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arXiv:2502.13380 · Physical Review A

Quantum noise spectroscopy by qudit spectators

Clara Javaherian, Christopher Ferrie

Published Jun 20, 2025• 0 citations
arXivHTMLPDF

Abstract

Quantum noise spectroscopy is a well-known method for detecting environmental noise spectrum and has various applications in quantum sensing, quantum network design, and quantum computing. In this work, a protocol for quantum noise spectroscopy by qudit spectators (arbitrary d-level quantum systems) is presented for noises with stochastic and stationary Gaussian distributions. The protocol uses Weyl basis decomposition, consisting of generalized Pauli matrices, as the theoretical tool, and the Alvarez-Suter noise spectroscopy method, by which the qudit is being exposed to a series of pulse sequences, and the noise polyspectra is extracted by multiple measurements of an observable of the qudit. The formalism is further developed and simulated for three theoretical frameworks: The first two frameworks utilize a simplified Weyl basis and are capable of detecting Z-type dephasing noise. One is specifically modeled for a qutrit (d=3), and the second framework is designed for all qudits and has been tested through simulations of a ququad (d=4) and a quoct (d=8). The third framework employs the full Weyl basis, enabling it to identify all types of XYZ-dephasing noise. The simulations for this framework have been conducted for a quoct (d=8) implemented by the Antimony atom. The analytical protocol for noise spectroscopy that has been introduced transforms qudit systems into quantum spectators, and the presented simulations demonstrate the accuracy and reliability of this noise spectroscopy protocol.

DOI
10.1103/drc2-8qbg

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Quantum noise spectroscopy is a well-known method for detecting environmental noise spectrum and has various applications in quantum sensing, quantum network design, and quantum computing. In this work, a protocol for quantum noise spectroscopy by qudit spectators (arbitrary d-level quantum systems) is presented for noises with stochastic and stationary Gaussian distributions. The protocol uses Weyl basis decomposition, consisting of generalized Pauli matrices, as the theoretical tool, and the Alvarez-Suter noise spectroscopy method, by which the qudit is being exposed to a series of pulse sequences, and the noise polyspectra is extracted by multiple measurements of an observable of the qudit. The formalism is further developed and simulated for three theoretical frameworks: The first two frameworks utilize a simplified Weyl basis and are capable of detecting Z-type dephasing noise. One is specifically modeled for a qutrit (d=3), and the second framework is designed for all qudits and has been tested through simulations of a ququad (d=4) and a quoct (d=8). The third framework employs the full Weyl basis, enabling it to identify all types of XYZ-dephasing noise. The simulations for this framework have been conducted for a quoct (d=8) implemented by the Antimony atom. The analytical protocol for noise spectroscopy that has been introduced transforms qudit systems into quantum spectators, and the presented simulations demonstrate the accuracy and reliability of this noise spectroscopy protocol.
Qubit noise spectroscopy (QNS) is a valuable tool for both the characterization of a qubit's environment and as a precursor to more effective qubit control to improve qubit fidelities. Existing approaches to QNS are what the classical spectrum estimation literature would call "non-parametric" approaches, in that a series of probe sequences are used to estimate noise power at a set of points or bands. In contrast, model-based approaches to spectrum estimation assume additional structure in the form of the spectrum and leverage this for improved statistical accuracy or other capabilities, such as superresolution. Here, we derive model-based QNS approaches using inspiration from classical signal processing, primarily though the recently developed Schrodinger wave autoregressive moving-average (SchWARMA) formalism for modeling correlated noise. We show, through both simulation and experimental data, how these model-based QNS approaches maintain the statistical and computational benefits of their classical counterparts, resulting in powerful new estimation approaches. Beyond the direct application of these approaches to QNS and quantum sensing, we anticipate that the flexibility of the underlying models will find utility in adaptive feedback control for quantum systems, in analogy with their role in classical adaptive signal processing and control.
We introduce multipulse quantum noise spectroscopy protocols for spectral estimation of the noise affecting multiple qubits coupled to Gaussian dephasing environments including both classical and quantum sources. Our protocols are capable of reconstructing all the noise auto- and cross-correlation spectra entering the multiqubit dynamics, providing access, in particular, to the asymmetric spectra associated with nonclassical environments. Our result relies on (i) an exact analytic solution for the reduced multiqubit dynamics that holds in the presence of an arbitrary Gaussian environment and dephasing-preserving control; (ii) the use of specific timing symmetries, which allow for a frequency comb to be engineered for all filter functions of interest, and for the spectra to be related to experimentally accessible observables. We show that quantum spectra have distinctive dynamical signatures, which we explore in two paradigmatic open-system models describing spin and charge qubits coupled to bosonic environments. Complete noise spectroscopy is demonstrated numerically in a realistic setting consisting of two-exciton qubits coupled to a phonon bath. The estimated spectra allow us to accurately predict the exciton dynamics as well as extract the temperature and spectral density of the quantum environment.
Qubit noise spectroscopy is an important tool for the experimental investigation of open quantum systems. However, conventional techniques for noise spectroscopy are time-consuming, because they require measurements of the noise spectral density at many different frequencies. Here we describe an alternative approach to noise spectroscopy, which requires fewer resources, and relies on direct measurement of arbitrary linear functionals of the noise spectral density. This method uses random pulse sequences with carefully controlled correlations, which are chosen using algorithms for phase retrieval. These measurements allow us to reconstruct sparse noise spectra via compressed sensing. Our simulations of the performance of the random pulse sequences on a realistic physical system, self-assembled quantum dots, reveal a speedup of an order of magnitude in extracting the noise spectrum, compared to conventional dynamical decoupling approaches.
Random pulse sequences are a powerful method for qubit noise spectroscopy, enabling efficient reconstruction of sparse noise spectra. Here, we advance this method in two complementary directions. First, we extend the method using a regularizer based on the total generalized variation (TGV) norm, in order to reconstruct a larger class of noise spectra, namely piecewise-linear noise spectra, which more realistically model many physical systems. We show through numerical simulations that the new method resolves finer spectral features, while maintaining an order-of-magnitude speedup over conventional approaches to noise spectroscopy. Second, we simplify the experimental implementation of the method, by introducing Rademacher measurements for reconstructing sparse noise spectra. These measurements use pseudorandom pulse sequences that can be generated in real time from a short random seed, reducing experimental complexity without compromising reconstruction accuracy. Together, these developments broaden the reach of random pulse sequences for accurate and efficient noise characterization in realistic quantum systems.
Understanding the physical origin of noise affecting quantum systems is important for nearly every quantum application. While quantum noise spectroscopy has been employed in various quantum systems, such as superconducting qubits and trapped ions, traditional spectroscopy methods are usually efficient in measuring noise spectra with mostly monotonically decaying contributions. However, there are important scenarios in which the noise spectrum is broadband and non-monotonous, thus posing a challenge to existing noise spectroscopy schemes.Here, we compared several methods for noise spectroscopy: spectral decomposition based on the CPMG sequence, the recently presented DYSCO sequence and a modified DYSCO sequence with a Gaussian envelope (gDYSCO).The performance of the sequences is quantified by analytic and numeric determination of the frequency resolution, bandwidth and sensitivity, revealing a supremacy of gDYSCO to reconstruct non-trivial features.Utilizing an ensemble of nitrogen-vacancy centres in diamond coupled to a high density 13C nuclear spin environment, we experimentally confirm our findings.The combination of the presented schemes offers potential to record high quality noise spectra as a prerequisite to generate quantum systems unlimited by their spin-bath environment.
A qubit subjected to pure dephasing due to classical Gaussian noise can be turned into a spectrometer of this noise by utilizing its readout under properly chosen dynamical decoupling (DD) sequences to reconstruct the power spectral density of the noise. We review the theory behind this DD-based noise spectroscopy technique, paying special attention to issues that arise when the environmental noise is non-Gaussian and/or it has truly quantum properties. While we focus on the theoretical basis of the method, we connect the discussed concepts with specific experiments, and provide an overview of environmental noise models relevant for solid-state based qubits, including quantum-dot based spin qubits, superconducting qubits, and NV centers in diamond.