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At least 685 records · Page 38

Poster error probability in the Mu-11 Sequential Ranging System

An expression is derived for the posterior error probability in the Mu-2 Sequential Ranging System. An algorithm is developed which closely bounds the exact answer and can be implemented in the machine software. A computer simulation is provided to illustrate the improved level of confidence in a ranging acquisition using this figure of merit as compared to that using only the prior probabilities. In a simulation of 20,000 acquisitions with an experimentally determined threshold setting, the algorithm detected 90% of the actual errors and made false indication of errors on 0.2% of the acquisitions.

Coyle, C. W.↗

Lower bounds on circuit depth of the quantum approximate optimization algorithm

The quantum approximate optimization algorithm (QAOA) is a method of approximately solving combinatorial optimization problems. While QAOA is developed to solve a broad class of combinatorial optimization problems, it is not clear which classes of problems are best suited for it. One factor in demonstrating quantum advantage is the relationship between a problem instance and the circuit depth required to implement the QAOA method. As errors in noisy intermediate-scale quantum (NISQ) devices increase exponentially with circuit depth, identifying lower bounds on circuit depth can provide insights into when quantum advantage could be feasible. In this work, we identify how the structure of problem instances can be used to identify lower bounds for circuit depth for each iteration of QAOA and examine the relationship between problem structure and the circuit depth for a variety of combinatorial optimization problems including MaxCut and MaxIndSet. Specifically, we show how to derive a graph, G, that describes a general combinatorial optimization problem and show that the depth of circuit is at least the chromatic index of G. By looking at the scaling of circuit depth, we argue that MaxCut, MaxIndSet, and some instances of vertex covering and Boolean satisfiability problems are suitable for QAOA approaches while knapsack and traveling salesperson problems are not.

97 MATHEMATICS AND COMPUTING↗

Trajectory Specification for High-Capacity Air Traffic Control

In the current air traffic management system, the fundamental limitation on airspace capacity is the cognitive ability of human air traffic controllers to maintain safe separation with high reliability. The doubling or tripling of airspace capacity that will be needed over the next couple of decades will require that tactical separation be at least partially automated. Standardized conflict-free four-dimensional trajectory assignment will be needed to accomplish that objective. A trajectory specification format based on the Extensible Markup Language is proposed for that purpose. This format can be used to downlink a trajectory request, which can then be checked on the ground for conflicts and approved or modified, if necessary, then uplinked as the assigned trajectory. The horizontal path is specified as a series of geodetic waypoints connected by great circles, and the great-circle segments are connected by turns of specified radius. Vertical profiles for climb and descent are specified as low-order polynomial functions of along-track position, which is itself specified as a function of time. Flight technical error tolerances in the along-track, cross-track, and vertical axes define a bounding space around the reference trajectory, and conformance will guarantee the required separation for a period of time known as the conflict time horizon. An important safety benefit of this regimen is that the traffic will be able to fly free of conflicts for at least several minutes even if all ground systems and the entire communication infrastructure fail. Periodic updates in the along-track axis will adjust for errors in the predicted along-track winds.

Paielli, Russell A.↗

Diagnostics of Mixed-State Topological Order and Breakdown of Quantum Memory

Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed states describing corrupted memories. Here we provide an intrinsic characterization of the breakdown of topological quantum memory, which both gives a bound on the performance of decoding algorithms and provides examples of topologically distinct mixed states. We employ three information-theoretical quantities that can be regarded as generalizations of the diagnostics of ground-state topological order, and serve as a definition for topological order in error-corrupted mixed states. We consider the topological contribution to entanglement negativity and two other metrics based on quantum relative entropy and coherent information. In the concrete example of the two-dimensional (2D) Toric code with local bit-flip and phase errors, we map three quantities to observables in 2D classical spin models and analytically show they all undergo a transition at the same error threshold. This threshold is an upper bound on that achieved in any decoding algorithm and is indeed saturated by that in the optimal decoding algorithm for the Toric code. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Error analysis of bent ray radio occultation measurments

There are two types of experimental measurement errors of the Doppler data associated with the radio occultation, random and systematic. Random errors are due to thermal noise in the transmission channel, and the phase lock loop, and quantization error in the digital circuitry. These are called noise type errors. The systematic errors are due to geometric uncertainty and equipment phase instability. Considered is the amount of uncertainty, due to random measurement errors, in the refractivity profiles reconstructed by this type of indirect sensing experiment. A class of refractivity profiles is defined which approximately fit the set of measured data. Bounds are placed on the extent of this class of solution profiles. To accomplish this, the sensivity of the reconstructed refractivity profiles to errors in the measured quantity and the statistics of the errors in the measurement are examined.

Saintgermain, R. L.↗

Free distance bounds for convolutional codes

The best asymptotic bounds presently known on free distance for convolutional codes are presented from a unified point of view. Upper and lower bounds for both time-varying and fixed codes are obtained. A comparison is made between bounds for nonsystematic and systematic codes which shows that more free distance is available with nonsystematic codes. This result is important when selecting codes for use with sequential or maximum-likelihood (Viterbi) decoding since the probability of decoding error is closely related to the free distance of the code. An ancillary result, used in proving the lower bound on free distance for time-varying nonsystematic codes, furnishes a generalization of two earlier bounds on the definite decoding minimum distance of convolutional codes.

Costello, D. J., Jr.↗

An Upper Bound on High Speed Satellite Collision Probability When Only One Object has Position Uncertainty Information

Upper bounds on high speed satellite collision probability, PC †, have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum PC. If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but potentially useful Pc upper bound.

Frisbee, Joseph H., Jr.↗

Scalable Yet Rigorous Floating-Point Error Analysis

Automated techniques for rigorous floating-point round-off error analysis are a prerequisite to placing important activities in HPC such as precision allocation, verification and code optimization on a formal footing. Yet existing techniques cannot provide tight bounds for expressions beyond a few dozen operators; barely enough for HPC. In this work, we offer an approach embedded in a new tool called SATIRE that scales error analysis by four orders of magnitude compared to today’s best-of-class tools. We explain how three key ideas underlying SATIRE help it attain such scale: path strength reduction, bound optimization and abstraction. SATIRE provides tight bounds and rigorous guarantees on significantly larger expressions with well over a hundred thousand operators, covering important examples including FFT, matrix multiplication and PDE stencils.

Das, Arnab↗

Heisenberg-limited Hamiltonian learning for interacting bosons

We develop a protocol for learning a class of interacting bosonic Hamiltonians from dynamics with Heisenberg-limited scaling. For Hamiltonians with an underlying bounded-degree graph structure, we can learn all parameters with root mean square error ϵ using ${\mathcal{O}}(1/\epsilon )$ total evolution time, which is independent of the system size, in a way that is robust against state-preparation and measurement error. In the protocol, we only use bosonic coherent states, beam splitters, phase shifters, and homodyne measurements, which are easy to implement on many experimental platforms. A key technique we develop is to apply random unitaries to enforce symmetry in the effective Hamiltonian, which may be of independent interest.

computer science↗

Universal Spreading of Conditional Mutual Information in Noisy Random Circuits

For this work, we study the evolution of conditional mutual information (CMI) in generic open quantum systems, focusing on one-dimensional random circuits with interspersed local noise. Unlike in noiseless circuits, where CMI spreads linearly while being bounded by the light cone, we find that noisy random circuits with an error rate 𝑝 exhibit superlinear propagation of CMI, which diverges far beyond the light cone at a critical circuit depth 𝑡 𝑐 ∝ 𝑝 −1 . We demonstrate that the underlying mechanism for such rapid spreading is the combined effect of local noise and a scrambling unitary, which selectively removes short-range correlations while preserving long-range correlations. To analytically capture the dynamics of CMI in noisy random circuits, we introduce a coarse-graining method, and we validate our theoretical results through numerical simulations. Furthermore, we identify a universal scaling law governing the spreading of CMI.

decoherence↗

Quarter 4 Report: Report on Final Findings and Opportunities for Future Work in the Use of Mixed Precision in Iterative Solvers

The fourth quarter of the project was spent developing an error analysis of the s-step Lanczos and CG algorithms. Our theoretical bounds and numerical experiments show that the numerical behavior of the algorithm can be significantly improved by using extra precision in a small part of the computation related to the computation and application of the Gram matrix. We have published a technical report which includes all steps of the analysis [8]; a shortened version for journal submission is in preparation. We plan to submit this paper in the following weeks. Activities related to this also include a collaboration with Ichitaro Yamazaki on gathering performance results for these new mixed precision s-step Krylov subspace methods using single/double precision on GPUs. Namely, we would like to obtain performance results that show that the performance overhead of using double the working precision in these select computations is minimal. Other activities include attending biweekly xSDK meetings and presenting a pitch talk on this work to the group on February 25, 2021. In the remainder of the document, we summarize our findings on the potential for mixed precision in classical Krylov subspace methods and s-step Krylov subspace methods, as well as key opportunities for future work.

97 MATHEMATICS AND COMPUTING↗

Attitude steering for space shuttle based synthetic aperture radars

A technique is presented to steer the antenna beam to the zero-Doppler line for a spacecraft platform which operates in a non-zero roll attitude. The purposes of employing this attitude steering technique are reduction of the Doppler centroid error caused by the variation in target elevation; reduction of the Doppler centroid bound; and reduction of the Doppler drift. It is shown that a fixed attitude sequence can be easily accommodated in the radar command sequence to achieve nearly zero-Doppler steering. Implementation of this technique improves the image quality as well as simplifies the processor design.

Chang, C. Y.↗

Formal Safety Certification of Aerospace Software

In principle, formal methods offer many advantages for aerospace software development: they can help to achieve ultra-high reliability, and they can be used to provide evidence of the reliability claims which can then be subjected to external scrutiny. However, despite years of research and many advances in the underlying formalisms of specification, semantics, and logic, formal methods are not much used in practice. In our opinion this is related to three major shortcomings. First, the application of formal methods is still expensive because they are labor- and knowledge-intensive. Second, they are difficult to scale up to complex systems because they are based on deep mathematical insights about the behavior of the systems (t.e., they rely on the "heroic proof"). Third, the proofs can be difficult to interpret, and typically stand in isolation from the original code. In this paper, we describe a tool for formally demonstrating safety-relevant aspects of aerospace software, which largely circumvents these problems. We focus on safely properties because it has been observed that safety violations such as out-of-bounds memory accesses or use of uninitialized variables constitute the majority of the errors found in the aerospace domain. In our approach, safety means that the program will not violate a set of rules that can range for the simple memory access rules to high-level flight rules. These different safety properties are formalized as different safety policies in Hoare logic, which are then used by a verification condition generator along with the code and logical annotations in order to derive formal safety conditions; these are then proven using an automated theorem prover. Our certification system is currently integrated into a model-based code generation toolset that generates the annotations together with the code. However, this automated formal certification technology is not exclusively constrained to our code generator and could, in principle, also be integrated with other code generators such as RealTime Workshop or even applied to legacy code. Our approach circumvents the historical problems with formal methods by increasing the degree of automation on all levels. The restriction to safety policies (as opposed to arbitrary functional behavior) results in simpler proof problems that can generally be solved by fully automatic theorem proves. An automated linking mechanism between the safety conditions and the code provides some of the traceability mandated by process standards such as DO-178B. An automated explanation mechanism uses semantic markup added by the verification condition generator to produce natural-language explanations of the safety conditions and thus supports their interpretation in relation to the code. It shows an automatically generated certification browser that lets users inspect the (generated) code along with the safety conditions (including textual explanations), and uses hyperlinks to automate tracing between the two levels. Here, the explanations reflect the logical structure of the safety obligation but the mechanism can in principle be customized using different sets of domain concepts. The interface also provides some limited control over the certification process itself. Our long-term goal is a seamless integration of certification, code generation, and manual coding that results in a "certified pipeline" in which specifications are automatically transformed into executable code, together with the supporting artifacts necessary for achieving and demonstrating the high level of assurance needed in the aerospace domain.

Denney, Ewen↗

Input and Output Performance of M-MRAC in the Presence of Bounded Disturbances

This paper presents performance analysis of novel modified model reference adaptive control (M-MRAC) architecture in conjunction with different robust adaptive laws for the uncertain linear systems subject to unknown but bounded disturbances. It is shown that for any robust adaptive law the tracking error of the M-MRAC system can be arbitrarily decreased in transient and in the steady-state by increasing the adaptation rate, without generating high frequency oscillations in the control signal, which are unavoidable in conventional MRAC systems for large adaptation rates. Moreover, the generated adaptive control signal arbitrary closely tracks the ideal control signal when the error feedback gain is simultaneously increased with the adaptation rate, according to derived rule. The results are demonstrated via simulations.

Stepanyan, Vahram↗

Error analysis of combined stereo/optical-flow passive ranging

The motion of an imaging sensor causes each imaged point of the scene to correspondingly describe a time trajectory on the image plane. The trajectories of all imaged points are reminiscent of a flow (e.g., of liquid) which is the source of the term 'optical flow'. Optical-flow ranging is a method by which the stream of two-dimensional images obtained from a forward-looking forward-moving passive sensor is used to compute depth (or range) to points in the field of view. Another well-known ranging method consists of triangulation based on stereo images obtained from at least two stationary sensors. In this paper we analyze the potential accuracies of a combined optical flow and stereo passive-ranging system in the context of helicopter nap-of-the-earth obstacle avoidance. The Cramer-Rao lower bound is developed for the combined system under the assumption of an unknown angular bias error common to both cameras of a stereo pair. It is shown that the depth accuracy degradations caused by a bias error is negligible for a combined optical-flow and stereo system as compared to a monocular optical-flow system.

Barniv, Yair↗

Uncovering Where Compensating Errors Could Hide in ENDF/B-VIII.0

Unconstrained physics spaces between two or more nuclear data observables in a library occur when their values can be simultaneously adjusted without violating the uncertainties in either differential information or simulations of relevant integral experiments. Differential data are often too imprecise to fully bound all nuclear data observables of interest for application simulations. Integral data are simulated with combinations of nuclear data so that an error in one observable may be hidden by a counterbalancing error in another. In this manner compensating errors may lurk within nuclear data libraries and these errors have the potential to undermine the predictive power of neutron transport simulations, particularly in situations where there is no conclusive validation experiment that resembles the application of interest. The EUCLID project (Experiments Underpinned by Computational Learning for Improvements in Nuclear Data) developed a preliminary workflow to identify these unconstrained physics spaces by bringing together results from a large collection of integral experiments with their simulated counter-parts as well as differential information that have a one-to-one correspondence to nuclear data. This wealth of information is processed by machine learning tools for subsequent refinement by human experts. Here, we show how the EUCLID work-flow is executed by applying it first to 239 Pu and then to 9 Be nuclear data in ENDF/B-VIII.0.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Uncovering Where Compensating Errors Could Hide in ENDF/B-VIII.0

Unconstrained physics spaces between two or more nuclear data observables in a library occur when their values can be simultaneously adjusted without violating the uncertainties in either differential information or simulations of relevant integral experiments. Differential data are often too imprecise to fully bound all nuclear data observables of interest for application simulations. Integral data are simulated with combinations of nuclear data so that an error in one observable may be hidden by a counterbalancing error in another. In this manner compensating errors may lurk within nuclear data libraries and these errors have the potential to undermine the predictive power of neutron transport simulations, particularly in situations where there is no conclusive validation experiment that resembles the application of interest. The EUCLID project (Experiments Underpinned by Computational Learning for Improvements in Nuclear Data) developed a preliminary workflow to identify these unconstrained physics spaces by bringing together results from a large collection of integral experiments with their simulated counter-parts as well as differential information that have a one-to-one correspondence to nuclear data. This wealth of information is processed by machine learning tools for subsequent refinement by human experts. Here, we show how the EUCLID work-flow is executed by applying it first to 239 Pu and then to 9 Be nuclear data in ENDF/B-VIII.0.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Error quantification and comparison of binary neutron star gravitational waveforms from numerical relativity codes

Future gravitational wave detections of merging binary neutron star systems have the possibility to tightly constrain the equation of state of dense nuclear matter. In order to extract such constraints, gravitational waveform models need to be calibrated to accurate numerical relativity simulations of the late inspiral and merger. In this work, we take an essential step toward classifying the error and potential systematics in current generation numerical relativity simulations of merging binary neutron stars. To this end, we perform a direct comparison of two codes (fil, spec), which differ in many aspects, including the numerical methods and discretizations used and equations solved. We find that despite these different approaches, the codes are—within current numerical resolution bounds—fully consistent, and broadly comparable in cost for a given accuracy level. Our results indicate that the error in the waveforms is primarily dominated by the hydrodynamic evolution, consistent with earlier findings in the literature. Finally, we also discuss current limitations and cost estimates for numerical relativity simulations to reach the accuracies required in the era of next-generation gravitational detectors.

gravitational waves↗