Realistic Noise Model Research Articles

Noise-induced barren plateaus in variational quantum algorithms

Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.

Cosmology from clustering, cosmic shear, CMB lensing, and cross correlations: combining Rubin observatory and Simons Observatory

ABSTRACT In the near future, the overlap of the Rubin Observatory Legacy Survey of Space and Time (LSST) and the Simons Observatory (SO) will present an ideal opportunity for joint cosmological data set analyses. In this paper, we simulate the joint likelihood analysis of these two experiments using six two-point functions derived from galaxy position, galaxy shear, and CMB lensing convergence fields. Our analysis focuses on realistic noise and systematics models and we find that the dark energy Figure of merit (FoM) increases by 53 per cent (92 per cent) from LSST-only to LSST+SO in Year 1 (Year 6). We also investigate the benefits of using the same galaxy sample for both clustering and lensing analyses, and find the choice improves the overall signal to noise by ${\sim}30{-}40{{\ \rm per\ cent}}$, which significantly improves the photo-z calibration and mildly improves the cosmological constraints. Finally, we explore the effects of catastrophic photo-z outliers finding that they cause significant parameter biases when ignored. We develop a new mitigation approach termed ‘island model’, which corrects a large fraction of the biases with only a few parameters while preserving the constraining power.

Investigation of effect of modulation frequency on high-density diffuse optical tomography image quality.

.Significance: By incorporating multiple overlapping functional near-infrared spectroscopy (fNIRS) measurements, high-density diffuse optical tomography (HD-DOT) images human brain function with fidelity comparable to functional magnetic resonance imaging (fMRI). Previous work has shown that frequency domain high-density diffuse optical tomography (FD-HD-DOT) may further improve image quality over more traditional continuous wave (CW) HD-DOT.Aim: The effects of modulation frequency on image quality as obtainable with FD-HD-DOT is investigated through simulations with a realistic noise model of functional activations in human head models, arising from 11 source modulation frequencies between CW and 1000 MHz.Approach: Simulations were performed using five representative head models with an HD regular grid of 158 light sources and 166 detectors and an empirically derived noise model. Functional reconstructions were quantitatively assessed with multiple image quality metrics including the localization error (LE), success rate, full width at half maximum, and full volume at half maximum (FVHM). All metrics were evaluated against CW-based models.Results: Compared to CW, localization accuracy is improved by >40% throughout brain depths of 13 to 25 mm below the surface with 300 to 500 MHz modulation frequencies. Additionally, the reliable field of view in brain tissue is enlarged by 35% to 48% within an optimal frequency of 300 MHz after considering realistic noise, depending on the dynamic range of the system.Conclusions: These results point to the tremendous opportunities in further development of high bandwidth FD-HD-DOT system hardware for applications in human brain mapping.

Selection of optimal external filter for colorimetric camera

A database of realizable filters is created and searched to obtain the best filter that, when placed in front of an existing camera, results in improved colorimetric capabilities for the system. The image data with the external filter is combined with image data without the filter to provide a six-band system. The colorimetric accuracy of the system is quantified using simulations that include a realistic signal-dependent noise model. Using a training data set, we selected the optimal filter based on four criteria: Vora Value, Figure of Merit, training average ΔE, and training maximum ΔE. Each selected filter was used on testing data. The filters chosen using the training ΔE criteria consistently outperformed the theoretical criteria.

Role of correlated noise in textural features extraction.

Predictive models of tumor response based on heterogeneity metrics in medical images, such as textural features, are highly suggestive. However, the demonstrated sensitivity of these features to noise does affect the model being developed. An in-depth analysis of the noise influence on the extraction of texture features was performed based on the assumption that an improvement in information quality can also enhance the predictive model. A heuristic approach was used that recognizes from the beginning that the noise has its own texture and it was analysed how it affects the quantitative signal data. A simple procedure to obtain noise image estimation is shown; one which makes it possible to extract the noise-texture features at each observation. The distance measured between the textural features in signal and estimated noise images allows us to determine the features affected in each observation by the noise and, for example, to exclude some of them from the model. A demonstration was carried out using synthetic images applying realistic noise models found in medical images. Drawn conclusions were applied to a public cohort of clinical images obtained using FDG-PET to show how the predictive model could be improved. A gain in the area under the receiver operating characteristic curve between 10 and 20% when noise texture information is used was shown. An improvement between 20 and 30% can be appreciated in the estimated model quality.

Evaluation of synthetic and experimental training data in supervised machine learning applied to charge-state detection of quantum dots

Automated tuning of gate-defined quantum dots is a requirement for large-scale semiconductor-based qubit initialisation. An essential step of these tuning procedures is charge-state detection based on charge stability diagrams. Using supervised machine learning to perform this task requires a large dataset for models to train on. In order to avoid hand labelling experimental data, synthetic data has been explored as an alternative. While providing a significant increase in the size of the training dataset compared to using experimental data, using synthetic data means that classifiers are trained on data sourced from a different distribution than the experimental data that is part of the tuning process. Here we evaluate the prediction accuracy of a range of machine learning models trained on simulated and experimental data, and their ability to generalise to experimental charge stability diagrams in two-dimensional electron gas and nanowire devices. We find that classifiers perform best on either purely experimental or a combination of synthetic and experimental training data, and that adding common experimental noise signatures to the synthetic data does not dramatically improve the classification accuracy. These results suggest that experimental training data as well as realistic quantum dot simulations and noise models are essential in charge-state detection using supervised machine learning.

Rapid ensemble measurement of protein diffusion and probe blinking dynamics in cells

We present a fluorescence fluctuation image correlation analysis method that can rapidly and simultaneously measure the diffusion coefficient, photoblinking rates, and fraction of diffusing particles of fluorescent molecules in cells. Unlike other image correlation techniques, we demonstrated that our method could be applied irrespective of a nonuniformly distributed, immobile blinking fluorophore population. This allows us to measure blinking and transport dynamics in complex cell morphologies, a benefit for a range of super-resolution fluorescence imaging approaches that rely on probe emission blinking. Furthermore, we showed that our technique could be applied without directly accounting for photobleaching. We successfully employed our technique on several simulations with realistic EMCCD noise and photobleaching models, as well as on Dronpa-C12-labeled β-actin in living NIH/3T3 and HeLa cells. We found that the diffusion coefficients measured using our method were consistent with previous literature values. We further found that photoblinking rates measured in the live HeLa cells varied as expected with changing excitation power.

Average fidelity and fidelity deviation in noisy quantum teleportation

We analyze the average fidelity (say, F) and the fidelity deviation (say, D) in noisy-channel quantum teleportation. Here, F represents how well teleportation is performed on average and D quantifies whether the teleportation is performed impartially on the given inputs, that is, the condition of universality. Our analysis results prove that the achievable maximum average fidelity ensures zero fidelity deviation, that is, perfect universality. This structural trait of teleportation is distinct from those of other limited-fidelity probabilistic quantum operations, for instance, universal-NOT or quantum cloning. This feature is confirmed again based on a tighter relationship between F and D in the qubit case. We then consider another realistic noise model where F decreases and D increases due to imperfect control. To alleviate such deterioration, we propose a machine-learning-based algorithm. We demonstrate by means of numerical simulations that the proposed algorithm can stabilize the system. Notably, the recovery process consists solely of the maximization of F, which reduces the control time, thus leading to a faster cure cycle.

Toward blind joint demosaicing and denoising of raw color filter array data

Raw color-filter-array (CFA) data collected in the real world are often noisy and signal-dependent, which makes it difficult to recover the full-resolution noise-free color image. Denoising and demosaicing are two popular tools developed for noisy CFA data in modern color imaging pipeline. However, most existing works on joint demosaicing and denoising (JDD) are based on ad hoc assumptions about image degradation process; while in practice little is known about noise statistics (e.g., noise level) and processing pipeline (e.g., gamma correction). We advocate a blind formulation of joint demosaicing and denoising (bJDD) problem in this paper and present a novel divide-and-conquer approach toward blind reconstruction from noisy raw CFA data. Instead of making over-simplified assumptions about noise statistics, we propose to develop a more realistic Poisson-Gaussian noise model for simulating noisy raw CFA data in the real world. We also introduce a sub-network to adaptively estimate the noise level map from the noisy input, which will provide supplementary information to the deep model for non-blind JDD. Finally, we have adopted a generative adversarial network (GAN) based network for further perceptual optimization. Our extensive experimental results have shown convincingly improved performance over existing state-of-the-art methods in terms of both subjective and objective quality metrics.

Sensitivity of present and future detectors across the black-hole binary gravitational wave spectrum

Black-holes are known to span at least 9 orders of magnitude in mass: from the stellar-mass objects observed by the Laser Interferometer Gravitational-Wave Observatory Scientific Collaboration and Virgo Collaboration, to supermassive black-holes like the one observed by the Event Horizon Telescope at the heart of M87. Regardless of the mass scale, all of these objects are expected to form binaries and eventually emit observable gravitational radiation, with more massive objects emitting at ever lower gravitational-wave frequencies. We present the tool, gwent, for modeling the sensitivities of current and future generations of gravitational wave detectors across the entire gravitational-wave spectrum of coalescing black-hole binaries (BHBs). We provide methods to generate sensitivity curves for pulsar timing arrays (PTAs) using a novel realistic PTA sensitivity curve generator (Hazboun, Romano and Smith 2019 Phys. Rev. D 100 104028), space-based interferometers using adaptive models that can represent a wide range of proposed detector designs (Amaro-Seoane et al 2017 arXiv:1702.00786), and ground-based interferometers using realistic noise models that can reproduce current (Abbott et al 2016 Phys. Rev. Lett. 116 061102), second, and third generation designs (Hild et al 2011 Class. Quantum Grav. 28 094013), as well as novel variations of the essential design parameters. To model the signal from BHBs at any mass scale, we use phenomenological waveforms capable of modeling the inspiral, merger, and ringdown for sources with varying mass ratios and spins (Khan et al 2016 Phys. Rev. D 93 044007; Husa et al 2016 Phys. Rev. D 93 044006). Using this adaptable framework, we produce signal-to-noise ratios (SNR) for the combination of any modeled parameter, associated with either the detector or the source. By allowing variation across each detector and source parameter, we can pinpoint the most important factors to determining the optimal performance for particular instrument designs. The adaptability of our detector and signal models can easily be extended to new detector designs and other models of gravitational wave signals.

Error Thresholds for Arbitrary Pauli Noise

The error threshold of a one-parameter family of quantum channels is defined as the largest noise level such that the quantum capacity of the channel remains positive. This in turn guarantees the existence of a quantum error correction code for noise modeled by that channel. Discretizing the single-qubit errors leads to the important family of Pauli quantum channels; curiously, multipartite entangled states can increase the threshold of these channels beyond the so-called hashing bound, an effect termed superadditivity of coherent information. In this work, we divide the simplex of Pauli channels into one-parameter families and compute numerical lower bounds on their error thresholds. We find substantial increases of error thresholds relative to the hashing bound for large regions in the Pauli simplex corresponding to biased noise, which is a realistic noise model in promising quantum computing architectures. The error thresholds are computed on the family of graph states, a special type of stabilizer state. In order to determine the coherent information of a graph state, we devise an algorithm that exploits the symmetries of the underlying graph, resulting in a substantial computational speed-up. This algorithm uses tools from computational group theory and allows us to consider symmetric graph states on a large number of vertices. Our algorithm works particularly well for repetition codes and concatenated repetition codes (or cat codes), for which our results provide the first comprehensive study of superadditivity for arbitrary Pauli channels. In addition, we identify a novel family of quantum codes based on tree graphs. The error thresholds of these tree graph states outperform repetition and cat codes in large regions of the Pauli simplex, and hence form a new code family with desirable error correction properties.

Compound Admittance Matrix Estimation of Three-Phase Untransposed Power Distribution Grids Using Synchrophasor Measurements

This article considers the problem of estimating the parameters of the compound admittance matrix of three-phase untransposed low- and medium-voltage electrical distribution networks using synchrophasor measurements from phasor measurement units (PMUs). The work proposes and analyzes the performance of a preprocessing strategy on the PMU's raw measurements, which consists in grouping the raw measurements in clusters and, then, using the averaged measurements from each cluster for admittance matrix estimation. This step reduces the noise level and discards similar measurements from each cluster, ultimately improving the estimation quality of regression-based estimation methods such as least squares (LS) and total least squares (TLS). The proposed approach uses a linear estimation model with phasor measurements of nodal voltages, nodal injection currents, and branch currents. We adopt a realistic measurement noise model in polar coordinates, which reflects the accuracy class of measuring instruments and is projected to rectangular coordinates. The proposed approach is validated by performing simulated experiments for different CIGRE and IEEE benchmark grids. Furthermore, the work includes different sensitivity analyses on the preprocessing policy (cluster type and size), availability of branch or injection currents measurements, as well as with different noise levels on the measurement data.

On the robustness of deep learning-based lung-nodule classification for CT images with respect to image noise

Robustness is an important aspect when evaluating a method of medical image analysis. In this study, we investigated the robustness of a deep learning (DL)-based lung-nodule classification model for CT images with respect to noise perturbations. A deep neural network (DNN) was established to classify 3D CT images of lung nodules into malignant or benign groups. The established DNN was able to predict malignancy rate of lung nodules based on CT images, achieving the area under the curve of 0.91 for the testing dataset in a tenfold cross validation as compared to radiologists’ prediction. We then evaluated its robustness against noise perturbations. We added to the input CT images noise signals generated randomly or via an optimization scheme using a realistic noise model based on a noise power spectrum for a given mAs level, and monitored the DNN’s output. The results showed that the CT noise was able to affect the prediction results of the established DNN model. With random noise perturbations at 100 mAs, DNN’s predictions for 11.2% of training data and 17.4% of testing data were successfully altered by at least once. The percentage increased to 23.4% and 34.3%, respectively, for optimization-based perturbations. We further evaluated robustness of models with different architectures, parameters, number of output labels, etc, and robustness concern was found in these models to different degrees. To improve model robustness, we empirically proposed an adaptive training scheme. It fine-tuned the DNN model by including perturbations in the training dataset that successfully altered the DNN’s perturbations. The adaptive scheme was repeatedly performed to gradually improve DNN’s robustness. The numbers of perturbations at 100 mAs affecting DNN’s predictions were reduced to 10.8% for training and 21.1% for testing by the adaptive training scheme after two iterations. Our study illustrated that robustness may potentially be a concern for an exemplary DL-based lung-nodule classification model for CT images, indicating the needs for evaluating and ensuring model robustness when developing similar models. The proposed adaptive training scheme may be able to improve model robustness.

Noise-resilient variational hybrid quantum-classical optimization

Variational hybrid quantum-classical optimization represents one of the most promising avenue to show the advantage of nowadays noisy intermediate-scale quantum computers in solving hard problems, such as finding the minimum-energy state of a Hamiltonian or solving some machine-learning tasks. In these devices noise is unavoidable and impossible to error-correct, yet its role in the optimization process is not well understood, especially from the theoretical viewpoint. Here we consider a minimization problem with respect to a variational state, iteratively obtained via a parametric quantum circuit, taking into account both the role of noise and the stochastic nature of quantum measurement outcomes. We show that the accuracy of the result obtained for a fixed number of iterations is bounded by a quantity related to the Quantum Fisher Information of the variational state. Using this bound, we study the convergence property of the quantum approximate optimization algorithm under realistic noise models, showing the robustness of the algorithm against different noise strengths.

Coherent transport of spin by adiabatic passage in quantum dot arrays

We introduce an adiabatic transfer protocol for spin states in large quantum dot arrays that is based on time-dependent modulation of the Heisenberg exchange interaction in the presence of a magnetic field gradient. We refer to this protocol as spin-CTAP (coherent transport by adiabatic passage) in analogy to a related protocol developed for charge state transfer in quantum dot arrays. The insensitivity of this adiabatic protocol to pulse imperfections has potential advantages for reading out extended spin qubit arrays. When the static exchange interaction varies across the array, a quantum-controlled version of spin-CTAP is possible, where the transfer process is conditional on the spin states in the middle of the array. This conditional operation can be used to generate N-qubit entangled GHZ states. Using a realistic noise model, we analyze the robustness of the spin-CTAP operations and find that high-fidelity (>95%) spin eigenstate transfer and GHZ state preparation is feasible in current devices.

Towards spaceborne monitoring of localized CO<sub>2</sub> emissions: an instrument concept and first performance assessment

Abstract. The UNFCCC (United Nations Framework Convention on Climate Change) requires the nations of the world to report their carbon dioxide (CO2) emissions. The independent verification of these reported emissions is a cornerstone for advancing towards the emission accounting and reduction measures agreed upon in the Paris Agreement. In this paper, we present the concept and first performance assessment of a compact spaceborne imaging spectrometer with a spatial resolution of 50×50 m2 that could contribute to the “monitoring, verification and reporting” (MVR) of CO2 emissions worldwide. CO2 emissions from medium-sized power plants (1–10 Mt CO2 yr−1), currently not targeted by other spaceborne missions, represent a significant part of the global CO2 emission budget. In this paper we show that the proposed instrument concept is able to resolve emission plumes from such localized sources as a first step towards corresponding CO2 flux estimates. Through radiative transfer simulations, including a realistic instrument noise model and a global trial ensemble covering various geophysical scenarios, it is shown that an instrument noise error of 1.1 ppm (1σ) can be achieved for the retrieval of the column-averaged dry-air mole fraction of CO2 (XCO2). Despite a limited amount of information from a single spectral window and a relatively coarse spectral resolution, scattering by atmospheric aerosol and cirrus can be partly accounted for in the XCO2 retrieval, with deviations of at most 4.0 ppm from the true abundance for two-thirds of the scenes in the global trial ensemble. We further simulate the ability of the proposed instrument concept to observe CO2 plumes from single power plants in an urban area using high-resolution CO2 emission and surface albedo data for the city of Indianapolis. Given the preliminary instrument design and the corresponding instrument noise error, emission plumes from point sources with an emission rate down to the order of 0.3 Mt CO2 yr−1 can be resolved, i.e., well below the target source strength of 1 Mt CO2 yr−1. This leaves a significant margin for additional error sources, like scattering particles and complex meteorology, and shows the potential for subsequent CO2 flux estimates with the proposed instrument concept.

Quantum classifier with tailored quantum kernel

Kernel methods have a wide spectrum of applications in machine learning. Recently, a link between quantum computing and kernel theory has been formally established, opening up opportunities for quantum techniques to enhance various existing machine-learning methods. We present a distance-based quantum classifier whose kernel is based on the quantum state fidelity between training and test data. The quantum kernel can be tailored systematically with a quantum circuit to raise the kernel to an arbitrary power and to assign arbitrary weights to each training data. Given a specific input state, our protocol calculates the weighted power sum of fidelities of quantum data in quantum parallel via a swap-test circuit followed by two single-qubit measurements, requiring only a constant number of repetitions regardless of the number of data. We also show that our classifier is equivalent to measuring the expectation value of a Helstrom operator, from which the well-known optimal quantum state discrimination can be derived. We demonstrate the performance of our classifier via classical simulations with a realistic noise model and proof-of-principle experiments using the IBM quantum cloud platform.

Extending the Frontier of Quantum Computers With Qutrits

We advocate for a fundamentally different way to perform quantum computation by using three-level qutrits instead of qubits. In particular, we substantially reduce the resource requirements of quantum computations by exploiting a third state for temporary variables (ancilla) in quantum circuits. Past work with qutrits has demonstrated only constant factor improvements, owing to the log2(3) binary-to-ternary compression factor. We present a novel technique using qutrits to achieve a logarithmic runtime decomposition of the Generalized Toffoli gate using no ancilla---an exponential improvement over the best qubit-only equivalent. Our approach features a 70x improvement in total two-qudit gate count over the qubit-only decomposition. This results in improvements for important algorithms for arithmetic and QRAM. Simulation results under realistic noise models indicate over 90% mean reliability (fidelity) for our circuit, versus under 30% for the qubit-only baseline. These results suggest that qutrits offer a promising path toward extending the frontier of quantum computers.

Interpreting High-resolution Spectroscopy of Exoplanets using Cross-correlations and Supervised Machine Learning

Abstract We present a new method for performing atmospheric retrieval on ground-based, high-resolution data of exoplanets. Our method combines cross-correlation functions with a random forest, a supervised machine-learning technique, to overcome challenges associated with high-resolution data. A series of cross-correlation functions are concatenated to give a “CCF-sequence” for each model atmosphere, which reduces the dimensionality by a factor of ∼100. The random forest, trained on our grid of ∼65,000 models, provides a likelihood-free method of retrieval. The precomputed grid spans 31 values of both temperature and metallicity, and incorporates a realistic noise model. We apply our method to HARPS-N observations of the ultra-hot Jupiter KELT-9b and obtain a metallicity consistent with solar (logM = − 0.2 ± 0.2). Our retrieved transit chord temperature ( K) is unreliable as strong ion lines lie outside of the extent of the training set, which we interpret as being indicative of missing physics in our atmospheric model. We compare our method to traditional nested sampling, as well as other machine-learning techniques, such as Bayesian neural networks. We demonstrate that the likelihood-free aspect of the random forest makes it more robust than nested sampling to different error distributions, and that the Bayesian neural network we tested is unable to reproduce complex posteriors. We also address the claim in Cobb et al. 2019 that our random forest retrieval technique can be overconfident but incorrect. We show that this is an artifact of the training set, rather than of the machine-learning method, and that the posteriors agree with those obtained using nested sampling.

Reactive Navigation Under Non-Parametric Uncertainty Through Hilbert Space Embedding of Probabilistic Velocity Obstacles

The probabilistic velocity obstacle (PVO) extends the concept of velocity obstacle (VO) to work in uncertain dynamic environments. In this paper, we show how a robust model predictive control (MPC) with PVO constraints under non-parametric uncertainty can be made computationally tractable. At the core of our formulation is a novel yet simple interpretation of our robust MPC as a problem of matching the distribution of PVO with a certain desired distribution. To this end, we propose two methods. Our first baseline method is based on approximating the distribution of PVO with a Gaussian Mixture Model (GMM) and subsequently performing distribution matching using Kullback Leibler (KL) divergence metric. Our second formulation is based on the possibility of representing arbitrary distributions as functions in Reproducing Kernel Hilbert Space (RKHS). We use this foundation to interpret our robust MPC as a problem of minimizing the distance between the desired distribution and the distribution of the PVO in the RKHS. Both the RKHS and GMM based formulation can work with any uncertainty distribution and thus allowing us to relax the prevalent Gaussian assumption in the existing works. We validate our formulation by taking an example of 2D navigation of quadrotors with a realistic noise model for perception and ego-motion uncertainty. In particular, we present a systematic comparison between the GMM and the RKHS approach and show that while both approaches can produce safe trajectories, the former is highly conservative and leads to poor tracking and control costs. Furthermore, RKHS based approach gives better computational times that are up to one order of magnitude lesser than the computation time of the GMM based approach.