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arXiv:2104.07835 · PRX Quantum

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

Joseph A. Valery, Shoumik Chowdhury, Glenn Jones, Nicolas Didier

Published May 18, 2022• 30 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/prxquantum.3.020337

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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.
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.
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.
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.
With superconducting transmon qubits --- a promising platform for quantum information processing --- two-qubit gates can be performed using AC signals to modulate a tunable transmon's frequency via magnetic flux through its SQUID loop. However, frequency tunablity introduces an additional dephasing mechanism from magnetic fluctuations. In this work, we experimentally study the contribution of instrumentation noise to flux instability and the resulting error rate of parametrically activated two-qubit gates. Specifically, we measure the qubit coherence time under flux modulation while injecting broadband noise through the flux control channel. We model the noise's effect using a dephasing rate model that matches well to the measured rates, and use it to prescribe a noise floor required to achieve a desired two-qubit gate infidelity. Finally, we demonstrate that low-pass filtering the AC signal used to drive two-qubit gates between the first and second harmonic frequencies can reduce qubit sensitivity to flux noise at the AC sweet spot (ACSS), confirming an earlier theoretical prediction. The framework we present to determine instrumentation noise floors required for high entangling two-qubit gate fidelity should be extensible to other quantum information processing systems.
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.