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arXiv:1908.11370

Assessing the Influence of Broadband Instrumentation Noise on Parametrically Modulated Superconducting Qubits

Eliot Fried, Prasahnt Sivarajah, Nicolas Didier, Eyob Alebachew Sete, Marcus Palmer Da Silva, Blake Johnson, Colm A. Ryan

Published Aug 29, 2019• 2 citations
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Abstract

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.

DOI
10.48550/arxiv.1908.11370

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•Jan 1, 2013•0 citations
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.
In state-of-the-art quantum computing platforms, including superconducting qubits and trapped ions, imperfections in the two-qubit entangling gates are the dominant contributions of error to systemwide performance. Recently, a novel two-qubit parametric gate was proposed and demonstrated with superconducting transmon qubits. This gate is activated through rf modulation of the transmon frequency and can be operated at an amplitude where the performance is first-order insensitive to flux noise. In this work we experimentally validate the existence of this ac sweet spot and demonstrate its dependence on white-noise power from room-temperature electronics. With these factors in place, we observe entangling-gate fidelity with coherence-limited performance. An ensemble of repeated observations has a median fidelity of 98.8%, with roughly 10% of observations above 99%.
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.
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.
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.
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.
For over three decades, the presence of magnetic flux noise with a power spectral density scaling roughly as SPhi(f)propto1/falphaS_Phi(f) propto 1/f^alphaSP​hi(f)propto1/falpha, where alphalesssim1alpha lesssim 1alphalesssim1, has been known to limit the low-frequency performance of dc superconducting quantum interference devices (SQUIDs). In recent years, experiments indicate that this same noise persists to frequencies up to 1~GHz and is a dominant source of dephasing in flux-sensitive superconducting quantum bits (qubits). Thus, the reduction of flux noise presents a major hurdle towards the successful realization of scalable quantum computers that are based on flux-based qubits. In this thesis, we present experimental measurements, theoretical analyses, and numerical simulations that support a more detailed understanding of both the microscopic and macroscopic properties of flux noise.Our experimental work begins with flux noise measurements of a large number of SQUIDs in the temperature range from 0.1~K to 4~K. We report on measurements of ten SQUIDs with systematically varied geometries and show that alphaalphaalpha increases as the temperature is lowered; in so doing, each spectrum pivots about a nearly constant frequency. The mean square flux noise, inferred by integrating the power spectra, grows rapidly with temperature and at a given temperature is approximately independent of the outer dimension of a given SQUID washer. We show that these results are incompatible with a model based on the random reversal of independent, spins that are located at the surface of the SQUID washer.In the course of our flux noise measurements, we became aware of a spurious contribution to low-frequency critical current noise in Josephson junctions---normally attributed to charge trapping in the barrier---arising from temperature instabilities inherent in cryogenic systems. These temperature fluctuations modify the critical current via its temperature dependence. By computing cross-correlations between measured temperature and critical current noise in Al-AlOx-Al junctions, we show that, despite excellent temperature stability, temperature fluctuations induce observable critical current fluctuations. Particularly, because 1/f1/f1/f critical current noise has decreased with improved fabrication techniques in recent years, it is important to understand and eliminate this additional noise source.Next, we introduce a numerical method of calculating the mean square flux noise PhisqPhisqPhisq from independently fluctuating spins on the surface of thin-film loops of arbitrary geometry. By reciprocity, PhisqPhisqPhisq is proportional to langleBbf(rbf)2ranglelangleBbf(rbf)^2ranglelangleBbf(rbf)2rangle, where Bbf(rbf)Bbf(rbf)Bbf(rbf) is the magnetic field generated by a circulating current around the loop and rbfrbfrbf varies over the loop surface. By discretizing the loop nonuniformly, we efficiently and accurately compute the current distribution and resulting magnetic field, which may vary rapidly across the loop. We use this method to compute PhisqPhisqPhisq in a number of scenarios in which we systematically vary physical parameters of the loop. We compare our simulations to an earlier analytic result predicting that PhisqproptoR/WPhisq propto R/WPhisqproptoR/W in the limit where the loop radius RRR is much greater than the linewidth WWW. We further show that the previously neglected contribution of edge spins to PhisqPhisqPhisq is significant---even dominant---in narrow-linewidth loops.To calculate theoretical dephasing rates in qubits, we consider flux noise with a spectral density SPhi(f)=A2/(f/1 hboxHz)alphaS_Phi(f) = A^2/(f/1~hbox{Hz})^alphaSP​hi(f)=A2/(f/1 hboxHz)alpha, where AAA is of the order of 1~muPhi0,hboxHz−1/2muPhi_0 , hbox{Hz}^{-1/2}muPhi0​,hboxHz−1/2 and 0.6leqalphaleq1.20.6 leq alpha leq 1.20.6leqalphaleq1.2; Phi0Phi_{0}Phi0​ is the flux quantum. For a qubit with an energy level splitting linearly coupled to the applied flux, our calculations of the dependence of the pure dephasing time tauphitau_phitaup​hi of Ramsey and echo pulse sequences on alphaalphaalpha for fixed AAA show that tauphitau_phitaup​hi decreases rapidly as alphaalphaalpha is reduced. We find that tauphitau_phitaup​hi is relatively insensitive to the noise bandwidth, f1leqfleqf2f_1 leq f leq f_2f1​leqfleqf2​, for all alphaalphaalpha provided the ultraviolet cutoff frequency f2>1/tauphif_2 > 1/tau_phif2​>1/taup​hi. We calculate the ratio tauphi,E/tauphi,Rtau_{phi,E} / tau_{phi,R}tauphi,E​/tauphi,R​ of the echo (EEE) and Ramsey (RRR) sequences, and the dependence of the decay function on alphaalphaalpha and f2f_2f2​. We investigate the case in which SPhi(f0)S_Phi(f_0)SP​hi(f0​) is fixed at the ``pivot frequency'' f0neq1f_0 neq 1f0​neq1~Hz while alphaalphaalpha is varied, and find that the choice of f0f_0f0​ can greatly influence the sensitivity of tauphi,Etau_{phi,E}tauphi,E​ and tauphi,Rtau_{phi,R}tauphi,R​ to the value of alphaalphaalpha.Finally, we conclude with a brief review of our principal results and conclusions. We also comment on promising avenues of future research.