Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2505.22606 · Physical Review Applied

Dynamical sweet and sour regions in bichromatically driven Floquet qubits

D. Dominic Briseño-Colunga, Bibek Bhandari, Debmalya Das, Long B. Nguyen, Yosep Kim, David Santiago, Irfan A. Siddiqi, Andrew N. Jordan, Justin Dressel

Published Dec 23, 2025• 1 citation
arXivHTMLPDF

Abstract

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., $1/f$) 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.

DOI
10.1103/5dmn-yjq5

Related papers

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

Jia-Ming Cheng, Yong-Chang Zhang, Xiang-Fa Zhou +1 more

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.

New Journal of Physics•Dec 1, 2022•2 citations

Optimization of Floquet fluxonium qubits with commensurable two-tone drives

Joachim Lauwens, Kristof Moors, Bart Sorée

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 $ϕ_{ac}(t)=ϕ_m\cos(mω_\mathrm{d} t)+ϕ_n\cos(nω_\mathrm{d} t+φ)$, where $m,n \in \mathbb{N}_{>0}$, 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.

arXiv:2506.06002•Physical review. B./Physical review. B•Jan 23, 2026•1 citation

Dynamical Sweet Spot Engineering via Two-Tone Flux Modulation of Superconducting Qubits

Joseph A. Valery, Shoumik Chowdhury, Glenn Jones +1 more

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.

arXiv:2104.07835•PRX Quantum•May 18, 2022•30 citations

Pareto Front Engineering of Dynamical Sweet Spots in Superconducting Qubits

Zhen Yang, Shan Jin, Yajie Hao +4 more

Operating superconducting qubits at dynamical sweet spots (DSSs) suppresses decoherence from low-frequency flux noise. A key open question is how long coherence can be extended under this strategy and what fundamental limits constrain it. Here we introduce a fully parameterized, multi-objective periodic-flux modulation framework that simultaneously optimizes energy relaxation $T_1$ and pure dephasing $T_φ$, thereby quantifying the tradeoff between them. For fluxonium qubits with realistic noise spectra, our method enhances $T_φ$ by a factor of 3-5 compared with existing DSS strategies while maintaining $T_1$ in the hundred-microsecond range. We further prove that, although DSSs eliminate first-order sensitivity to low-frequency noise, relaxation rate cannot be reduced arbitrarily close to zero, establishing an upper bound on achievable $T_1$. At the optimized working points, we identify double-DSS regions that are insensitive to both DC and AC flux, providing robust operating bands for experiments. As applications, we design single- and two-qubit control protocols at these operating points and numerically demonstrate high-fidelity gate operations. These results establish a general and useful framework for Pareto-front engineering of DSSs that substantially improves coherence and gate performance in superconducting qubits.

quant-pharXiv:2601.19209•Communications Physics•Jan 28, 2026•0 citations

Engineering Dynamical Sweet Spots to Protect Qubits from 1/f Noise

Ziwen Huang, Pranav Mundada, András Gyenis +3 more

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 $1/f$ 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.

arXiv:2004.12458•Physical Review Applied•Mar 22, 2021•65 citations

Flux control of superconducting qubits at dynamical sweet spots

Nicolas Didier

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.

arXiv:1912.09416•Dec 19, 2019•7 citations
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.
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.
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.
Operating superconducting qubits at dynamical sweet spots (DSSs) suppresses decoherence from low-frequency flux noise. A key open question is how long coherence can be extended under this strategy and what fundamental limits constrain it. Here we introduce a fully parameterized, multi-objective periodic-flux modulation framework that simultaneously optimizes energy relaxation T1T_1T1​ and pure dephasing TφT_φTφ​, thereby quantifying the tradeoff between them. For fluxonium qubits with realistic noise spectra, our method enhances TφT_φTφ​ by a factor of 3-5 compared with existing DSS strategies while maintaining T1T_1T1​ in the hundred-microsecond range. We further prove that, although DSSs eliminate first-order sensitivity to low-frequency noise, relaxation rate cannot be reduced arbitrarily close to zero, establishing an upper bound on achievable T1T_1T1​. At the optimized working points, we identify double-DSS regions that are insensitive to both DC and AC flux, providing robust operating bands for experiments. As applications, we design single- and two-qubit control protocols at these operating points and numerically demonstrate high-fidelity gate operations. These results establish a general and useful framework for Pareto-front engineering of DSSs that substantially improves coherence and gate performance in superconducting qubits.
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.
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.