scholarly journals Pauli error estimation via Population Recovery

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 549
Author(s):  
Steven T. Flammia ◽  
Ryan O'Donnell
Keyword(s):  
Error Estimation ◽  
Quantum Noise ◽  
Measurement Data ◽  
Simple Algorithm ◽  
Error Rates ◽  
Measurement Noise ◽  
Population Recovery ◽  
State Preparation ◽  
Noise Models ◽  
Recovery Problem

Motivated by estimation of quantum noise models, we study the problem of learning a Pauli channel, or more generally the Pauli error rates of an arbitrary channel. By employing a novel reduction to the "Population Recovery" problem, we give an extremely simple algorithm that learns the Pauli error rates of an n-qubit channel to precision ϵ in ℓ∞ using just O(1/ϵ2)log⁡(n/ϵ) applications of the channel. This is optimal up to the logarithmic factors. Our algorithm uses only unentangled state preparation and measurements, and the post-measurement classical runtime is just an O(1/ϵ) factor larger than the measurement data size. It is also impervious to a limited model of measurement noise where heralded measurement failures occur independently with probability ≤1/4.We then consider the case where the noise channel is close to the identity, meaning that the no-error outcome occurs with probability 1−η. In the regime of small η we extend our algorithm to achieve multiplicative precision 1±ϵ (i.e., additive precision ϵη) using just O(1ϵ2η)log⁡(n/ϵ) applications of the channel.

scholarly journals Measurement Noise Model for Depth Camera-Based People Tracking

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4488
Author(s):  
Otto Korkalo ◽  
Tapio Takala
Keyword(s):  
Real Life ◽  
Measurement Noise ◽  
Noise Model ◽  
Depth Camera ◽  
Depth Sensor ◽  
People Tracking ◽  
Plan View ◽  
Depth Cameras ◽  
Depth Sensors ◽  
Noise Models

Depth cameras are widely used in people tracking applications. They typically suffer from significant range measurement noise, which causes uncertainty in the detections made of the people. The data fusion, state estimation and data association tasks require that the measurement uncertainty is modelled, especially in multi-sensor systems. Measurement noise models for different kinds of depth sensors have been proposed, however, the existing approaches require manual calibration procedures which can be impractical to conduct in real-life scenarios. In this paper, we present a new measurement noise model for depth camera-based people tracking. In our tracking solution, we utilise the so-called plan-view approach, where the 3D measurements are transformed to the floor plane, and the tracking problem is solved in 2D. We directly model the measurement noise in the plan-view domain, and the errors that originate from the imaging process and the geometric transformations of the 3D data are combined. We also present a method for directly defining the noise models from the observations. Together with our depth sensor network self-calibration routine, the approach allows fast and practical deployment of depth-based people tracking systems.

scholarly journals Study of a least-squares-based algorithm for autoregressive signals subject to white noise

2003 ◽  
Vol 2003 (3) ◽  
pp. 93-101 ◽  
Author(s):  
Wei Xing Zheng
Keyword(s):  
Least Squares ◽  
Simple Algorithm ◽  
Measurement Noise ◽  
The Other ◽  
Parameter Estimates ◽  
Variance Ratio ◽  
Noise Variance ◽  
Parameter Estimator ◽  
Algorithmic Structure ◽  
Bias Compensation

A simple algorithm is developed for unbiased parameter identification of autoregressive (AR) signals subject to white measurement noise. It is shown that the corrupting noise variance, which determines the bias in the standard least-squares (LS) parameter estimator, can be estimated by simply using the expected LS errors when the ratio between the driving noise variance and the corrupting noise variance is known or obtainable in some way. Then an LS-based algorithm is established via the principle of bias compensation. Compared with the other LS-based algorithms recently developed, the introduced algorithm requires fewer computations and has a simpler algorithmic structure. Moreover, it can produce better AR parameter estimates whenever a reasonable guess of the noise variance ratio is available.

scholarly journals Semi-empiric noise modeling of a Cargo eVTOL UAV by means of system identification from flight noise measurement data

2021 ◽  
Author(s):  
Michael Schmähl ◽  
Christian Rieger ◽  
Sebastian Speck ◽  
Mirko Hornung
Keyword(s):  
System Identification ◽  
Measurement Data ◽  
Noise Measurement ◽  
Geographical Information ◽  
Noise Model ◽  
Technical Literature ◽  
Noise Modeling ◽  
Horizontal Flight ◽  
Aerial Vehicle ◽  
Noise Models

AbstractThis publication shows the semi-empiric noise modeling of an electric-powered vertical takeoff and landing (eVTOL) unmanned aerial vehicle (UAV) by means of system identification from flight noise measurement data. This work aims to provide noise models with a compact analytical ansatz for horizontal and vertical flight which are suited for integration into a geographical information system. Therefore, flight noise measurement campaigns were conducted and evaluated. An existing noise model ansatz is adapted to the eVTOL UAV under consideration and noise models are computed from the measurement data using the output error method. The resulting models are checked for plausibility by comparing them to technical literature. The horizontal flight noise model is subjected to a correlation analysis and the influence of meteorological effects are examined. To achieve a higher level of accuracy in future noise modelings, an optimization of the microphone positions as well as the flight trajectory is carried out.

scholarly journals Efficient Exact Inference for Dynamical Systems with Noisy Measurements using Sequential Approximate Bayesian Computation

2020 ◽  
Author(s):  
Yannik Schälte ◽  
Jan Hasenauer
Keyword(s):  
Approximate Bayesian Computation ◽  
Measurement Noise ◽  
Supplementary Information ◽  
Parameter Estimates ◽  
Bayesian Computation ◽  
Implicit Assumption ◽  
Exact Inference ◽  
Link Type ◽  
Approximate Bayesian ◽  
Noise Models

AbstractMotivationApproximate Bayesian Computation (ABC) is an increasingly popular method for likelihood-free parameter inference in systems biology and other fields of research, since it allows analysing complex stochastic models. However, the introduced approximation error is often not clear. It has been shown that ABC actually gives exact inference under the implicit assumption of a measurement noise model. Noise being common in biological systems, it is intriguing to exploit this insight. But this is difficult in practice, since ABC is in general highly computationally demanding. Thus, the question we want to answer here is how to efficiently account for measurement noise in ABC.ResultsWe illustrate exemplarily how ABC yields erroneous parameter estimates when neglecting measurement noise. Then, we discuss practical ways of correctly including the measurement noise in the analysis. We present an efficient adaptive sequential importance sampling based algorithm applicable to various model types and noise models. We test and compare it on several models, including ordinary and stochastic differential equations, Markov jump processes, and stochastically interacting agents, and noise models including normal, Laplace, and Poisson noise. We conclude that the proposed algorithm could improve the accuracy of parameter estimates for a broad spectrum of applications.AvailabilityThe developed algorithms are made publicly available as part of the open-source python toolbox pyABC (https://github.com/icb-dcm/pyabc)[email protected] informationSupplementary information is available at bioRxiv online. Supplementary code and data are available online at http://doi.org/10.5281/zenodo.3631120.

Weak measurement for improving the efficiency of remote state preparation in noisy

2018 ◽  
Vol 18 (11&12) ◽  
pp. 975-987
Author(s):  
Ming-Ming Wang ◽  
Zhi-Guo Qu
Keyword(s):  
Communication Systems ◽  
Quantum Communication ◽  
Quantum Noise ◽  
Weak Measurement ◽  
Remote State Preparation ◽  
Amplitude Damping ◽  
Output State ◽  
State Preparation ◽  
Phase Damping ◽  
Bit Flip

Quantum communication provides a new way for transmitting highly sensitive information. But the existence of quantum noise inevitably affects the security and reliability of a quantum communication system. The technique of weak measurement and its reversal measurement (WMRM) has been proposed to suppress the effect of quantum noise, especially, the amplitude-damping noise. Taking a GHZ based remote state preparation (RSP) scheme as an example, we discuss the effect of WMRM for suppressing four types of quantum noise that usually encountered in real-world, i.e., not only the amplitude-damping noise, but also the bit-flip, phase-flip (phase-damping) and depolarizing noise. And we give a quantitative study on how much a quantum output state can be improved by WMRM in noisy environment. It is shown that the technique of WMRM has certain effect for improving the fidelity of the output state in the amplitude-damping noise, and only has little effect for suppressing the depolarizing noise, while has no effect for suppressing the bit-flip and phase-flip (phase-damping) noise. Our result is helpful for improving the efficiency of entanglement-based quantum communication systems in real implementation.

scholarly journals Efficient exact inference for dynamical systems with noisy measurements using sequential approximate Bayesian computation

2020 ◽  
Vol 36 (Supplement_1) ◽  
pp. i551-i559
Author(s):  
Yannik Schälte ◽  
Jan Hasenauer
Keyword(s):  
Approximate Bayesian Computation ◽  
Approximation Error ◽  
Measurement Noise ◽  
Supplementary Information ◽  
Parameter Estimates ◽  
Bayesian Computation ◽  
Implicit Assumption ◽  
Exact Inference ◽  
Approximate Bayesian ◽  
Noise Models

Abstract Motivation Approximate Bayesian computation (ABC) is an increasingly popular method for likelihood-free parameter inference in systems biology and other fields of research, as it allows analyzing complex stochastic models. However, the introduced approximation error is often not clear. It has been shown that ABC actually gives exact inference under the implicit assumption of a measurement noise model. Noise being common in biological systems, it is intriguing to exploit this insight. But this is difficult in practice, as ABC is in general highly computationally demanding. Thus, the question we want to answer here is how to efficiently account for measurement noise in ABC. Results We illustrate exemplarily how ABC yields erroneous parameter estimates when neglecting measurement noise. Then, we discuss practical ways of correctly including the measurement noise in the analysis. We present an efficient adaptive sequential importance sampling-based algorithm applicable to various model types and noise models. We test and compare it on several models, including ordinary and stochastic differential equations, Markov jump processes and stochastically interacting agents, and noise models including normal, Laplace and Poisson noise. We conclude that the proposed algorithm could improve the accuracy of parameter estimates for a broad spectrum of applications. Availability and implementation The developed algorithms are made publicly available as part of the open-source python toolbox pyABC (https://github.com/icb-dcm/pyabc). Supplementary information Supplementary data are available at Bioinformatics online.

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