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arXiv:1802.03095 · Physical Review A

Microwave-activated controlled- Z gate for fixed-frequency fluxonium qubits

Konstantin Nesterov, Ivan Pechenezhskiy, Chen Wang, Vladimir Manucharyan, Maxim Vavilov

Published Sep 24, 2018• 38 citations
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Abstract

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-$Z$ gate for two fluxoniums connected either capacitively or inductively, with qubit transitions fixed near $500\phantom{\rule{3.33333pt}{0ex}}\mathrm{MHz}$. 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.

DOI
10.1103/physreva.98.030301

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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.
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.
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 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.
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.
Tunable couplers have recently become one of the most powerful tools for implementing two-qubit gates between superconducting qubits.A tunable coupler typically includes a nonlinear element, such as a superconducting quantum interference device, which is used to tune the resonance frequency of an LC circuit connecting two qubits.Here we propose a complimentary approach where instead of tuning the resonance frequency of the tunable coupler by applying a quasistatic control signal, we excite by microwave the degree of freedom associated with the coupler itself.Because of strong effective longitudinal coupling between the coupler and the qubits, the frequency of this transition strongly depends on the computational state, leading to different phase accumulations in different states.Using this method, we experimentally demonstrate a controlled-Z gate of 44-ns duration on a fluxonium-based quantum processor, obtaining a fidelity of 97.6% ± 0.4% characterized by cross-entropy benchmarking.
All-microwave control of fixed-frequency superconducting quantum systems offers the potential to reduce control circuit complexity and increase system coherence. Nevertheless, due to the limited control flexibility in qubit parameters, one has to address several issues, such as quantum crosstalk and frequency crowding, for scaling up qubit architecture with nontunable elements. This paper proposes a microwave-activated two-qubit gate scheme for two fixed-frequency transmon qubits coupled via a fixed-frequency transmon coupler. The protocol relies on applying a microwave pulse exclusively to the coupler, enabling the implementation of a controlled-ZZZ gate. We show that the gate fidelity exceeding 0.999 can be achieved within 150 ns, excluding decoherence effects. Moreover, we also show that leakage from the computational subspace to noncomputational states can also be effectively suppressed.