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arXiv:2212.09216 · Quantum Science and Technology

Digital noise spectroscopy with a quantum sensor

Guoqing Wang, Yuan Zhu, Boning Li, Changhao Li, Lorenza Viola, Alexandre Cooper, Paola Cappellaro

Published Mar 27, 2024• 11 citations
arXivHTMLPDF

Abstract

Abstract We introduce and experimentally demonstrate a quantum sensing protocol to sample and reconstruct the autocorrelation of a noise process using a single-qubit sensor under digital control modulation. This Walsh noise spectroscopy method exploits simple sequences of spin-flip pulses to generate a complete basis of digital filters that directly sample the power spectrum of the target noise in the sequency domain, from which the autocorrelation function in the time domain, as well as the power spectrum in the frequency domain, can be reconstructed using linear transformations. Our method, which can also be seen as an implementation of frame-based noise spectroscopy, solves the fundamental difficulty in sampling continuous functions with digital filters by introducing a transformation that relates the arithmetic and logical time domains. In comparison to standard, frequency-based dynamical-decoupling noise spectroscopy protocols, the accuracy of our method is only limited by sampling and discretization in the time domain and can be easily improved, even under limited evolution time due to decoherence and hardware limitations. Finally, we experimentally reconstruct the autocorrelation function of the effective magnetic field produced by the nuclear-spin bath on the electronic spin of a single nitrogen-vacancy center in diamond, discuss practical limitations of the method, and avenues to further improve the reconstruction accuracy.

DOI
10.1088/2058-9565/ad3846

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cond-mat.mes-hallCross-listedarXiv:2609.16643•Sep 16, 2026•0 citations
Abstract We introduce and experimentally demonstrate a quantum sensing protocol to sample and reconstruct the autocorrelation of a noise process using a single-qubit sensor under digital control modulation. This Walsh noise spectroscopy method exploits simple sequences of spin-flip pulses to generate a complete basis of digital filters that directly sample the power spectrum of the target noise in the sequency domain, from which the autocorrelation function in the time domain, as well as the power spectrum in the frequency domain, can be reconstructed using linear transformations. Our method, which can also be seen as an implementation of frame-based noise spectroscopy, solves the fundamental difficulty in sampling continuous functions with digital filters by introducing a transformation that relates the arithmetic and logical time domains. In comparison to standard, frequency-based dynamical-decoupling noise spectroscopy protocols, the accuracy of our method is only limited by sampling and discretization in the time domain and can be easily improved, even under limited evolution time due to decoherence and hardware limitations. Finally, we experimentally reconstruct the autocorrelation function of the effective magnetic field produced by the nuclear-spin bath on the electronic spin of a single nitrogen-vacancy center in diamond, discuss practical limitations of the method, and avenues to further improve the reconstruction accuracy.
Knowing a quantum system's environment is critical for its practical use as a quantum device. Qubit sensors can reconstruct the noise spectral density of a classical bath, provided long enough coherence time. Here, we present a protocol that can unravel the characteristics of a more complex environment, comprising both unknown coherently coupled quantum systems, and a larger quantum bath that can be modeled as a classical stochastic field. We exploit the rich environment of a nitrogen-vacancy center in diamond, tuning the environment behavior with a bias magnetic field, to experimentally demonstrate our method. We show how to reconstruct the noise spectral density even when limited by relatively short coherence times, and identify the local spin environment. Importantly, we demonstrate that the reconstructed model can have predictive power, describing the spin qubit dynamics under control sequences not used for noise spectroscopy, a feature critical for building robust quantum devices. At lower bias fields, where the effects of the quantum nature of the bath are more pronounced, we find that more than a single classical noise model are needed to properly describe the spin coherence under different controls, due to the back action of the qubit onto the bath.
The optimization of dynamical decoupling and quantum error correction for a particular qubit realization is based on a detailed knowledge of the noise properties. Spectroscopy of single-axis noise using dynamical decoupling pulse sequences has garnered much recent attention. Here we consider noise spectroscopy based on a spin-locking type pulse sequence, i.e. a continuous-wave (CW) on-resonance driving field. We show that a heuristic filter function approach produces a qualitatively correct (but quantitatively incorrect) result, whereas a 0th-order average Hamiltonian calculation is shown to agree with the result predicted by the generalized Bloch equations. We further calculate up to 2nd-order average Hamiltonian corrections and show the deviation from the generalized Bloch equation result. This shows that noise spectroscopy using continuous fields, in some cases simpler to implement and more robust to errors than pulsed schemes, can be rigorously analyzed and criteria for reliable measurements can be established. Finally, a solid-state nuclear magnetic resonance experiment is presented which demonstrates that the CW and pulsed methods agree within experimental error. The noise, due to magnetization fluctuations in a dipolar coupled proton spin bath, is found to obey a roughly 1/ω power law decay in the range of frequencies ω investigated.
Detecting and characterizing decoherence-inducing noise sources is critical for developing robust quantum technologies and deploying quantum sensors operating at molecular scales. However, current noise spectroscopies rely on severe approximations that sacrifice accuracy and precision. We propose a novel approach to overcome these limitations. It self-consistently extracts noise spectra that characterize the interactions between a quantum sensor and its environment from commonly performed dynamical decoupling-based coherence measurements. Our approach adopts minimal assumptions and is resilient to measurement errors. We quantify confidence intervals and sensitivity measures to identify experiments that improve spectral reconstruction. We employ our method to reconstruct the noise spectrum of a nitrogen-vacancy sensor in diamond, resolving previously undetected nuclear species at the diamond surface and revealing that previous measurements had overestimated the strength of low-frequency noise by an order of magnitude. Our method uncovers previously hidden structure with unprecedented accuracy, setting the stage for precision noise spectroscopy-based quantum metrology.
Detecting and characterizing decoherence-inducing noise sources is critical for developing robust quantum technologies and deploying quantum sensors operating at molecular scales. However, current noise spectroscopies rely on severe approximations that sacrifice accuracy and precision. We propose a novel approach to overcome these limitations. It self-consistently extracts noise spectra that characterize the interactions between a quantum sensor and its environment from commonly performed dynamical decoupling-based coherence measurements. Our approach adopts minimal assumptions and is resilient to measurement errors. We quantify confidence intervals and sensitivity measures to identify experiments that improve spectral reconstruction. We employ our method to reconstruct the noise spectrum of a nitrogen-vacancy sensor in diamond, resolving previously undetected nuclear species at the diamond surface and revealing that previous measurements had overestimated the strength of low-frequency noise by an order of magnitude. Our method uncovers previously hidden structure with unprecedented accuracy, setting the stage for precision noise spectroscopy-based quantum metrology.
Abstract The undesired interaction of a quantum system with its environment generally leads to a coherence decay of superposition states in time. A precise knowledge of the spectral content of the noise induced by the environment is crucial to protect qubit coherence and optimize its employment in quantum device applications. We experimentally show that the use of neural networks (NNs) can highly increase the accuracy of noise spectroscopy, by reconstructing the power spectral density that characterizes an ensemble of carbon impurities around a nitrogen-vacancy (NV) center in diamond. NNs are trained over spin coherence functions of the NV center subjected to different Carr–Purcell sequences, typically used for dynamical decoupling (DD). As a result, we determine that deep learning models can be more accurate than standard DD noise-spectroscopy techniques, by requiring at the same time a much smaller number of DD sequences.
Noise spectroscopy with quantum sensors is a powerful tool for characterising the properties of the sensor environment and detecting critical magnetic phenomena. While replacing single sensors with large ensembles promises substantial gains in measurement sensitivity and field of view, the output becomes difficult to interpret when there is a variable coupling to targets across the sensing ensemble. In this work we present an analysis procedure for accessing the true source noise spectrum using ensemble coherence from dynamical decoupling measurements. We show that sequence timing plays a dual role in ensemble noise spectroscopy, setting both the frequency selectivity and the weighted collection of signal across the ensemble, and demonstrate how incorporation of the coupling distribution allows accurate parameter extraction of the noise. We apply this procedure to a model system, shallow nitrogen-vacancy centres in diamond, and show that consistent information about the spectral character of MHz-range surface noise can be obtained from two sensing ensembles featuring distinct depth distributions. Our results pave the way for using large quantum sensor ensembles for quantitative, broadband noise spectroscopy, with straightforward extension to other solid-state and molecular sensing platforms.