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Physical Review Applied

Two-Fluxonium Cross-Resonance Gate

Ebru Dogan, Dario Rosenstock, Loïck Le Guevel, Haonan Xiong, Raymond Mencia, Aaron Somoroff, Konstantin Nesterov, Maxim Vavilov, Vladimir Manucharyan, Chen Wang

Published Aug 4, 2023• 37 citations
Publisher

Abstract

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 $\mathcal{F}=0.9949(6)$ 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.

DOI
10.1103/physrevapplied.20.024011

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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{10}^{\ensuremath{-}4}10\ensuremath−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 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 circuit is an artificial atom with a strongly anharmonic spectrum: When biased at a half flux quantum, the lowest qubit transition is an order of magnitude smaller in frequency than those to higher levels. Similar to conventional atomic systems, such a frequency separation between the computational and noncomputational subspaces allows independent optimizations of the qubit coherence and two-qubit interactions. Here, we describe a controlled-ZZZ gate for two fluxoniums connected either capacitively or inductively, with qubit transitions fixed near 500MHz500\phantom{\rule{3.33333pt}{0ex}}\mathrm{MHz}500MHz. The gate is activated by a microwave drive at a resonance involving the second excited state. We estimate intrinsic gate fidelities over 99.9% with gate times below 100 ns.
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 ${10}^{\ensuremath{-}4}$ for a currently achievable magnitude of the flux noise and qubit relaxation time.
Fluxonium qubit is a promising elementary building block for quantum information processing due to its long coherence time combined with a strong anharmonicity. In this paper, we realize a 60-ns direct gate on two inductively coupled fluxoniums, which behave almost exactly as a pair of transversely coupled spin- 1 / 2 systems. The -gate fidelity, estimated using randomized benchmarking, was as high as 99.94%. Furthermore, the fidelity remains above 99.9% for 24 days without any recalibration between measurements. Compared with the 99.96% fidelity of a 60-ns identity gate, our data brings the investigation of the nondecoherence-related errors during logical operations down to 2 × 10 − 4 . The present result adds a simple and robust two-qubit gate into the still relatively small family of the “beyond three nines” gates on superconducting qubits.
We analyze the cross-resonance effect for fluxonium circuits and investigate a two-qubit gate scheme based on selective darkening of a transition. In this approach, two microwave pulses at the frequency of the target qubit are applied simultaneously with a proper ratio between their amplitudes to achieve a controlled-not operation. We study in detail coherent gate dynamics and calculate gate error. With nonunitary effects accounted for, we demonstrate that gate error below ${10}^{\ensuremath{-}4}$ is possible for realistic hardware parameters. This number is facilitated by long coherence times of computational transitions and strong anharmonicity of fluxoniums, which easily prevents excitation to higher excited states during the gate microwave drive.
We demonstrate a controlled-Z gate between capacitively coupled fluxonium qubits with transition frequencies 72.3 MHz72.3~\textrm{MHz}72.3 MHz and 136.3 MHz136.3~\textrm{MHz}136.3 MHz. The gate is activated by a 61.6 ns61.6~\textrm{ns}61.6 ns long pulse at the frequency between non-computational transitions ∣10⟩−∣20⟩|10\rangle - |20\rangle∣10⟩−∣20⟩ and ∣11⟩−∣21⟩|11\rangle - |21\rangle∣11⟩−∣21⟩, during which the qubits complete only 444 and 888 Larmor periods, respectively. The measured gate error of (8±1)×10−3(8\pm1)\times 10^{-3}(8±1)×10−3 is limited by decoherence in the non-computational subspace, which will likely improve in the next generation devices. Although our qubits are about fifty times slower than transmons, the two-qubit gate is faster than microwave-activated gates on transmons, and the gate error is on par with the lowest reported. Architectural advantages of low-frequency fluxoniums include long qubit coherence time, weak hybridization in the computational subspace, suppressed residual ZZZZZZ-coupling rate (here 46 kHz46~\mathrm{kHz}46 kHz), and absence of either excessive parameter matching or complex pulse shaping requirements.