally equivalent to the fermionic-simulation gates such as √ SWAP-like and controlled-phase gates.The gate error can be tuned below 10 -4 for a pulse duration under 100 ns without excessive circuit parameter matching.Given that the fluxonium coherence time can exceed 1 ms, our gate scheme is promising for large-scale quantum processors.
We present a gradient-based method to construct memory-efficient, high-fidelity, single-qubit gates for fluxonium qubits. These gates are constructed using a sequence of single-flux quantum (SFQ) pulses that are sent to the qubit through either capacitive or inductive coupling. The schedule of SFQ pulses is constructed with an on-ramp and an off-ramp applied prior to and after a pulse train, where the pulses are spaced at intervals equal to the qubit period. We reduce the optimization problem to the scheduling of a fixed number of SFQ pulses in the on-ramp and solve it by relaxing the discretization constraint of the SFQ clock as an intermediate step, allowing the use of the Broyden-Fletcher-Goldfarb-Shanno optimizer. Using this approach, gate fidelities of 99.99 % can be achieved for inductive coupling and 99.9 % for capacitive coupling, with leakage being the main source of coherent errors for both approaches.