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arXiv:2004.12458 · Physical Review Applied

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

Ziwen Huang, Pranav Mundada, András Gyenis, David Schuster, Andrew Houck, Jens Koch

Published Mar 22, 2021• 65 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevapplied.15.034065

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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.
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.
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.
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.
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.
A central challenge in building a scalable quantum computer with superconducting qubits is simultaneously achieving long coherence times and fast two-qubit gates. Currently, fast (tunable) gates are obtained at the expense of coherence time. The authors propose a ``flatsonium'' qubit, based on the highly nonlinear fluxonium qubit, that yields both coherence and tunability---jackpot. Dephasing due to global flux noise is reduced by engineering flux-insensitive sweet spots in the qubit spectrum at the frequencies of interest, while leakage errors are eliminated by the typically large anharmonicity of its energy spectrum.