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arXiv:2604.25705 · Physical Review A

Universal Characterization of Classical Qubit Noise

Yuan-De Jin, Zheng-Fei Ye, Wen-Long Ma

quant-phSubmitted Apr 28, 2026• Announced Apr 29, 2026• 0 citations
v1 · Apr 28, 2026v2 · Sep 22, 2026
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Abstract

We propose a general method to fully characterize a classical stochastic noise process causing qubit dephasing through repetitive Ramsey interferometry measurements (RIMs) on the qubit. Compared to filter-function-based spectroscopy, our method does not require complicated dynamical decoupling pulses and can directly detect arbitrary-order correlation functions of such noise processes. We show that each RIM with a short evolution time and suitably chosen control pulses can perform a direct sampling of the noise field and the $n$-point correlations of the RIM outcomes are proportional to the $n$-point correlation functions of the noise processes. Then we numerically demonstrate this method for characterizing two typical examples of classical noises, including the Ornstein-Uhlenbeck processes producing Gaussian noises and an ensemble of TLFs producing non-Gaussian noises. Our method is independent of qubit lifetime and robust against qubit decoherence and measurement errors, thus offering a universal and efficient protocol for qubit noise spectroscopy across diverse platforms.

DOI
10.1103/6kzz-gld6
Comments
8 pages, 4 figures (with 4 pages, 1 figure supplement)

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We propose a general method to fully characterize a classical stochastic noise process causing qubit dephasing through repetitive Ramsey interferometry measurements (RIMs) on the qubit. Compared to filter-function-based spectroscopy, our method does not require complicated dynamical decoupling pulses and can directly detect arbitrary-order correlation functions of such noise processes. We show that each RIM with a short evolution time and suitably chosen control pulses can perform a direct sampling of the noise field and the nnn-point correlations of the RIM outcomes are proportional to the nnn-point correlation functions of the noise processes. Then we numerically demonstrate this method for characterizing two typical examples of classical noises, including the Ornstein-Uhlenbeck processes producing Gaussian noises and an ensemble of TLFs producing non-Gaussian noises. Our method is independent of qubit lifetime and robust against qubit decoherence and measurement errors, thus offering a universal and efficient protocol for qubit noise spectroscopy across diverse platforms.
We present a procedure for direct characterization of the dephasing noise acting on a single qubit by making repeated measurements of the qubit coherence under suitably chosen sequences of controls. We show that this allows a numerical reconstruction of the short-time noise correlation function and that it can be combined with a series of measurements under free evolution to allow a characterization of the noise correlation function over many orders of magnitude range in time scale. We also make an analysis of the robustness and reliability of the estimated correlation functions. Application to a simple model of two uncorrelated noise fluctuators using decoupling pulse sequences shows that the approach provides a useful route for the experimental characterization of dephasing noise and its statistical properties in a variety of condensed phase and atomic systems.
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We introduce open-loop quantum control protocols for characterizing the spectral properties of non-Gaussian noise, applicable to both classical and quantum dephasing environments. By engineering a multidimensional frequency comb via repetition of suitably designed pulse sequences, the desired high-order spectra may be related to observable properties of the qubit probe. We prove that access to a high time resolution is key to achieving spectral reconstruction over an extended bandwidth, overcoming the limitations of existing schemes. Non-Gaussian spectroscopy is demonstrated for a classical noise model describing quadratic dephasing at an optimal point, as well as a quantum spin-boson model out of equilibrium. In both cases, we obtain spectral reconstructions that accurately predict the qubit dynamics in the non-Gaussian regime.
Fluctuations of the qubit frequencies are one of the major problems to overcome on the way to scalable quantum computers. Of particular importance are fluctuations with a correlation time that exceeds the decoherence time due to decay and dephasing by fast processes. The statistics of the fluctuations can be characterized by measuring the correlators of the outcomes of periodically repeated Ramsey measurements. We describe qubit dynamics during repeated measurements and evaluate the two-time correlator for noise from two-level systems and two- and three-time correlators for Gaussian noise. The explicit expressions for the correlators are compared with simulations. We find that, even though the three-time correlators for noise from two-level systems and for Gaussian noise are generally significantly different, already ten two-level systems can mimic Gaussian noise provided they are symmetric. This is not the case for asymmetric systems.
We report a direct measurement of the low-frequency noise spectrum in a superconducting flux qubit. Our method uses the noise sensitivity of a free-induction Ramsey interference experiment, comprising free evolution in the presence of noise for a fixed period of time followed by single-shot qubit-state measurement. Repeating this procedure enables Fourier-transform noise spectroscopy with access to frequencies up to the achievable repetition rate, a regime relevant to dephasing in ensemble-averaged time-domain measurements such as Ramsey interferometry. Rotating the qubit's quantization axis allows us to measure two types of noise: effective flux noise and effective critical-current or charge noise. For both noise sources, we observe that the very same 1/f1/f1/f-type power laws measured at considerably higher frequencies ($0.2\ensuremath{-}20$ MHz) are consistent with the noise in the $0.01\ensuremath{-}100$-Hz range measured here. We find no evidence of temperature dependence of the noises over $65\ensuremath{-}200$ mK, and also no evidence of time-domain correlations between the two noises. These methods and results are pertinent to the dephasing of all superconducting qubits.
We introduce Single-Shot Cross-Spectroscopy (SSCS), a method for extracting the auto- and cross-power spectral densities of dephasing noise in a qubit pair. The method uses straightforward input, namely, single-shot readouts from single-qubit Ramsey-type experiments, without requiring the reconstruction of qubit energy fluctuations from repeated measurements, and is resilient against errors in state preparation and measurement. We apply it to experimental data from a semiconductor spin-qubit device and obtain noise spectra over five orders of magnitude in frequency (5 mHz–500 Hz). Compared to other techniques, for spin qubits, SSCS enables access to noise correlations in the previously inaccessible intermediate-frequency range (1–500 Hz), and can be further extended with faster readout. The method is directly applicable to other qubit platforms, and the upper frequency it can probe is set by the repetition rate of a single-qubit preparation and measurement.