Enhanced Quantum Signal Control and Sensing Under Multicolored Noise via Generalized Filter Function Framework

TL;DR

The paper addresses the challenge of spectrally complex noise in quantum devices by introducing a generalized filter-function framework with tunable system-noise coupling. By integrating COCOA optimization, it designs band-selective, hardware-feasible control pulses that suppress noise while preserving high-fidelity operations, achieving near $0.9999$ fidelity for single- and two-qubit gates and up to $10$ dB improvements in sensing precision. Key contributions include the formalism for tunable coupling, a noise-susceptibility metric, robust $X_\pi$ and CZ gates, and an AC-signal sensing scheme with spectral selectivity. The approach provides a universal, practically implementable pathway to robust quantum control and high-precision quantum sensing in the presence of multi-colored noise.

Abstract

We introduce a generalized filter-function framework that treats noise coupling strength as a tunable control parameter, enabling target noise suppression across user-defined frequency bands. By optimizing this generalized filter function, we design band-selective control pulses that achieve $0.9999$ fidelity of single- and two-qubit gates under strong noise with diverse spectral profiles. We further extend the method to selectively enhance the signal-to-noise ratio for quantum sensing of AC signals with an enhanced precision of up to $10$ dB. The resulting control pulses are experimentally feasible, offering a practical pathway toward robust quantum operations and high-precision signal processing under spectrally complex noises.

Figures (13)

• Figure 1: Comparisons of $X_\pi$ gates in the presence of multi-colored noise. (a) Different waveforms of the control field. (b) The corresponding filter functions of these waveforms, plotted alongside the noise spectrum (gray curve) and target bands (gray area). (c) log view of average X-gate fidelity implemented by mixed noise RCP, Cos $9\pi$-pulse, and static noise RCP against time-dependent noise with different amplitude.(The curve of Cos $\pi$-pulse is in the middle of two closed curves, which is not shown.) The Gray dotted line is the fitted curve $y=2x+b$ to get the noise susceptibility. The nested graph in (c) is the infidelity of mixed noise RCP with a wider noise amplitude range. (d) The fitted noise susceptibility varies with the width of the noise spectrum.
• Figure 2: Comparison of CZ gates in the presence of low-frequency noise. (a) Dependence of Qubit A's frequency and its noise-coupling strengths $c_{z_A}, c_{zz}$ on the applied magnetic flux $\Phi(t)$. (b) Waveforms of the RCP (blue solid) and peak amplitudes (dashed lines) for sine/cosine-modulated pulses. (c) Filter functions of different pulse shapes with shaded regions denoting targeted suppression bands. (d) Average CZ-gate fidelity versus amplitude of the time-dependent noise for the RCP, standard square pulse, a net-zero pulse with square function and sine function. The nested log-scale inset shows the gate infidelity, with a gray dotted line fitting $y=2x + b$ to quantify noise susceptibility. (e) Noise susceptibility $C$ as a function of the PSD bandwidth $\gamma$. Values are normalized to the RCP’s minimum susceptibility. Data points (dots) are plotted by fitting the infidelities from the inset in (d).
• Figure 3: Results of the optimized sensing. (a) Flux bias $\Phi(t)$ for the optimized control and PDD. (b) The corresponding filter functions in a logarithmic scale, highlighting noise-suppression (shaded) and signal-amplification (unshaded) regions. (c) the improvement in the variance of the simulation results of the optimized waveform versus PDD as noise amplitude $A$ increases, as well as the improvement in the theoretical fisher information. (d) The Gaussian distribution of the measured $B$ values under each control scheme.
• Figure S1: Optimized results of X gate for high-frequency noise. (a) The waveform of robust control pulse (RCP, blue) and Cos $\pi$-pulse (orange). (b) The filter function of RCP (blue) and Cos $\pi$-pulse (orange) overlapped with the corresponding noise spectrum (gray).
• Figure S2: Optimized results of X gates for low-frequency and mixed noise. (a), (c) The pulse waveforms of Cos -pulse, static RCP, and the RCP for low-frequency(a) and mixed (c) noise. (b), (d) is the corresponding filter function for (a), (c). The shadow areas indicate the target optimization bands and the simulation results of the corresponding noise spectrum are drawn in the filter function diagram.