Optimally band-limited spectroscopy of control noise using a qubit sensor

Norris, Leigh; Lucarelli, Dennis; Frey, Virginia; Mavadia, Sandeep; Biercuk, Michael J.; Viola, Lorenza

doi:10.1103/physreva.98.032315

Cited by 40 publications

(54 citation statements)

References 57 publications

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“…, as predicting each inner product χ k is Figure 8. The posterior Gaussian Process and true spectrum for a 1/f α model (21), demonstrating that the Gaussian Process formalism does not consider the additional structure provided by the spectral model. For this simulation, each experiment was repeated N=50 times and α was chosen uniformly at random in the interval [1/2,1].…”

Section: Small Data: Hyperparameterized Nonlinear Regressionmentioning

confidence: 99%

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Bayesian quantum noise spectroscopy

et al. 2018

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As commonly understood, the noise spectroscopy problem-characterizing the statistical properties of a noise process affecting a quantum system by measuring its response-is mathematically ill-posed, in the sense that no unique noise process leads to a set of responses unless extra assumptions are taken into account. Ad-hoc solutions assume an implicit structure, which is often never determined. Thus, it is unclear when the method will succeed or whether one should trust the solution obtained. Here, we propose to treat the problem from the point of view of statistical estimation theory. We develop a Bayesian solution to the problem which allows one to easily incorporate assumptions which render the problem solvable. We compare several numerical techniques for noise spectroscopy and find the Bayesian approach to be superior in many respects. initial states, to apply suitable control sequences, and to measure a set of convenient observables. The main difficulty is that noise correlations influence the dynamics of the quantum system in a highly nonlinear way. Thus, inferring these correlations in detail from the response of the quantum system is generally an ill-posed problem, unless a priori information on the noise is assumed. Even when standard assumptions, such as Gaussian noise or a dephasing coupling are satisfied, the problem remains nonlinear and inverting it carries along a set of non-trivial complications that in turn constrain the type of noise that can be characterized. For example, in [8-12] a control-induced frequency comb approach is used in order to overcome the nonlinear character of the problem but it comes at the cost of being only effective when the noise correlations are smooth functions in frequency space.We propose that many of these problems can be ameliorated, or at least properly quantified, using a statistically principled approach. Within the statistical phrasing of the problem we provide a Bayesian solution [17], complete with a numerical implementation. We show the problem can be solved analytically in the limit of large of amounts of experimental data. At the other extreme-the small-data limit-a numerically stable Monte Carlo algorithm [18] approximates the full Bayesian solution. Our two approaches provide a robust solution to the software side of the noise spectroscopy problem, and can be used to improve state-of-the-art spectroscopy protocols [8][9][10][11][12]. These two regimes are schematically depicted in figure 1. Though the physical model we consider is simplified to illustrate the novel aspects of this work, we note that our approach is very versatile. We discuss this later.We summarize the performance of our approach for the large-and small-data limits in section 6, with complete details including all source code in the supplementary material. In the large data limit, our approach can give almost an order of magnitude improvement in performance over state-of-the-art estimation strategies. By contrast, in the small-data regime, we can even achieve two orders of magnitude improv...

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Section: Small Data: Hyperparameterized Nonlinear Regressionmentioning

confidence: 99%

“…These works can thus be seen as complementary 7 . Recent work has utilized Bayesian parameter estimation in trap ion noise spectroscopy experiments [20,21] as well as optomechanical systems [22].Our paper is organized as follows. In section 2 we motivate the problem from a physical perspective.…”

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confidence: 99%

Bayesian quantum noise spectroscopy

et al. 2018

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“…In particular, obtaining a quantitatively accurate characterization of noise is instrumental to validate theoretical modeling and prediction as well as to design physical-layer quantum control strategies that are optimally tailored to realistic time-dependent noise environments. Acquiring this knowledge is the overarching goal of quantum noise spectroscopy (QNS), a body of techniques through which noise spectra or correlation functions are estimated based on measurements of dynamical observables of the quantum system of interest (a single qubit sensor in the simplest case) under appropriately chosen external controls and measurements [2][3][4][5][6][7][8]. In conjunction with algorithmic error mitigation that can be achieved through proper quantum-circuit design and compiling [9,10], spectral properties inferred from QNS are expected to play an important role in enabling near-term intermediate-scale quantum information processors [11].…”

Section: Introductionmentioning

confidence: 99%

“…The fact that sequence repetition also enforces the emergence of a comb structure in all FFs relevant to high-order dephasing spectra offers a direct means to probe non-Gaussian classical as well as quantum bosonic environments [6,41]. Lastly, compared to other DDbased techniques, such as N -pulse Carr-Purcell-Meiboom-Gill spectroscopy [2], the frequency-comb approach is less susceptible to spectral leakage [5], since it takes higher-order harmonics into account in principle.…”

Section: Introductionmentioning

confidence: 99%

Extending comb-based spectral estimation to multiaxis quantum noise

et al. 2019

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We show how to achieve full spectral characterization of general multiaxis additive noise. Our pulsed spectral estimation technique is based on sequence repetition and frequency-comb sampling and is applicable even to models where a large qubit energy-splitting is present (as is typically the case for spin qubits in semiconductors, for example), as long as the noise is stationary and a second-order (Gaussian) approximation to the controlled reduced dynamics is viable. Our new result is crucial to extending the applicability of these protocols, now standard in dephasing-dominated platforms such as silicon-based qubits, to experimental platforms where both T1 and T2 processes are significant, such as superconducting qubits.

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“…Those descriptions usually do not account for other sources of error, such as dephasing, but we know that 1/f-noise severely affects all solid-state devices [28], including quantum dots and superconducting circuits. There have been some experimental attempts at characterizing noise sources outside actual circuits, directly exploring the dynamics of the quantum scatterer using time-resolved methods [29][30][31][32][33][34][35][36][37][38][39][40] or Fourier transform spectroscopy [41][42][43][44][45][46]. Those detailed studies require time-resolved measurements and direct control of the quantum scatterer in many cases, something which may be unfeasible or undesirable in waveguide-QED setups.…”

Section: Introductionmentioning

confidence: 99%

Correlated dephasing noise in single-photon scattering

Ramos

García-Ripoll

2018

New J. Phys.

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We develop a theoretical framework to describe the scattering of photons against a two-level quantum emitter with arbitrary correlated dephasing noise. This is particularly relevant to waveguide-QED setups with solid-state emitters, such as superconducting qubits or quantum dots, which couple to complex dephasing environments in addition to the propagating photons along the waveguide. Combining input-output theory and stochastic methods, we predict the effect of correlated dephasing in single-photon transmission experiments with weak coherent inputs. We discuss homodyne detection and photon counting of the scattered photons and show that both measurements give the modulus and phase of the single-photon transmittance despite the presence of noise and dissipation. In addition, we demonstrate that these spectroscopic measurements contain the same information as standard time-resolved Ramsey interferometry, and thus they can be used to fully characterize the noise correlations without direct access to the emitter. The method is exemplified with paradigmatic correlated dephasing models such as colored Gaussian noise, white noise, telegraph noise, and 1/fnoise, as typically encountered in solid-state environments.quantum emitter in addition to the dissipative dynamics due to the coupling to photons in the waveguide. We then relate the correlations in that noise to the average scattering matrix of individual photons and coherent wavepackets, and develop strategies to extract those correlations from actual experiments, in conjunction with earlier approaches to scattering tomography [49].The paper and our main results are organized as follows. In section 2 we introduce the model for a noisy twolevel emitter in a waveguide. We describe dephasing noise as a stationary stochastic process Δ(t) and derive the stochastic input-output equations. In section 3, we review the standard procedure of Ramsey interferometry and show how to quantify the noise correlations via the Ramsey envelope C f (t). We also introduce paradigmatic correlated noise models, which will be essential to understand the scattering results in the next sections. In particular, section 4 shows that the same information provided by Ramsey spectroscopy can be obtained from single-photon scattering experiments, where we only manipulate the qubit through the scattered photons. We solve the stochastic input-output equations for a qubit that interacts with a single propagating photon, and show that the averaged single-photon scattering matrix can be related one-to-one to the Ramsey envelope. We also discuss analytical predictions for scattering under realistic dephasing models such as colored Gaussian noise and 1/f noise. We show how the noise correlations modify the spectral lineshapes on each case, recovering simple limits such as the Lorentzian profiles that are fitted in most waveguide-QED experiments. Section 5 generalizes these ideas, showing how to measure the averaged scattering matrix using weak coherent state inputs together with homodyne or photon countin...

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Optimally band-limited spectroscopy of control noise using a qubit sensor

Cited by 40 publications

References 57 publications

Bayesian quantum noise spectroscopy

Bayesian quantum noise spectroscopy

Extending comb-based spectral estimation to multiaxis quantum noise

Correlated dephasing noise in single-photon scattering

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