QOC — Filter functions & noise-tailored control

Accurate noise spectroscopy using quantum sensing ensembles

2026-09-15T00:00:00Z

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.

Direct characterization of classical dephasing noise for a qubit

2026-04-28T00:00:00Z

We propose a general method to characterize classical stochastic noise causing qubit dephasing through repetitive Ramsey interferometry measurements (RIMs) on the qubit. Compared to filter-function-based spectroscopy, our method with simpler pulse control is less constrained by probe coherence time and can directly detect arbitrary-order correlation functions of quasistatic noise processes. We show that each RIM with a short evolution time and suitably chosen control pulses directly samples the noise field and the $n$-point correlations of the RIM outcomes are proportional to the $n$-point correlation functions of the noise processes. We demonstrate the method numerically for two representative cases: an Ornstein-Uhlenbeck Gaussian process and a non-Gaussian ensemble of two-level fluctuators. While practical constraints such as readout contrast and sampling cost persist, our method offers a direct route to quasistatic classical noise spectroscopy across diverse platforms.

Control-centric quantum noise spectroscopy of time-ordered polyspectra

2026-04-09T00:00:00Z

Precise environmental-noise characterisation in open quantum systems is a key step toward high-fidelity quantum control and targeted decoherence suppression in computing and sensing applications. Non-parametric quantum noise spectroscopy (QNS) provides a general-purpose, model-agnostic framework for estimating the spectral properties of an environment. The ability to perform such protocols under realistic constraints is key to their practical applicability. Notably, it is important to account for control constraints and understand how they limit the ability to learn about noise correlations as experiment-agnostic objects. We show how adopting a control-centric point of view allows one to recast the noise spectroscopy problem in such a way that (i) the central objects are now the time-ordered polyspectra, (ii) control filter functions are no longer encumbered by time-ordering. In particular, we show that this approach enables the seamless generalisation of frequency-comb QNS protocols to arbitrary control scenarios without introducing additional control symmetries that effectively remove time-ordering from filter functions, improving estimation in typically pathological scenarios. We demonstrate the targeted reconstruction of the time-ordered polyspectra across classical Gaussian and quantum non-Gaussian environments via simulations.

Robust Parametric Quantum Gate Against Stochastic Time-Varying Noise

2026-03-25T00:00:00Z

The performance of quantum processors in the noisy intermediate-scale quantum (NISQ) era is severely constrained by environmental noise and other uncertainties. While the recently proposed quantum control robustness landscape (QCRL) offers a powerful framework for generating robust control pulses for parametric gate families, its application has been practically restricted to quasi-static noise. To address the spectrally complex, time-varying noise prevalent in reality, we propose filter function-enhanced QCRL (FF-QCRL), which integrates filter function formalism into the QCRL framework. The resulting FF-QCRL algorithm minimizes a generalized robustness metric that faithfully encodes the impact of stochastic processes, enabling robust pulse-family generation for parametric gates under realistic time-varying noise. Numerical validation in a representative single-qubit setting confirms the effectiveness of the proposed method.

Superresolution in Quantum Noise Spectroscopy via Filter Design

2026-02-11T00:00:00Z

Resolving signals with closely spaced frequencies is central to applications in communications, spectroscopy and sensing. Recent results have shown that quantum sensing protocols can exhibit superresolution, the ability to discriminate between spectral lines with arbitrarily small frequency separation. Here, we revisit this problem from the perspective of quantum control theory, utilizing the filter function formalism to derive general, analytic conditions on quantum control protocols for achieving superresolution. Building on these conditions, we develop an optimal control framework, the utility of which is demonstrated through numerical identification of superresolution control protocols in the presence of realistic, experimentally-relevant constraints. We further extend our results to entangled initial states and assess their potential advantage. Our approach is broadly applicable to a wide variety of quantum sensing platforms, and it provides a systematic path to discover novel protocols that surpass conventional resolution limits in these systems.

Resource-Efficient Noise Spectroscopy for Generic Quantum Dephasing Environments

2026-01-26T00:00:00Z

We present a resource-efficient method based on repetitive weak measurements to directly measure the noise spectrum of a generic quantum environment that causes qubit phase decoherence. The weak measurement is induced by a Ramsey interferometry measurement (RIM) on the qubit and periodically applied during the free evolution of the environment. We prove that the measurement correlation of such repetitive RIMs approximately corresponds to a direct sampling of the noise correlation function, thus enabling direct noise spectroscopy of the environment. Compared to dynamical-decoupling-based noise spectroscopy, this method can efficiently measure the full noise spectrum with the detected frequency range not limited by qubit coherence time. This method is also more resource-efficient than the correlation spectroscopy, as for the same detection accuracy with $N$ sampling times, it takes total detection time $O(N)$ while the latter one takes time $O(N^2)$. We numerically demonstrate this method for both bosonic and spin baths.

Quantum Noise Spectroscopy of Nanoscale Charge Defects in Silicon Carbide at Room Temperature

2025-12-27T00:00:00Z

The nanoscale charge environment critically influences semiconductor physics and device performance. While conventional bulk characterization techniques provide volume-averaged defect properties, they lack the spatial resolution to resolve nanoscale charge heterogeneity and identify microscopic noise sources. Here, we utilize single PL5 centers in 4H-SiC as room-temperature broadband quantum sensors to fill in the gap. We report the first real-time, nanoscale observation of singlecharge tunneling dynamics in a commercial semiconductor at room temperature, by monitoring the random telegraph noise using optically detected magnetic resonance (ODMR). This capability enables an electrical noise imaging technique, showing distinct noise variations across different wafer substrates. By employing dynamical decoupling, we extend noise spectroscopy from near-DC to MHz frequencies, uncovering significant noise spectral density correlations across frequency bands. Finally, we probe MHz-GHz noise and identify its origin via T1 relaxation spectroscopy, obtaining the first nanoscale electron paramagnetic resonance (EPR) spectroscopic fingerprint of charge defects in SiC. These techniques open avenues for characterizing noise environments in semiconductor devices, providing critical insights for optimizing SiC fabrication processes, defect control, and advancing quantum technologies.

Group-Theoretic Reinforcement Learning of Dynamical Decoupling Sequences

2025-12-15T00:00:00Z

Dynamical decoupling seeks to mitigate phase decoherence in qubits by applying a carefully designed sequence of effectively instantaneous electromagnetic pulses. Although analytic solutions exist for pulse timings that are optimal under specific noise regimes, identifying the optimal timings for a realistic noise spectrum remains challenging. We propose a reinforcement learning (RL)-based method for designing pulse sequences on qubits. Our novel action set enables the RL agent to efficiently navigate this inherently non-convex optimization landscape. The action set, derived from Thompson's group $F$, is applicable to a broad class of sequential decision problems whose states can be represented as bounded sequences. We demonstrate that our RL agent can learn pulse sequences that minimize dephasing without requiring explicit knowledge of the underlying noise spectrum. This work opens the possibility for real-time learning of optimal dynamical decoupling sequences on qubits which are dephasing-limited. The model-free nature of our algorithm suggests that the agent may ultimately learn optimal pulse sequences even in the presence of unmodeled physical effects, such as pulse errors or non-Gaussian noise.

Non-Gaussian Noise Magnetometry Using Local Spin Qubits

2025-05-06T00:00:00Z

Atomic scale qubits, as may be realized in nitrogen vacancy (NV) centers in diamond, offer the opportunity to study magnetic field noise with nanometer scale spatial resolution. Using these spin qubits, one can learn a great deal about the magnetic-field noise correlations, and correspondingly the collective-mode spectra, in quantum materials and devices. However, to date these tools have been essentially restricted to studying Gaussian noise processes -- equivalent to linear-response. In this work we will show how to extend these techniques beyond the Gaussian regime and show how to unambiguously measure higher-order magnetic noise cumulants in a local, spatially resolved way. We unveil two protocols for doing this; the first uses a single spin-qubit and different dynamical decoupling sequences to extract non-Markovian and non-Gaussian spin-echo noise. The second protocol uses two-qubit coincidence measurements to study spatially non-local cumulants in the magnetic noise. We then demonstrate the utility of these protocols by considering a model of a bath of non-interacting two-level systems, as well as a model involving spatially correlated magnetic fluctuations near a second-order Ising phase transition. In both cases, we highlight how this technique can be used to measure in a real many-body system how fluctuation dynamics converge towards the central limit theorem as a function of effective bath size. We then conclude by discussing some promising applications and extensions of this method.

Quantum speed limits in dephasing dynamics of a qubit system coupled to thermal environments

2025-03-25T00:00:00Z

We theoretically study the quantum speed limits (QSLs) of a qubit system coupled to a thermal dephasing environment with an Ohmic-like spectral density. Based on the geometric QSLs time bound, which is derived by employing the trace distance to quantify the geodesic between two distinguishable states in dynamical evolution, we study the influences of the temperature and spectral density of the environment on the QSLs time of the dephasing qubit. We also investigate the interplay between the QSLs time, the environmental temperature, and the spectral density of the environment. It has been demonstrated that, the QSLs time closely depends on the transition frequency and the dynamical behavior (e.g., coherence trapping) of the dephasing qubit. For a fixed Ohmicity parameter of the environmental spectral density, the increase of environmental temperature can enhance the QSLs time bound. In addition, when the environmental temperature remains constant, the increase in the Ohmicity parameter initially leads to a reduction in the QSLs time bound, which is then followed by an increase of the time bound of QSLs. Our results can help to better understand the QSLs in the dynamics of open quantum systems and have potential application in the modulation of QSLs time in the dephasing qubit by engineering the spectral density of the environment.

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

2025-03-17T00:00:00Z

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.

Spectrum analysis with parametrically modulated transmon qubits

2025-03-07T00:00:00Z

Exploring the noise spectrum impacting a qubit and extending its coherence duration are fundamental components of quantum technologies. In this study, we introduce parametric spectroscopy, a method that merges parametric modulation of a qubit's energy gap with dynamical decoupling sequences. The parametric modulation provides high sensitivity to extensive regions of the noise spectrum, while dynamical decoupling reduces the effect of driving noise. Our theoretical study shows that parametric spectroscopy enables access to the difficult high-frequency domain of the flux spectrum in transmons.

Expedited Noise Spectroscopy of Transmon Qubits

2025-02-02T00:00:00Z

There has been tremendous progress in the physical realization of quantum computing hardware in recent times, bringing us closer than ever before to realizing the promise of quantum computing. However, noise continues to pose a crucial challenge when it comes to scaling up present day quantum processors. While decoherence limits the qubits ability to store information for long periods in the presence of uncontrollable noise sources, the erroneous implementation of control methods for state preparation and measurements leads to faulty implementations of quantum circuits. Conventional noise spectroscopy protocols can characterize and model environmental noise but are usually resource intensive and lengthy. Moreover, the underlying noise can vary in nature over time, making noise profile extraction futile as this new information cannot be harnessed to improve quantum error correction or dynamical decoupling protocols. In this work, we address this challenge using a machine learning-based methodology to quickly extract noise spectra of multiple qubits and demonstrate a possible noise mitigation strategy. The procedure involves implementing undemanding dynamical decoupling sequences to record coherence decays of the investigated qubits and then predict the underlying noise spectra with the help of a convolution neural network pre-trained on a synthetic dataset. While our protocol is virtually hardware-agnostic, we validate its effectiveness using superconducting qubits available on the IBM Quantum platform. We further use these rapidly obtained, yet accurate, noise spectra to design bespoke dynamic decoupling sequences and perform time-dependent noise spectroscopy.

Fast, accurate, and error-resilient variational quantum noise spectroscopy

2024-11-26T00:00:00Z

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.

Model-Based Qubit Noise Spectroscopy

2024-05-20T00:00:00Z

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.

Qubit fidelity under stochastic Schrödinger equations driven by colored noise

2024-01-22T00:00:00Z

Environmental noise on a controlled quantum system is generally modeled by a dissipative Lindblad equation. This equation describes the average state of the system via the density matrix $ρ$. One way of deriving this Lindblad equation is by introducing a stochastic operator evolving under white noise in the Schrödinger equation. However, white noise, where all noise frequencies contribute equally in the power spectral density, is not a realistic noise profile as lower frequencies generally dominate the spectrum. Furthermore, the Lindblad equation does not fully describe the system as a density matrix $ρ$ does not uniquely describe a probabilistic ensemble of pure states $\{ψ_j\}_j$. In this work, we introduce a method for solving for the full distribution of qubit fidelity driven by important stochastic Schrödinger equation cases, where qubits evolve under more realistic noise profiles, e.g. Ornstein-Uhlenbeck noise. This allows for predictions of the mean, variance, and higher-order moments of the fidelities of these qubits, which can be of value when deciding on the allowed noise levels for future quantum computing systems, e.g. deciding what quality of control systems to procure. Furthermore, these methods will prove to be integral in the optimal control of qubit states under (classical) control system noise.

Open-loop quantum control of small-size networks for high-order cumulants and cross-correlations sensing

2024-01-11T00:00:00Z

Quantum control techniques represent one of the most efficient tools to attain high-fidelity quantum operations and a convenient approach for quantum sensing and quantum noise spectroscopy. In this work, we investigate dynamical decoupling while processing an entangling two-qubit gate based on an Ising-xx interaction, each qubit being affected by pure dephasing classical correlated 1/ f -noises. To evaluate the gate error, we used the Magnus expansion introducing generalized filter functions that describe decoupling while processing and allow us to derive an approximate analytic expression as a hierarchy of nested integrals of noise cumulants. The error is separated in contributions of Gaussian and non-Gaussian noise, the corresponding generalized filter functions being calculated up to the fourth order. By exploiting the properties of selected pulse sequences, we show that it is possible to extract the second-order statistics (spectrum and cross-spectrum) and to highlight non-Gaussian features contained in the fourth-order cumulant. We discuss the applicability of these results to state-of-the-art small networks based on solid-state platforms.

Characterizing the magnetic noise power spectrum of dark spins in diamond

2023-12-19T00:00:00Z

Coherence times of spin qubits in solid-state platforms are often limited by the presence of a spin bath. While some properties of these typically dark bath spins can be indirectly characterized via the central qubit, it is important to characterize their properties by direct measurement. Here we use pulsed electron paramagnetic resonance (pEPR) based Carr-Purcell-Meiboom-Gill (CPMG) dynamical decoupling to measure the magnetic noise power spectra for ensembles of P1 (substitutional nitrogen) centers in diamond that typically form the bath for NV (nitrogen-vacancy) centers. The experiments on the P1 centers were performed on a low [N] CVD (chemical vapor deposition) sample and a high [N] HPHT (high-temperature, high-pressure) sample at 89 mT. We characterize the NV centers of the latter sample using the same 2.5 GHz pEPR spectrometer. All power spectra show two distinct features, a broad component that is observed to scale as approximately $1/ω^{0.7-1.0}$, and a prominent peak at the $^{13}$C Larmor frequency. The behavior of the broad component is consistent with an inhomogeneous distribution of Lorentzian spectra due to clustering of P1 centers, which has recently been shown to be prevalent in HPHT diamond. It is unknown if such clustering occurs in CVD diamond. We develop techniques utilizing harmonics of the CPMG filter function to improve characterization of high-frequency signals, which we demonstrate on the $^{13}$C nuclear Larmor frequency. At 190 mT this is 2.04 MHz, 5.7 times higher than the CPMG modulation frequency ($<357$ kHz, hardware-limited). We assess the robustness of our methods in the presence of finite pulse widths and flip angle errors. Understanding the interactions of dark spins will inform methods of diamond fabrication for quantum technology. These techniques are applicable to ac magnetometry for nanoscale nuclear magnetic resonance and chemical sensing.

Decoherence reduction via continuous dynamical decoupling: Analytical study of the role of the noise spectrum

2023-11-14T00:00:00Z

We analyze the robust character against non-static noise of clock transitions implemented via a method of continuous dynamical decoupling (CDD) in a hyperfine Zeeman multiplet in ^{87}\textrm{Rb}. The emergence of features specific to the quadratic corrections to the linear Zeeman effect is evaluated. Our analytical approach, which combines methods of stochastic analysis with time-dependent perturbation theory, allows tracing the decoherence process for generic noise sources. Working first with a basic CDD scheme, it is shown that the amplitude and frequency of the (driving) field of control can be appropriately chosen to force the non-static random input to have a (time-dependent) perturbative character. Moreover, in the dressed-state picture, the effect of noise is described in terms of an operative random variable whose properties, dependent on the driving field, can be analytically characterized. In this framework, the relevance of the spectral density of the fluctuations to the performance of the CDD technique is precisely assessed. In particular, the range of noise correlation times where the method of decoherence reduction is still efficient is identified. The results obtained in the basic CDD framework are extrapolated to concatenated schemes. The generality of our approach allows its applicability beyond the specific atomic system considered.

Resource-efficient digital characterization and control of classical non-Gaussian noise

2023-04-07T00:00:00Z

We show the usefulness of frame-based characterization and control [PRX Quantum 2, 030315 (2021)] for non-Markovian open quantum systems subject to classical non-Gaussian dephasing. By focusing on the paradigmatic case of random telegraph noise and working in a digital window frame, we demonstrate how to achieve higher-order control-adapted spectral estimation for noise-optimized dynamical decoupling design. We find that, depending on the operating parameter regime, control that is optimized based on non-Gaussian noise spectroscopy can substantially outperform standard Walsh decoupling sequences as well as sequences that are optimized based solely on Gaussian noise spectroscopy. This approach is also intrinsically more resource-efficient than frequency-domain comb-based methods.

Measuring the environment of a Cs qubit with dynamical decoupling sequences

2023-03-13T00:00:00Z

We report the experimental implementation of dynamical decoupling on a small, non-interacting ensemble of up to 25 optically trapped, neutral Cs atoms. The qubit consists of the two magnetic-insensitive Cs clock states $\left| F=3, m_F=0 \right>$ and $\left|F=4, m_F=0\right>$, which are coupled by microwave radiation. We observe a significant enhancement of the coherence time when employing Carr-Purcell-Meiboom-Gill (CPMG) dynamical decoupling. A CPMG sequence with ten refocusing pulses increases the coherence time of 16.2(9) ms by more than one order of magnitude to 178(2) ms. In addition, we make use of the filter function formalism and utilize the CPMG sequence to measure the background noise floor affecting the qubit coherence, finding a power-law noise spectrum $1/ω^α$ with $\mathitα = 0.89(2)$. This finding is in very good agreement with an independent measurement of the noise in the intensity of the trapping laser. Moreover, the measured coherence evolutions also exhibit signatures of low-frequency noise originating at distinct frequencies. Our findings point toward noise spectroscopy of engineered atomic baths through single-atom dynamical decoupling in a system of individual Cs impurities immersed in an ultracold $^{87}$Rb bath.

Accessing the Full Capabilities of Filter Functions: A Tool for Detailed Noise and Control Susceptibility Analysis

2023-03-03T00:00:00Z

The filter function formalism from quantum control theory is typically used to determine the noise susceptibility of pulse sequences by looking at the overlap between the filter function of the sequence and the noise power spectral density. Importantly, the square modulus of the filter function is used for this method, hence directional and phase information is lost. In this work, we take advantage of the full filter function including directional and phase information. By decomposing the filter function with phase preservation before taking the modulus, we are able to consider the contributions to $x$-, $y$- and $z$-rotation separately. Continuously driven systems provide noise protection in the form of dynamical decoupling by cancelling low-frequency noise, however, generating control pulses synchronously with an arbitrary driving field is not trivial. Using the decomposed filter function we look at the controllability of a system under arbitrary driving fields, as well as the noise susceptibility, and also relate the filter function to the geometric formalism.

Random Pulse Sequences for Qubit Noise Spectroscopy

2023-03-02T00:00:00Z

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.

Deep learning enhanced noise spectroscopy of a spin qubit environment

2023-01-12T00:00:00Z

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 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. Neural networks 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.

Digital noise spectroscopy with a quantum sensor

2022-12-19T00:00:00Z

We introduce and experimentally demonstrate a quantum sensing protocol to sample and reconstruct the auto-correlation 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 auto-correlation 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 the sampling and discretization in the time space and can be easily improved, even under limited evolution time due to decoherence and hardware limitations. Finally, we experimentally reconstruct the auto-correlation 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 for further improving the reconstruction accuracy.

Fourier Transform Noise Spectroscopy

2022-10-01T00:00:00Z

Spectral characterization of noise environments that lead to the decoherence of qubits is critical to developing robust quantum technologies. While dynamical decoupling offers one of the most successful approaches to characterize noise spectra, it necessitates applying large sequences of $π$ pulses that increase the complexity and cost of the method. Here, we introduce a noise spectroscopy method that utilizes only the Fourier transform of free induction decay or spin echo measurements, thus removing the need for the application many $π$ pulses. We show that our method faithfully recovers the correct noise spectra for a variety of different environments (including $1/f$-type noise) and outperforms previous dynamical decoupling schemes while significantly reducing their experimental overhead. We also discuss the experimental feasibility of our proposal and demonstrate its robustness in the presence of statistical measurement error. Our method is applicable to a wide range of quantum platforms and provides a simpler path toward a more accurate spectral characterization of quantum devices, thus offering possibilities for tailored decoherence mitigation.

Full-permutation dynamical decoupling in triple-quantum-dot spin qubits

2022-08-24T00:00:00Z

Dynamical decoupling of spin qubits in silicon can enhance fidelity and be used to extract the frequency spectra of noise processes. We demonstrate a full-permutation dynamical decoupling technique that cyclically exchanges the spins in a triple-dot qubit. This sequence not only suppresses both low frequency charge-noise- and magnetic-noise-induced errors; it also refocuses leakage errors to first order, which is particularly interesting for encoded exchange-only qubits. For a specific construction, which we call NZ1y, the qubit is isolated from error sources to such a degree that we measure a remarkable exchange pulse error of $5\times10^{-5}$. This sequence maintains a quantum state for roughly 18,000 exchange pulses, extending the qubit coherence from $T_2^*=2~μ$s to $T_2 = 720~μ$s. We experimentally validate an error model that includes $1/f$ charge noise and $1/f$ magnetic noise in two ways: by direct exchange-qubit simulation, and by integration of the assumed noise spectra with derived filter functions, both of which reproduce the measured error and leakage with respect to changing the repetition rate.

Optimally Band-Limited Noise Filtering for Single Qubit Gates

2022-06-07T00:00:00Z

We introduce a quantum control protocol that produces smooth, experimentally implementable control sequences optimized to combat temporally correlated noise for single qubit systems. The control ansatz is specifically chosen to be a functional expansion of discrete prolate spheroidal sequences, a discrete time basis known to be optimally concentrated in time and frequency, and quite attractive when faced with experimental control hardware constraints. We leverage the filter function formalism to transform the control problem into a filter design problem, and show that the frequency response of a quantum system can be carefully tailored to avoid the most relevant dynamical contributions of noise processes. Using gradient ascent, we obtain optimized filter functions and exploit them to elucidate important details about the relationship between filter function design, control bandwidth, and noise characteristics. In particular, we identify regimes of optimal noise suppression and in turn, optimal control bandwidth directly proportional to the size of the frequency bands where the noise power is large. In addition to providing guiding principles for filter design, our approach enables the development of controls that simultaneously yield robust noise filtering and high fidelity single qubit logic operations in a wide variety of complex noise environments.

Quantum Control for Time-dependent Noise by Inverse Geometric Optimization

2022-05-05T00:00:00Z

Quantum systems are exceedingly difficult to engineer because they are sensitive to various types of noises. In particular, time-dependent noises are frequently encountered in experiments but how to overcome them remains a challenging problem. In this work, we extend and apply the recently proposed robust control technique of inverse geometric optimization to time-dependent noises by working it in the filter-function formalism. The basic idea is to parameterize the control filter function geometrically and minimize its overlap with the noise spectral density. This then effectively reduces the noise susceptibility of the controlled system evolution. We show that the proposed method can produce high-quality robust pulses for realizing desired quantum evolutions under realistic noise models, and thus will find practical applications for current physical platforms.

Quantum Control Noise Spectroscopy with Optimal Suppression of Dephasing

2022-04-22T00:00:00Z

We extend quantum noise spectroscopy (QNS) of amplitude control noise to settings where dephasing noise or detuning errors make significant contributions to qubit dynamics. Previous approaches to characterize amplitude noise are limited by their vulnerability to low-frequency dephasing noise and static detuning errors, which can overwhelm the target control noise signal and introduce bias into estimates of the amplitude noise spectrum. To overcome this problem, we leverage optimal control to identify a family of amplitude control waveforms that optimally suppress low-frequency dephasing noise and detuning errors, while maintaining the spectral concentration in the amplitude filter essential for spectral estimation. The waveforms found via numerical optimization have surprisingly simple analytic forms, consisting of oscillating sine waves obeying particular amplitude and frequency constraints. In numerically simulated QNS experiments, these waveforms demonstrate superior robustness, enabling accurate estimation of the amplitude noise spectrum in regimes where existing approaches are biased by low-frequency dephasing noise and detuning errors.