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New Journal of Physics

Enhancing quantum coherence of a fluxonium qubit by employing flux modulation with tunable-complex-amplitude

Jia-Ming Cheng, Yong-Chang Zhang, Xiang-Fa Zhou, Zheng-Wei Zhou

Published Dec 1, 2022• 2 citations
Publisher

Abstract

Abstract We propose to protect fluxonium qubits that are away from half flux quantum against environmental noises, especially 1 / f flux noise, by adopting a modulated flux with tunable-complex-amplitude. Using open-system Floquet theory, we derive a Lindblad equation and extract decoherent rates for pure-dephasing, excitation and relaxation. After examining intrinsic attributes of the flux driven fluxonium qubit, we put forward an analytic manner to locate dynamical sweet spots for fast and weak driving. Continuous families of dynamical sweet spots are found in the parameter plane of relative amplitude factor and relative phase. Around a family of dynamical sweet spots or between two families of dynamical sweet spots, there exist continuous regions with long coherent times that exceed 100 μ s . Taking advantage of the two noise-insensitive channels: relative amplitude factor and relative phase, a flux driven fluxonium qubit can become immune to flux noises from both the dc and ac flux amplitudes. And the optimal driving amplitudes are no longer isolated at a certain driving frequency, but become continuous. This is in sharp contrast to the usual schemes based on flux modulation with real-amplitude. As a result, there are plenty of manipulating flexibility in our flux driving scheme with tunable-complex-amplitude, which may be useful in logical operations among flux driven fluxonium qubits or other flux qubits.

DOI
10.1088/1367-2630/acacbd

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Abstract We propose to protect fluxonium qubits that are away from half flux quantum against environmental noises, especially 1 / f flux noise, by adopting a modulated flux with tunable-complex-amplitude. Using open-system Floquet theory, we derive a Lindblad equation and extract decoherent rates for pure-dephasing, excitation and relaxation. After examining intrinsic attributes of the flux driven fluxonium qubit, we put forward an analytic manner to locate dynamical sweet spots for fast and weak driving. Continuous families of dynamical sweet spots are found in the parameter plane of relative amplitude factor and relative phase. Around a family of dynamical sweet spots or between two families of dynamical sweet spots, there exist continuous regions with long coherent times that exceed 100 μ s . Taking advantage of the two noise-insensitive channels: relative amplitude factor and relative phase, a flux driven fluxonium qubit can become immune to flux noises from both the dc and ac flux amplitudes. And the optimal driving amplitudes are no longer isolated at a certain driving frequency, but become continuous. This is in sharp contrast to the usual schemes based on flux modulation with real-amplitude. As a result, there are plenty of manipulating flexibility in our flux driving scheme with tunable-complex-amplitude, which may be useful in logical operations among flux driven fluxonium qubits or other flux qubits.
Scaling up superconducting quantum processors with optimized performance requires a sufficient flexibility in the choice of operating points for single and two qubit gates to maximize their fidelity and cope with imperfections. Flux control is an efficient technique to manipulate the parameters of tunable qubits, in particular to activate entangling gates. At flux sensitive points of operation, the ubiquitous presence of 1/f flux noise however gives rise to dephasing by inducing fluctuations of the qubit frequency. We show how two-tone modulation of the flux bias, a bichromatic modulation, gives rise to a continuum of dynamical sweet spots where dephasing due to slow flux noise is suppressed to first order for a wide range of time-averaged qubit frequencies. The qubits can be operated at these dynamical sweet spots to realize protected entangling gates and to avoid collisions with two-level-system defects.
Protecting superconducting qubits from low-frequency noise by operating them on dynamical sweet-spot manifolds has proven to be a promising setup, theoretically as well as experimentally . These dynamical sweet spots are induced by an externally applied Floquet drive, and various drive forms have been studied in different types of qubits. In this work we study the effects of using two-tone drives on the applied magnetic flux of the form ϕac(t)=ϕmcos⁡(mωdt)+ϕncos⁡(nωdt+φ)ϕ_{ac}(t)=ϕ_m\cos(mω_\mathrm{d} t)+ϕ_n\cos(nω_\mathrm{d} t+φ)ϕac​(t)=ϕm​cos(mωd​t)+ϕn​cos(nωd​t+φ), where m,n∈N>0m,n \in \mathbb{N}_{>0}m,n∈N>0​, on the coherence times of fluxonium qubits. The optimal drive parameters are found through analysis using perturbation theory and numerical calculations. We show that this type of drive allows for more tunability of the quasi-energy spectrum, creating higher and wider peaks of the dephasing time without affecting the relaxation times too strongly. Further we show that the second commensurable drive tone can be used to implement an improved phase gate compared to implementations with a single tone, supported by Monte Carlo simulations.
Current superconducting quantum processors require strategies for coping with material defects and imperfect parameter targeting in order to scale up while maintaining high performance.To that end, in situ control of qubit frequencies with magnetic flux can be used to avoid spurious resonances.However, increased dephasing due to 1/f flux noise limits performance at all of these operating points except for noise-protected sweet spots, which are sparse under dc flux bias and monochromatic flux modulation.Here we experimentally demonstrate that two-tone flux modulation can be used to create a continuum of dynamical sweet spots, greatly expanding the range of qubit frequencies achievable while first-order insensitive to slow flux noise.To illustrate some advantages of this flexibility, we use bichromatic flux control to reduce the error rates and gate times of parametric entangling operations between transmons.Independent of the gate scheme, the ability to use flux control to freely select qubit frequencies while maintaining qubit coherence represents an important step forward in the robustness and scalability of near-term superconducting qubit devices.
Modern superconducting and semiconducting quantum hardware use external charge and microwave flux drives to both tune and operate devices. However, each external drive is susceptible to low-frequency (e.g., 1/f1/f1/f) noise that can drastically reduce the decoherence lifetime of the device unless the drive is placed at specific operating points that minimize the sensitivity to fluctuations. We show that operating a qubit in a driven frame using two periodic drives of distinct commensurate frequencies can have advantages over both monochromatically driven frames and static frames with constant offset drives. Employing Floquet theory, we analyze the spectral and lifetime characteristics of a two-level system under weak and strong bichromatic drives, identifying drive-parameter regions with high coherence (sweet spots) and highlighting regions where coherence is limited by additional sensitivity to noise at the drive frequencies (sour spots). We present analytical expressions for quasienergy gaps and dephasing rates, demonstrating that bichromatic driving can alleviate the trade-off between DC and AC noise robustness observed in monochromatic drives. This approach reveals continuous manifolds of doubly dynamical sweet spots, along which drive parameters can be varied without compromising coherence. Our results motivate further study of bichromatic Floquet engineering as a powerful strategy for maintaining tunability in high-coherence quantum systems.
Superconducting qubits provide a promising architecture for scalability in quantum information processing, but their coherence times are currently limited by environmental noise, miring such processors in the noisy intermediate-scale regime. Operating at ``sweet spots'' (turning points in a qubit's microwave spectrum) can substantially reduce the dephasing due to 1/f1/f1/f flux noise. The authors extend this concept to boost noise mitigation with an external drive, yielding $d\phantom{\rule{0}{0ex}}y\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}m\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}l$ sweet spots and turning static sweet ``spots'' into manifolds. This simple, powerful approach adds flexibility to the choice of operating points, and could enhance coherence times by more than an order of magnitude.
Protecting qubits from environmental noise while maintaining strong coupling for fast high-fidelity control is a central challenge for quantum information processing. Here, we demonstrate a control scheme for superconducting fluxonium qubits that eliminates qubit decay through the control channel by suppressing the environmental density of states at the transition frequency. Adding a low-pass filter on the flux line allows for flux-biasing and, at the same time, coherently controlling the fluxonium qubit by parametrically driving it at integer fractions of its transition frequency. We compare the filtered to the unfiltered configuration and find a 5-times-longer T 1 , and a 10-times-improved T 2 -echo time in the filtered case. We demonstrate coherent control with up to 11-photon subharmonic drives, highlighting the strong nonlinearity of the fluxonium potential. Measured Rabi frequencies and drive-induced frequency shifts show excellent agreement with numerical and analytical models. Furthermore, we show the equivalence of a 3-photon subharmonic drive to an on-resonance drive by benchmarking subharmonic gate fidelities above 99.94%. These results open up a scalable path for full qubit control through a single Purcell-protected channel, providing strong suppression of control-induced decoherence and enabling wiring-efficient superconducting quantum processors.