QEC-fidelity
Code for paper "Universal Optimization and Tighter Fidelity Bounds for Approximate Quantum Error Correction" https://doi.org/10.48550/arXiv.2607.24968
Wu, Jing [Fermi National Accelerator Laboratory (F↗
SEARCH · Engineering Papers
Results for “Error bounds”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Exploring the feasibility of lossy compression for PDE simulations
Checkpoint restart plays an important role in high-performance computing (HPC) applications, allowing simulation runtime to extend beyond a single job allocation and facilitating recovery from hardware failure. Yet, as machines grow in size and in complexity, traditional approaches to checkpoint restart are becoming prohibitive. Current methods store a subset of the application’s state and exploit the memory hierarchy in the machine. However, as the energy cost of data movement continues to dominate, further reductions in checkpoint size are needed. Lossy compression, which can significantly reduce checkpoint sizes, offers a potential to reduce computational cost in checkpoint restart. This article investigates the use of numerical properties of partial differential equation (PDE) simulations, such as bounds on the truncation error, to evaluate the feasibility of using lossy compression in checkpointing PDE simulations. Restart from a checkpoint with lossy compression is considered for a fail-stop error in two time-dependent HPC application codes: PlasComCM and Nek5000. Results show that error in application variables due to a restart from a lossy compressed checkpoint can be masked by the numerical error in the discretization, leading to increased efficiency in checkpoint restart without influencing overall accuracy in the simulation.
97 MATHEMATICS AND COMPUTING↗
EFT asymptotics: the growth of operator degeneracy
We establish formulae for the asymptotic growth (with respect to the scaling dimension) of the number of operators in effective field theory, or equivalently the number of S-matrix elements, in arbitrary spacetime dimensions and with generic field content. This we achieve by generalising a theorem due to Meinardus and applying it to Hilbert series---partition functions for the degeneracy of (subsets of) operators. Although our formulae are asymptotic, numerical experiments reveal remarkable agreement with exact results at very low orders in the EFT expansion, including for complicated phenomenological theories such as the standard model EFT. Our methods also reveal phase transition-like behaviour in Hilbert series. We discuss prospects for tightening the bounds and providing rigorous errors to the growth of operator degeneracy, and of extending the analytic study and utility of Hilbert series to EFT.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Covariance operator estimation: Sparsity, lengthscale, and ensemble Kalman filters
This paper investigates covariance operator estimation via thresholding. For Gaussian random fields with approximately sparse covariance operators, we establish non-asymptotic bounds on the estimation error in terms of the sparsity level of the covariance and the expected supremum of the field. We prove that thresholded estimators enjoy an exponential improvement in sample complexity compared with the standard sample covariance estimator if the field has a small correlation lengthscale. As an application of the theory, we study thresholded estimation of covariance operators within ensemble Kalman filters.
Covariance operator estimation↗
A simple derivation of the coding theorem and some applications.
Upper bounds on probability of error achieved by using block codes on general time-discrete memoryless channel
CODING SYSTEM↗
Estimates of epsilon capacity for certain linear communication channels.
Epsilon capacity of linear communication channels, determining upper and lower bounds on rate of error free transmission
Root, W. L.↗
Noncommuting observables in quantum detection and estimation theory
In quantum detection theory, the optimum detection operators must commute; admitting simultaneous approximate measurement of noncommuting observables cannot yield a lower Bayes cost. In addition, the lower bounds on mean square errors of parameter estimates, predicted by the quantum mechanical Cramer-Rao inequality, cannot be reduced by such means.
Helstrom, C. W.↗
Noncommunting observables in quantum detection and estimation theory
In quantum detection theory the optimum detection operators must commute; admitting simultaneous approximate measurement of noncommuting observables cannot yield a lower Bayes cost. The lower bounds on mean square errors of parameter estimates predicted by the quantum-mechanical Cramer-Rao inequality can also not be reduced by such means.
Helstrom, C. W.↗
Simulation techniques for estimating error in the classification of normal patterns
Methods of efficiently generating and classifying samples with specified multivariate normal distributions were discussed. Conservative confidence tables for sample sizes are given for selective sampling. Simulation results are compared with classified training data. Techniques for comparing error and separability measure for two normal patterns are investigated and used to display the relationship between the error and the Chernoff bound.
Whitsitt, S. J.↗
Modulation/demodulation techniques for satellite communications. Part 2: Advanced techniques. The linear channel
A theory is presented for deducing and predicting the performance of transmitter/receivers for bandwidth efficient modulations suitable for use on the linear satellite channel. The underlying principle used is the development of receiver structures based on the maximum-likelihood decision rule. The application of the performance prediction tools, e.g., channel cutoff rate and bit error probability transfer function bounds to these modulation/demodulation techniques.
Omura, J. K.↗
Measurement accuracies in band-limited extrapolation
The problem of numerical instability associated with extrapolation algorithms is addressed. An attempt is made to estimate the bounds for the acceptable errors and to place a ceiling on the measurement accuracy and computational accuracy needed for the extrapolation. It is shown that in band limited (or visible angle limited) extrapolation the larger effective aperture L' that can be realized from a finite aperture L by over sampling is a function of the accuracy of measurements. It is shown that for sampling in the interval L/b absolute value of xL, b1 the signal must be known within an error e sub N given by e sub N squared approximately = 1/4(2kL') cubed (e/8b L/L')(2kL') where L is the physical aperture, L' is the extrapolated aperture, and k = 2pi lambda.
Kritikos, H. N.↗
Modulation/demodulation techniques for satellite communications. Part 3: Advanced techniques. The nonlinear channel
A theory for deducing and predicting the performance of transmitter/receivers for bandwidth efficient modulations suitable for use on the nonlinear satellite channel is presented. The underlying principle used throughout is the development of receiver structures based on the maximum likelihood decision rule and aproximations to it. The bit error probability transfer function bounds developed in great detail in Part 4 is applied to these modulation/demodulation techniques. The effects of the various degrees of receiver mismatch are considered both theoretically and by numerous illustrative examples.
Omura, J. K.↗
Investigation of several aspects of LANDSAT-4 data quality
No insurmountable problems in change detection analysis were found when portions of scenes collected simultaneously by LANDSAT 4 MSS and either LANDSAT 2 or 3. The cause of the periodic noise in LANDSAT 4 MSS images which had a RMS value of approximately 2DN should be corrected in the LANDSAT D instrument before its launch. Analysis of the P-tape of the Arkansas scene shows bands within the same focal plane very well registered except for the thermal band which was misregistered by approximately three 28.5 meter pixels in both directions. It is possible to derive tight confidence bounds for the registration errors. Preliminary analyses of the Sacramento and Arkansas scenes reveals a very high degree of consistency with earlier results for bands 3 vs 1, 3 vs 4, and 3 vs 5. Results are presented in table form. It is suggested that attention be given to the standard deviations of registrations errors to judge whether or not they will be within specification once any known mean registration errors are corrected. Techniques used for MTF analysis of a Washington scene produced noisy results.
Wrigley, R. C.↗
Permanence analysis of a concatenated coding scheme for error control
A concatenated coding scheme for error control in data communications is analyzed. In this scheme, the inner code is used for both error correction and detection, however, the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. Probability of undetected error is derived and bounded. A particular example, proposed for the planetary program, is analyzed.
Costello, D. J., Jr.↗
Probability of undetected error after decoding for a concatenated coding scheme
A concatenated coding scheme for error control in data communications is analyzed. In this scheme, the inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. Probability of undetected error is derived and bounded. A particular example, proposed for NASA telecommand system is analyzed.
Costello, D. J., Jr.↗
Calculating the obscuration ratio due to particle surface contamination
A useful method for the calculation of the obscuration ratio due to particle surface contamination is described. Equations are developed for calculating the obscuration ratio for spherical particles (with diameters greater than 1 micron) and fibers for surfaces where the particle size distribution is either known to be or assumed to be of the form of a MIL-STD-1246A distribution. A simple approximation to the obscuration ratio discrete data is then derived, where the contribution from a single size interval only is treated. This derivation obtains tighter bounds on the approximation error than are provided by the usual direct approach.
Barengoltz, Jack↗
Generalized minimum shift-keying modulation techniques
The simultaneous data demodulation and phase tracking of an MSK signal using the Viterbi algorithm is described and two variations of MSK modulation are studied. The MSK with overlay is a dual rate modulation technique where low-and high-rate data are superimposed on an MSK signal. Here the demodulator uses the Viterbi algorithm to estimate both the low-and high-rate data simultaneously. The MSK with pseudorandom sequence spreading combats intentional or unintentional jamming. A simplified receiver for these spread spectrum MSK signals is found, which takes into consideration the effect of random phase perturbations. The performance of these demodulators is evaluated using transfer function bounds for the bit error probability. It is shown that with a reasonable short overlay period, at a relatively high signal-to-noise ratio (13 dB), there is a small (0.7 dB) loss of performance. For demodulation of the spread spectrum MSK signal, a simplified receiver is derived, and its performance in the presence of continuous jamming is evaluated.
Sadr, Ramin↗
Effect of earth albedo variation on the performance of a spatial acquisition subsystem aboard a planetary spacecraft
The effect of Earth albedo variation on the pointing and tracking subsystem of a planetary optical communication package is analyzed. By studying the Cramer-Rao bound of the tracking error variance, it is shown that, when the Earth albedo is precisely known, the variance in spatial tracking error is inversely proportional to the total signal count. In contrast, a small uncertainty in the Earth albedo can result in an irreducible error in the tracking subsystem.
Chen, C.-C.↗