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At least 19 records

QPatLib: A community repository of measurement-based quantum computing patterns

QPatLib is a community repository of measurement‑based quantum computing (MBQC) patterns and associated metadata, intended to support reuse, benchmarking, and reproducible comparison of MBQC constructions across platforms and compilers. Patterns in QPatLib are expressed in a standardized, human‑readable measurement calculus representation. Details can be found here: https://doi.org/10.48550/arXiv.2605.12502

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QPatLib v1.0 — Measurement-based quantum simulation Pauli string unitary pattern collections

This Zenodo record accompanies the paper “Scalable Measurement-Based Quantum Simulation Patterns for Benchmarking” arXiv.2605.12502 and provides QPatLib v1.0 measurement-pattern datasets in human-readable JSONL together with a ZIP archive of OpenQASM 3.0 circuits used for validation and reproducibility. The patterns and circuits implement Pauli string unitaries for benchmark cases. Cases include all possible string combinations for less than 6 qubits and strings used in Hamiltonians for certain diatomic molecules for 6 or more qubits. Format: Each pattern_*.jsonl file is containins measurement patterns for all subsets for a given model/instance and subset strategy: it begins with a preamble containing model metadata, subset definitions, provenance, and (when feasible) full-pattern test results, followed by one pattern entry per subset. Each subset entry includes a required pattern_ascii field storing the measurement pattern in the measurement-calculus/Graphix standard with signal shifting, written left-to-right in the canonical order nodes → edges → measurements (with signal dependencies) → byproduct corrections (X/Z). The circuits are included as circuit_files.zip. Patterns in this record were validated against the corresponding circuits and checked for causal flow. Codes for generating these patterns can be found at QPatLib repository on Github

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A mathematical framework for ejecta cloud dynamics with application to source models and piezoelectric mass measurements

We present a mathematical framework for describing the dynamical evolution of an ejecta cloud generated by a generic ejecta source model. We consider a piezoelectric sensor fielded in the path of an ejecta cloud, for experimental configurations in which the ejecta are created at a singly shocked planar surface and fly ballistically through vacuum to the stationary sensor. To do so, we introduce the concept of a time- and velocity-dependent ejecta “areal mass function.” We derive expressions for the analytic (“true”) accumulated ejecta areal mass at the sensor and the measured (“inferred”) value obtained via the standard method for analyzing piezoelectric voltages. In this way, we derive an exact expression and upper bound for the error imposed upon a piezoelectric ejecta mass measurement (in a perfect system) by the assumption of instantaneous creation, which is commonly required for momentum diagnostic analyses. This error term is zero for truly instantaneous source models; otherwise, the standard piezoelectric analysis is guaranteed to overestimate the true mass. When combined with a piezoelectric dataset, this framework provides a unique solution for the ejecta particle velocity distribution, subject to the assumptions inherent in the data analysis. The framework also leads to strong boundary conditions that any ejecta source model must satisfy in order to be consistent with apparently global properties of piezoelectric measurements from a wide range of experiments. We demonstrate this methodology by applying it to the Richtmyer–Meshkov instability+self-similar velocity distribution ejecta source model currently under development at Los Alamos National Laboratory.

97 MATHEMATICS AND COMPUTING↗

A game theoretic approach to a finite-time disturbance attenuation problem

A disturbance attenuation problem over a finite-time interval is considered by a game theoretic approach where the control, restricted to a function of the measurement history, plays against adversaries composed of the process and measurement disturbances, and the initial state. A zero-sum game, formulated as a quadratic cost criterion subject to linear time-varying dynamics and measurements, is solved by a calculus of variation technique. By first maximizing the quadratic cost criterion with respect to the process disturbance and initial state, a full information game between the control and the measurement residual subject to the estimator dynamics results. The resulting solution produces an n-dimensional compensator which expresses the controller as a linear combination of the measurement history. A disturbance attenuation problem is solved based on the results of the game problem. For time-invariant systems it is shown that under certain conditions the time-varying controller becomes time-invariant on the infinite-time interval. The resulting controller satisfies an H(infinity) norm bound.

Rhee, Ihnseok↗

Architectures and random properties of symplectic quantum circuits

Parametrized and random unitary (or orthogonal) n-qubit circuits play a central role in quantum information. As such, one could naturally assume that circuits implementing symplectic transformations would attract similar attention. However, this is not the case, as $\mathbb{SP}(d/2)$—the group of d × d unitary symplectic matrices—has thus far been overlooked. In this work, we aim at starting to fill this gap. We begin by presenting a universal set of generators $\mathcal{G}$ for the symplectic algebra $\mathfrak{sp}(d/2)$, consisting of one- and two-qubit Pauli operators acting on neighboring sites in a one-dimensional lattice. Here, we uncover two critical differences between such set, and equivalent ones for unitary and orthogonal circuits. Namely, we find that the operators in $\mathcal{G}$ cannot generate arbitrary local symplectic unitaries and that they are not translationally invariant. We then review the Schur–Weyl duality between the symplectic group and the Brauer algebra, and use tools from Weingarten calculus to prove that Pauli measurements at the output of Haar random symplectic circuits can converge to Gaussian processes. As a by-product, such analysis provides us with concentration bounds for Pauli measurements in circuits that form t-designs over $\mathbb{SP}(d/2)$. To finish, we present tensor-network tools to analyze shallow random symplectic circuits, and we use these to numerically show that computational-basis measurements anti-concentrate at logarithmic depth.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Method for Assessing Effectiveness and Technical Capabilities Required for Integrated Deterrence (NSLP-Final Report-Draft2022)

The United States faces an ever-increasingly multi-polar security environment dominated by great power competition with China and a lingering Russian threat as well as from would-be regional hegemons led by ambitions from Iran and North Korea. Our adversaries are pursuing and expanding the strategic means by-which they have an asymmetric offset (e.g., cyber, space, and other modes below the level of armed conflict). To combat and deter against the widening range of hostile actions, the U.S. must have additional capabilities with-which to deter. All of which drives us towards a more thoughtful integrated approach to deterrence, attempting to best align deterrent tools with the adversary actions in order to maximize the credibility of our deterrent. Such an approach complicates our deterrence strategy and demands a methodology to assess whether the U.S. has the deterrent tools necessary to deter the adversarial actions most costly to the U.S. To address this complexity, we create a framework to comprehensively and systematically assess our deterrent tools as qualitatively measured against the adversarial actions we wish to deter. Deterrence is ultimately an operation in the cognitive domain and at the heart of the framework presented here is the fundamental deterrence calculus which we use as the defining measure of whether a tool will credibly deter a given action. We describe the eight levers of the deterrence calculus and distill these levers to four products that are used to qualitatively assess the overall effectiveness of deterrence tools against adversarial actions. Credibility is determined by two principal variables: the technical credibility of the deterrent tool, and the principle of proportionality. Technical credibility of realized deterrence products is assessed through development of key mission requirements and hardware (e.g., components) that will impose costs, deny benefits, or encourage restraint. The principle of proportionality qualitatively asserts that for a deterrent tool to be cognitively credible, the costs imposed against, or benefits denied by, an action are commensurate to the magnitude of costs received from the adversarial action. By basing this framework on these two fundamentals, it is possible to compare deterrent tools in a systematic approach across the broad spectrum of hostile actions.

42 ENGINEERING↗

Questions Revisited: A Close Examination of Calculus of Inference and Inquiry

In this paper I examine more closely the way in which probability theory, the calculus of inference, is derived from the Boolean lattice structure of logical assertions ordered by implication. I demonstrate how the duality between the logical conjunction and disjunction in Boolean algebra is lost when deriving the probability calculus. In addition, I look more closely at the other lattice identities to verify that they are satisfied by the probability calculus. Last, I look towards developing the calculus of inquiry demonstrating that there is a sum and product rule for the relevance measure as well as a Bayes theorem. Current difficulties in deriving the complete inquiry calculus will also be discussed.

Knuth, Kevin H.↗

Analytic solutions for Asay foil trajectories with implications for ejecta source models and mass measurements

We consider the trajectory of an Asay foil ejecta diagnostic for scenarios where ejecta are produced at a singly shocked planar surface and fly ballistically through a perfect vacuum to the sensor. We do so by building upon a previously established mathematical framework derived for the analytic study of stationary sensors. First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source model. The result is an integrodifferential equation of motion for the foil trajectory. This equation yields an easily calculable closed-form implicit solution for the foil trajectory in instant-production scenarios. From there, we derive a boundary condition that particle velocity distributions must satisfy if their associated foil trajectories are to exhibit a smooth initial acceleration, as occurs in some experiments. This condition is identical to one derived previously from a consideration of piezoelectric voltage data obtained in similar experiments. We also compare techniques for inferring accumulated ejecta masses from foil trajectories, first by deriving the exact solution, and then by quantifying the error imposed by a frequently used approximate solution (both subject to the assumption of instantaneous ejecta production). Finally, we examine the common practice of presenting inferred cumulative ejecta masses as a function of implied ejecta velocity, establishing the conditions under which this methodology is most meaningful.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Analytical Identification Method of Generalized Short‐Circuit Ratio Using Phasor Measurement Units

This paper introduces a novel analytical approach for the identification of the admittance matrix and the generalized short-circuit ratio (gSCR) in power systems integrated with renewable energy sources. The proposed method leverages voltage and current measurements from phasor measurement units (PMUs) to construct a least squares objective function, which is then solved using matrix calculus and partial derivatives. Unlike conventional optimization algorithms, this approach provides an analytical solution that substantially reduces data requirements, enabling the efficient and accurate identification of the gSCR with smaller datasets. Additionally, its fixed computational complexity allows for real-time updates as new data are collected, ensuring continuous refinement of the system of equations and enabling rapid, precise gSCR calculations. The method also exhibits strong robustness against measurement noise, making it well-suited for practical applications in dynamic power systems. The combination of reduced data requirements, real-time adaptability, noise robustness and fixed computational load establishes this method as a highly efficient and reliable tool for real-time power system stability analysis. Case studies on an EPRI 36-bus system demonstrate the method's effectiveness, highlighting its accuracy in closely matching true gSCR values, even under diverse disturbances and noisy conditions.

Han, Zelei [Hohai University, Nanjing (China)] (OR↗

System identification and model reduction using modulating function techniques

Weighted least squares (WLS) and adaptive weighted least squares (AWLS) algorithms are initiated for continuous-time system identification using Fourier type modulating function techniques. Two stochastic signal models are examined using the mean square properties of the stochastic calculus: an equation error signal model with white noise residuals, and a more realistic white measurement noise signal model. The covariance matrices in each model are shown to be banded and sparse, and a joint likelihood cost function is developed which links the real and imaginary parts of the modulated quantities. The superior performance of above algorithms is demonstrated by comparing them with the LS/MFT and popular predicting error method (PEM) through 200 Monte Carlo simulations. A model reduction problem is formulated with the AWLS/MFT algorithm, and comparisons are made via six examples with a variety of model reduction techniques, including the well-known balanced realization method. Here the AWLS/MFT algorithm manifests higher accuracy in almost all cases, and exhibits its unique flexibility and versatility. Armed with this model reduction, the AWLS/MFT algorithm is extended into MIMO transfer function system identification problems. The impact due to the discrepancy in bandwidths and gains among subsystem is explored through five examples. Finally, as a comprehensive application, the stability derivatives of the longitudinal and lateral dynamics of an F-18 aircraft are identified using physical flight data provided by NASA. A pole-constrained SIMO and MIMO AWLS/MFT algorithm is devised and analyzed. Monte Carlo simulations illustrate its high-noise rejecting properties. Utilizing the flight data, comparisons among different MFT algorithms are tabulated and the AWLS is found to be strongly favored in almost all facets.

Shen, Yan↗

Formal Modeling of Multi-Agent Systems using the Pi-Calculus and Epistemic Logic

Multi-agent systems have become important recently in computer science, especially in artificial intelligence (AI). We allow a broad sense of agent, but require at least that an agent has some measure of autonomy and interacts with other agents via some kind of agent communication language. We are concerned in this paper with formal modeling of multi-agent systems, with emphasis on communication. We propose for this purpose to use the pi-calculus, an extension of the process algebra CCS. Although the literature on the pi-calculus refers to agents, the term is used there in the sense of a process in general. It is our contention, however, that viewing agents in the AI sense as agents in the pi-calculus sense affords significant formal insight. One formalism that has been applied to agents in the AI sense is epistemic logic, the logic of knowledge. The success of epistemic logic in computer science in general has come in large part from its ability to handle concepts of knowledge that apply to groups. We maintain that the pi-calculus affords a natural yet rigorous means by which groups that are significant to epistemic logic may be identified, encapsulated, structured into hierarchies, and restructured in a principled way. This paper is organized as follows: Section 2 introduces the pi-calculus; Section 3 takes a scenario from the classical paper on agent-oriented programming [Sh93] and translates it into a very simple subset of the n-calculus; Section 4 then shows how more sophisticated features of the pi-calculus may bc brought into play; Section 5 discusses how the pi-calculus may be used to define groups for epistemic logic; and Section 6 is the conclusion.

Rorie, Toinette↗

Space Mathematics: A Resource for Secondary School Teachers

A collection of mathematical problems related to NASA space science projects is presented. In developing the examples and problems, attention was given to preserving the authenticity and significance of the original setting while keeping the level of mathematics within the secondary school curriculum. Computation and measurement, algebra, geometry, probability and statistics, exponential and logarithmic functions, trigonometry, matrix algebra, conic sections, and calculus are among the areas addressed.

Kastner, Bernice↗

Polarization effects on hard target calibration of lidar systems

The theory of hard target calibration of lidar backscatter data, including laboratory measurements of the pertinent target reflectance parameters, is extended to include the effects of polarization of the transmitted and received laser radiation. The bidirectional reflectance-distribution function model of reflectance is expanded to a 4 x 4 matrix allowing Mueller matrix and Stokes vector calculus to be employed. Target reflectance parameters for calibration of lidar backscatter data are derived for various lidar system polarization configurations from integrating sphere and monostatic reflectometer measurements. It is found that correct modeling of polarization effects is mandatory for accurate calibration of hard target reflectance parameters and, therefore, for accurate calibration of lidar backscatter data.

Kavaya, Michael J.↗

Effective Field Theory of Random Quantum Circuits

Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, and a hallmark of quantum chaos—universal Wigner–Dyson level statistics—has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive the universal random matrix behavior of a large family of random circuits. In particular, we rederive the Wigner–Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method of evaluating integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the study of quantum circuits. The effective field theory derived here provides both a method to quantitatively characterize the quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and a path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Do-calculus enables estimation of causal effects in partially observed biomolecular pathways

Abstract Motivation Estimating causal queries, such as changes in protein abundance in response to a perturbation, is a fundamental task in the analysis of biomolecular pathways. The estimation requires experimental measurements on the pathway components. However, in practice many pathway components are left unobserved (latent) because they are either unknown, or difficult to measure. Latent variable models (LVMs) are well-suited for such estimation. Unfortunately, LVM-based estimation of causal queries can be inaccurate when parameters of the latent variables are not uniquely identified, or when the number of latent variables is misspecified. This has limited the use of LVMs for causal inference in biomolecular pathways. Results In this article, we propose a general and practical approach for LVM-based estimation of causal queries. We prove that, despite the challenges above, LVM-based estimators of causal queries are accurate if the queries are identifiable according to Pearl’s do-calculus and describe an algorithm for its estimation. We illustrate the breadth and the practical utility of this approach for estimating causal queries in four synthetic and two experimental case studies, where structures of biomolecular pathways challenge the existing methods for causal query estimation. Availability and implementation The code and the data documenting all the case studies are available at https://github.com/srtaheri/LVMwithDoCalculus. Supplementary information Supplementary data are available at Bioinformatics online.

59 BASIC BIOLOGICAL SCIENCES↗

Multi-instanton calculus in $c$ = 1 string theory

We formulate a strategy for computing the complete set of non-perturbative corrections to closed string scattering in c = 1 string theory from the worldsheet per spective. This requires taking into account the effect of multiple ZZ-instantons, including higher instantons constructed from ZZ boundary conditions of type (m, 1), with a careful treatment of the measure and contour in the integration over the instanton moduli space. The only a priori ambiguity in our prescription is a normalization constant $\mathcal{N}_m$ that ap pears in the integration measure for the (m, 1)-type ZZ instanton, at each positive integer m. We investigate leading corrections to the closed string reflection amplitude at the n instanton level, i.e. of order e -n/g s , and find striking agreement with our recent proposal on the non-perturbative completion of the dual matrix quantum mechanics, which in turn fixes $\mathcal{N}_m$ for all m.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗