Quantum accuracy threshold for concatenated distance-3 code

2006 ◽  
Vol 6 (2) ◽  
pp. 97-165 ◽  
Author(s):  
P. Aliferis ◽  
D. Gottesman ◽  
J. Preskill
Keyword(s):  
Lower Bound ◽  
Fault Tolerant ◽  
Combinatorial Analysis ◽  
Noise Model ◽  
Computer Assisted ◽  
Quantum Code ◽  
Stochastic Noise ◽  
Noise Models ◽  
New Criteria ◽  
Inductive Analysis

We prove a new version of the quantum threshold theorem that applies to concatenation of a quantum code that corrects only one error, and we use this theorem to derive a rigorous lower bound on the quantum accuracy threshold $\varepsilon_0$. Our proof also applies to concatenation of higher-distance codes, and to noise models that allow faults to be correlated in space and in time. The proof uses new criteria for assessing the accuracy of fault-tolerant circuits, which are particularly conducive to the inductive analysis of recursive simulations. Our lower bound on the threshold, $\varepsilon_0 \ge 2.73\times 10^{-5}$ for an adversarial independent stochastic noise model, is derived from a computer-assisted combinatorial analysis; it is the best lower bound that has been rigorously proven so far.

scholarly journals Accuracy threshold for postselected quantum computation

2008 ◽  
Vol 8 (3&4) ◽  
pp. 181-244 ◽  
Author(s):  
P. Aliferis ◽  
D. Gottesman ◽  
J. Preskill
Keyword(s):  
Lower Bound ◽  
Quantum Computation ◽  
Error Detection ◽  
Fault Tolerant ◽  
Error Correcting Codes ◽  
Stochastic Noise ◽  
Strongly Correlated ◽  
Error Detecting ◽  
Error Detecting Code

We prove an accuracy threshold theorem for fault-tolerant quantum computation based on error detection and postselection. Our proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla states are protected by a concatenated error-detecting code and the preparation is aborted if an error is detected. The proof applies to independent stochastic noise but (in contrast to proofs of the quantum accuracy threshold theorem based on concatenated error-correcting codes) not to strongly-correlated adversarial noise. Our rigorously established lower bound on the accuracy threshold, $1.04\times 10^{-3}$, is well below Knill's numerical estimates.

Universal fault tolerant quantum computation on bilinear nearest neighbor arrays

2008 ◽  
Vol 8 (3&4) ◽  
pp. 330-344
Author(s):  
A.M. Stephens ◽  
A.G. Fowler ◽  
L.C.L. Hollenberg
Keyword(s):  
Lower Bound ◽  
Quantum Computation ◽  
Error Rate ◽  
Nearest Neighbor ◽  
Fault Tolerant ◽  
Quantum Code ◽  
Memory Errors ◽  
Memory Failure ◽  
Qubit Gate ◽  
Readout Error

Assuming an array that consists of two parallel lines of qubits and that permits only nearest neighbor interactions, we construct physical and logical circuitry to enable universal fault tolerant quantum computation under the $[[7,1,3]]$ quantum code. A rigorous lower bound to the fault tolerant threshold for this array is determined in a number of physical settings. Adversarial memory errors, two-qubit gate errors and readout errors are included in our analysis. In the setting where the physical memory failure rate is equal to one-tenth of the physical gate error rate, the physical readout error rate is equal to the physical gate error rate, and the duration of physical readout is ten times the duration of a physical gate, we obtain a lower bound to the asymptotic threshold of $1.96\times10^{-6}$.

scholarly journals Belief Merging Operators as Maximum Likelihood Estimators

2020 ◽  
Author(s):  
Patricia Everaere ◽  
Sebastien Konieczny ◽  
Pierre Marquis
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Noise Model ◽  
Belief Merging ◽  
The World ◽  
Natural Noise ◽  
True State ◽  
Merging Process ◽  
Rationality Postulates ◽  
Noise Models

We study how belief merging operators can be considered as maximum likelihood estimators, i.e., we assume that there exists a (unknown) true state of the world and that each agent participating in the merging process receives a noisy signal of it, characterized by a noise model. The objective is then to aggregate the agents' belief bases to make the best possible guess about the true state of the world. In this paper, some logical connections between the rationality postulates for belief merging (IC postulates) and simple conditions over the noise model under consideration are exhibited. These results provide a new justification for IC merging postulates. We also provide results for two specific natural noise models: the world swap noise and the atom swap noise, by identifying distance-based merging operators that are maximum likelihood estimators for these two noise models.

scholarly journals LSSVR Model of G-L Mixed Noise-Characteristic with Its Applications

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 629 ◽  
Author(s):  
Shiguang Zhang ◽  
Ting Zhou ◽  
Lin Sun ◽  
Wei Wang ◽  
Baofang Chang
Keyword(s):  
Wind Speed ◽  
Regression Models ◽  
Historical Data ◽  
Least Square ◽  
Noise Model ◽  
Noise Distribution ◽  
Short Term ◽  
Mixed Noise ◽  
Noise Models ◽  
Better Than

Due to the complexity of wind speed, it has been reported that mixed-noise models, constituted by multiple noise distributions, perform better than single-noise models. However, most existing regression models suppose that the noise distribution is single. Therefore, we study the Least square S V R of the Gaussian–Laplacian mixed homoscedastic ( G L M − L S S V R ) and heteroscedastic noise ( G L M H − L S S V R ) for complicated or unknown noise distributions. The ALM technique is used to solve model G L M − L S S V R . G L M − L S S V R is used to predict short-term wind speed with historical data. The prediction results indicate that the presented model is superior to the single-noise model, and has fine performance.

Estimate of PRNU Noise Based on Different Noise Models for Source Camera Identification

2010 ◽  
Vol 2 (2) ◽  
pp. 21-33 ◽  
Author(s):  
Irene Amerini ◽  
Roberto Caldelli ◽  
Vito Cappellini ◽  
Francesco Picchioni ◽  
Alessandro Piva
Keyword(s):  
Noise Model ◽  
Digital Content ◽  
Wavelet Domain ◽  
Multimedia Forensics ◽  
Source Camera Identification ◽  
Camera Identification ◽  
Novel Method ◽  
Photo Response ◽  
Noise Models ◽  
Open Issues

Identification of the source that has generated a digital content is considered one of the main open issues in multimedia forensics community. The extraction of photo-response non-uniformity (PRNU) noise has been so far indicated as a mean to identify sensor fingerprint. Such a fingerprint can be estimated from multiple images taken by the same camera by means of a de-noising filtering operation. In this paper, the authors propose a novel method for estimating the PRNU noise in source camera identification. In particular, a MMSE digital filter in the un-decimated wavelet domain, based on a signal-dependent noise model, is introduced and compared with others commonly adopted for this purpose. A theoretical framework and experimental results are provided and discussed.

scholarly journals Validating Aircraft Noise Models

Proceedings ◽  
2020 ◽  
Vol 59 (1) ◽  
pp. 12
Author(s):  
Ran Giladi ◽  
Eliav Menachi
Keyword(s):  
Noise Level ◽  
Health Hazard ◽  
Aircraft Noise ◽  
Noise Model ◽  
Aviation Industry ◽  
Noise Abatement ◽  
Statistical Variation ◽  
Huge Impact ◽  
Aircraft Type ◽  
Noise Models

Aircraft noise, especially at takeoffs and landings, became a major environmental nuisance and a health hazard for the population around metropolitan airports. In the battle for a better quality of life, wellbeing, and health, aircraft noise models are essential for noise abatement, control, enforcement, evaluation, policy-making, and shaping the entire aviation industry. Aircraft noise models calculate noise and exposure levels based on aircraft types, engines and airframes, aircraft flight paths, environment factors, and more. Validating the aircraft noise model is a mandatory step towards the model credibility, especially when these models play such a key role with a huge impact on society, economy, and public health. Yet, no validation procedure was offered, and it turns out to be a challenging task. The actual, measured, aircraft noise level is known to be subject to statistical variation, even for the same aircraft type at the same situation and flight phase, executing the same flight procedure, with similar environmental factors and at the same place. This study tries to validate the FAA’s AEDT aircraft noise model, by trying to correlate the specific flight path of an aircraft with its measured noise level. The results show that the AEDT noise model underestimates the actual noise level, and four validation steps should be performed to correct or tune aircraft noise databases and flight profiles.

Effect of Ge-Nanoislands on the Low-Frequency Noise in Si/SiOx/Ge Structures

2013 ◽  
Vol 854 ◽  
pp. 21-27 ◽  
Author(s):  
N.P. Garbar ◽  
Valeriya N. Kudina ◽  
V.S. Lysenko ◽  
S.V. Kondratenko ◽  
Yu.N. Kozyrev
Keyword(s):  
High Surface ◽  
Low Frequency ◽  
Noise Model ◽  
Frequency Noise ◽  
Low Frequency Noise ◽  
Physical Processes ◽  
Noise Sources ◽  
Noise Component ◽  
First Time ◽  
Noise Models

Low-frequency noise of the structures with Ge-nanoclusters of rather high surface density grown on the oxidized silicon surface is investigated for the first time. It was revealed that the 1/f γ noise, where γ is close to unity, is the typical noise component. Nevertheless, the 1/f γ noise sources were found to be distributed nonuniformly upon the oxidized silicon structure with Ge-nanoclusters. The noise features revealed were analyzed in the framework of widely used noise models. However, the models used appeared to be unsuitable to explain the noise behavior of the structures studied. The physical processes that should be allowed for to develop the appropriate noise model are discussed.

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 A flow-map model for analyzing pseudothresholds in fault-tolerant quantum computing

2006 ◽  
Vol 6 (3) ◽  
pp. 193-212 ◽  
Author(s):  
K.M. Svore ◽  
A.W. Cross ◽  
I.L. Chuang ◽  
A.V. Aho
Keyword(s):  
Quantum Computing ◽  
Fault Tolerance ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Upper Bounds ◽  
Component Failure ◽  
Simulation Procedure ◽  
Component Failure Rates ◽  
Flow Map ◽  
Noise Models

An arbitrarily reliable quantum computer can be efficiently constructed from noisy components using a recursive simulation procedure, provided that those components fail with probability less than the fault-tolerance threshold. Recent estimates of the threshold are near some experimentally achieved gate fidelities. However, the landscape of threshold estimates includes pseudothresholds, threshold estimates based on a subset of components and a low level of the recursion. In this paper, we observe that pseudothresholds are a generic phenomenon in fault-tolerant computation. We define pseudothresholds and present classical and quantum fault-tolerant circuits exhibiting pseudothresholds that differ by a factor of $4$ from fault-tolerance thresholds for typical relationships between component failure rates. We develop tools for visualizing how reliability is influenced by recursive simulation in order to determine the asymptotic threshold. Finally, we conjecture that refinements of these methods may establish upper bounds on the fault-tolerance threshold for particular codes and noise models.

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