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arXiv:2202.04583 · Physical Review Applied

cnot Gates for Fluxonium Qubits via Selective Darkening of Transitions

Konstantin Nesterov, Chen Wang, Vladimir Manucharyan, Maxim Vavilov

Published Sep 23, 2022• 20 citations
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Abstract

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.

DOI
10.1103/physrevapplied.18.034063

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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{10}^{\ensuremath{-}4}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 present a theoretical analysis of the selective darkening method for implementing quantum controlled-NOT (CNOT) gates. This method, which we have recently proposed and demonstrated, consists of driving two transversely coupled quantum bits (qubits) with a driving field that is resonant with one of the two qubits. For specific relative amplitudes and phases of the driving field felt by the two qubits, one of the two transitions in the degenerate pair is darkened or, in other words, becomes forbidden by effective selection rules. In these driving conditions, the evolution of the two-qubit state realizes a CNOT gate. The gate speed is found to be limited only by the coupling energy J , which is the fundamental speed limit for any entangling gate. Numerical simulations show that at gate speeds corresponding to 0.48 J and 0.07 J , the gate fidelity is 99% and 99.99%, respectively, and increases further for lower gate speeds. In addition, the effect of higher-lying energy levels and weak anharmonicity is studied, as well as the scalability of the method to systems of multiple qubits. We conclude that in all these respects this method is competitive with existing schemes for creating entanglement, with the added advantages of being applicable for qubits operating at fixed frequencies (either by design or for the exploitation of coherence sweet-spots) and having the simplicity of microwave-only operation.
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.
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 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 propose and analyze two types of microwave-activated gates between a fluxonium and a transmon qubit, namely a cross-resonance (CR) and a CPHASE gate. The large frequency difference between a transmon and a fluxonium makes the realization of a two-qubit gate challenging. For a medium-frequency fluxonium qubit, the transmon-fluxonium system allows for a cross-resonance effect mediated by the higher levels of the fluxonium over a wide range of transmon frequencies. This allows one to realize the cross-resonance gate by driving the fluxonium at the transmon frequency, mitigating typical problems of the cross-resonance gate in transmon-transmon chips related to frequency targeting and residual ZZZZZZ coupling. However, when the fundamental frequency of the fluxonium enters the low-frequency regime below 100MHz100\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}100MHz, the cross-resonance effect decreases leading to long gate times. For this range of parameters, a fast microwave CPHASE gate can be implemented using the higher levels of the fluxonium. In both cases, we perform numerical simulations of the gate showing that a gate fidelity above 9999%99 can be obtained with gate times between 100 and 300ns300\phantom{\rule{0.16em}{0ex}}\mathrm{ns}300ns. Next to a detailed gate analysis, we perform a study of chip yield for a surface code lattice of fluxonia and transmons interacting via the proposed cross-resonance gate. We find a much better yield as compared to a transmon-only architecture with the cross-resonance gate as native two-qubit gate.