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Universal Fast-Flux Control of a Coherent, Low-Frequency Qubit

Helin Zhang, Srivatsan Chakram, Tanay Roy, Nathan Earnest, Yao Lu, Ziwen Huang, Daniel Weiss, Jens Koch, David Schuster

Published Jan 15, 2021• 104 citations
Publisher

Abstract

The heavy-fluxonium circuit is a promising building block for superconducting quantum processors due to its long relaxation and dephasing time at the flux-frustration point. However, the suppressed charge matrix elements and low transition frequency make it challenging to perform fast single-qubit gates using standard protocols. We report on new protocols for reset, fast coherent control,and readout that allow high-quality operation of the qubit with a 14 MHz transition frequency, an order of magnitude lower in energy than the ambient thermal energy scale. We utilize higher levels of the fluxonium to read out the qubit state and to initialize the qubit with 97% fidelity corresponding to cooling it to 190 μK. Instead of using standard microwave pulses, we control the qubit only with fast-flux pulses, generating control fields much larger than the qubit frequency. We develop a universal set of gates based on nonadiabatic Landau-Zener transitions that act in 20-60 ns, less than the single-qubit Larmor period. We measure qubit coherence of T1,T2e∼300 μs for a fluxonium in a 2D architecture and realize single-qubit gates with an average gate fidelity of 99.8% as characterized by randomized benchmarking.

DOI
10.6082/1j995-c5a34

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arXiv:2011.02634•Physical Review X•May 3, 2021•68 citations
The heavy-fluxonium circuit is a promising building block for superconducting quantum processors due to its long relaxation and dephasing time at the flux-frustration point. However, the suppressed charge matrix elements and low transition frequency make it challenging to perform fast single-qubit gates using standard protocols. We report on new protocols for reset, fast coherent control,and readout that allow high-quality operation of the qubit with a 14 MHz transition frequency, an order of magnitude lower in energy than the ambient thermal energy scale. We utilize higher levels of the fluxonium to read out the qubit state and to initialize the qubit with 97% fidelity corresponding to cooling it to 190 μK. Instead of using standard microwave pulses, we control the qubit only with fast-flux pulses, generating control fields much larger than the qubit frequency. We develop a universal set of gates based on nonadiabatic Landau-Zener transitions that act in 20-60 ns, less than the single-qubit Larmor period. We measure qubit coherence of T1,T2e∼300 μs for a fluxonium in a 2D architecture and realize single-qubit gates with an average gate fidelity of 99.8% as characterized by randomized benchmarking.
Control architectures that reduce hardware overhead while maintaining high-fidelity operations are essential for the continued scaling of superconducting quantum processors. Here we experimentally realize a unified control architecture for fluxonium qubits, in which both transverse (XYXYXY) and longitudinal (ZZZ) operations are implemented through a single flux-control channel driven by a single arbitrary waveform generator channel. This architecture imposes competing requirements on the shared control channel, which must simultaneously support low-frequency flux transmission for reset operations while strongly attenuating broadband noise near the qubit transition frequency. We address this challenge through frequency-selective cryogenic filtering together with compensated waveform synthesis that corrects the pulse distortion introduced by the filtered control line. Experimentally, this approach preserves coherence times above 100 μμμs while enabling active reset with approximately 98% fidelity and 20-ns single-qubit gates with fidelities exceeding 99.99%. We further demonstrate FPGA-native instruction-level waveform synthesis based on reusable pulse primitives for unified flux control. These results establish unified flux control as a scalable architecture for fluxonium qubits that reduces control hardware overhead while preserving high-fidelity operation.
This thesis reports recent achievements toward scalable quantum computing with fluxonium, a superconducting artificial atom with rich energy spectrum and selection rules similar to those found in natural atoms. We show how such spectral properties can be harnessed to protect the qubit from energy relaxation and dephasing. At half-integer flux quantum bias, we show that fluxonium’s |0〉→ |1〉qubit transition has high coherence by design, with T1, T2≈500 μs in one device, the highest reported in superconducting circuits so far. Yet, the qubit exhibits the same level of addressability found in more conventional superconducting qubits (Tgate<50 ns). In addition, a controlled-Z gate can be implemented by sending a short2π-pulse at a frequency near the |1〉→|2〉transition of the target qubit. Preliminary results suggest that this gate can be used to entangle two fluxonium qubits with high fidelity. We also discuss experimental techniques employed to characterize the qubits, and present a perspective on future fluxonium-based quantum technologies.
Superconducting qubits provide a promising path toward building large-scale quantum computers. The simple and robust transmon qubit has been the leading platform, achieving multiple milestones. However, fault-tolerant quantum computing calls for qubit operations at error rates significantly lower than those exhibited in the state of the art. Consequently, alternative superconducting qubits with better error protection have attracted increasing interest. Among them, fluxonium is a particularly promising candidate, featuring large anharmonicity and long coherence times. Here, we engineer a fluxonium-based quantum processor that integrates high qubit coherence, fast frequency tunability, and individual-qubit addressability for reset, readout, and gates. With simple and fast gate schemes, we achieve an average single-qubit gate fidelity of 99.97% and a two-qubit gate fidelity of up to 99.72%. This performance is comparable to the highest values reported in the literature of superconducting circuits. Thus our work, within the realm of superconducting qubits, reveals an alternative qubit platform that is competitive with the transmon system.
Owing to their strong dipole moment and long coherence times, superconducting qubits have demonstrated remarkable success in hybrid quantum circuits. However, most qubit architectures are limited to the GHz frequency range, severely constraining the class of systems they can interact with. The fluxonium qubit, on the other hand, can be biased to very low frequency while being manipulated and read out with standard microwave techniques. Here, we design and operate a heavy fluxonium with an unprecedentedly low transition frequency of 1.8 MHz. We demonstrate resolved sideband cooling of the “hot” qubit transition with a final ground state population of 97.7%, corresponding to an effective temperature of 23 μ K . We further demonstrate coherent manipulation with coherence times T 1 = 34 μ s , T 2 * = 39 μ s , and single-shot readout of the qubit state. Importantly, by directly addressing the qubit transition with a capacitively coupled waveguide, we showcase its high sensitivity to a radio-frequency field. Through cyclic qubit preparation and interrogation, we transform this low-frequency fluxonium qubit into a frequency-resolved charge sensor. This method results in a charge sensitivity of 33 μ e / Hz , or an energy sensitivity (in joules per hertz) of 2.8 ℏ . This method rivals state-of-the-art transport-based devices, while maintaining inherent insensitivity to dc-charge noise. The high charge sensitivity combined with large capacitive shunt unlocks new avenues for exploring quantum phenomena in the 1–10 MHz range, such as the strong-coupling regime with a resonant macroscopic mechanical resonator. Published by the American Physical Society 2024
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.