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arXiv:2601.19209 · Communications Physics

Pareto Front Engineering of Dynamical Sweet Spots in Superconducting Qubits

Zhen Yang, Shan Jin, Yajie Hao, Guangwei Deng, Xiu-Hao Deng, Re-Bing Wu, Xiaoting Wang

quant-phSubmitted Jan 27, 2026• Announced Jan 28, 2026• 0 citations• Revised Jul 30, 2026 (v2)
v1 · Jan 27, 2026v2 · Jul 30, 2026
arXivHTMLPDF

Abstract

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.

DOI
10.1038/s42005-026-02778-2

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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.
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.
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.
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.
The control of highly coherent qubits is crucial to building scalable superconducting quantum processors; in particular, the performance of entangling gates relies on the coherence times of individual qubits. Parametrically activated entangling gates between two coupled qubits are realized through rf flux modulation of one qubit. Here the authors discuss modulation amplitudes at which the qubit is first-order insensitive to 1/f1/f1/f flux noise: ``sweet spots'' in the ac flux. By properly filtering the white flux noise from the control electronics, one can realize high-fidelity two-qubit gates at a sweet spot. Recently this protection from flux noise has also been seen experimentally.
Fault-tolerant quantum computing requires quantum gates that combine short duration, high fidelity, and robustness to noise. As quantum processors scale, robustness becomes increasingly important because exhaustive characterization and frequent recalibration of individual gates become impractical. We present a comprehensive optimal-control framework for controlled-Z (CZ) gates between directly coupled, frequency-tunable transmons that systematically accounts for intrinsic Hamiltonian errors and realistic decoherence mechanisms, including energy relaxation and dephasing. Using smooth, single-shot flux pulses, we obtain 12-ns CZ gates---close to the theoretical speed limit of 11.6 ns---with intrinsic errors suppressed to the 2×10−52\times10^{-5}2×10−5 level. We construct dephasing noise models, calibrated against published experimental measurements, that capture fast dephasing from room-temperature control electronics and slow dephasing from 1/f1/f1/f flux noise. Using these models, we identify dephasing sweet spots that suppress sensitivity to dephasing noise. We further exploit transmon asymmetry as a design parameter to access distinct noise-resilient operating regimes. These results establish an experimentally applicable framework for balancing gate speed, fidelity, and noise robustness while reducing characterization and recalibration overhead.
Quantum computers utilize qubits to store and process quantum information. In superconducting quantum computers, qubits are implemented as quantum superconducting resonant circuits. The circuits are operated only at the two energy states, which form the computational basis for the qubit. To suppress leakage to uncomputational states, superconducting qubits are designed to be anharmonic oscillators, which is achieved using one or more Josephson junctions, a nonlinear superconducting element. One of the main challenges in developing quantum computers is minimizing the decoherence caused by environmental noise. Decoherence is characterized by two coherence times, T1 for depolarization processes and T2 for dephasing. This thesis reviews and investigates the decoherence properties of superconducting qubits. The main goal of the thesis is to analyze the tradeoff between anharmonicity and dephasing in a qubit unimon. Recently developed unimon incorporates a single Josephson junction shunted by a linear inductor and a capacitor. Unimon is tunable by external magnetic flux, and at the half flux quantum bias, the Josephson energy is partially canceled by the inductive energy, allowing unimon to have relatively high anharmonicity while remaining fully protected against low-frequency charge noise. In addition, at the sweet spot with respect to the magnetic flux, unimon becomes immune to first-order perturbations in the flux. The sweet spot, however, is relatively narrow, making unimon susceptible to dephasing through the quadratic coupling to the flux noise. In the first chapter of this thesis, we present a comprehensive look into the basic theory of superconducting qubits, starting with two-state quantum systems, followed by superconductivity and superconducting circuit elements, and finally combining these two by introducing circuit quantum electrodynamics (cQED), a framework for building superconducting qubits. We follow with a theoretical discussion of decoherence in two-state quantum systems, described by the Bloch-Redfield formalism. We continue the discussion by estimating decoherence using perturbation theory, with special care put into the dephasing due to the low-frequency 1/f noise. Finally, we review the theoretical model of unimon, which is used in the numerical analysis. As a main result of this thesis, we suggest a design parameter regime for unimon, which gives the best ratio between anharmonicity and T2.