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Results for “Interactive Theorem Proving”

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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Formally Verified ZTA Requirements for OT/ICS Environments with Isabelle/HOL

The clean energy transformation includes the integration of distributed energy resources with the power grid, which has led to a substantial increase in the complexity of power grids infrastructure and the underlying operational technology environment. Power grids infrastructure represents an operational technology environment that has become a system of systems, integrating heterogeneous devices which are both software-and hardware-intensive; as a result, there are increasing demands to exploit advances in the commodity of software-hardware infrastructures to improve energy systems requirements such as cybersecurity and resilience. In such a setting, system requirements at different levels mix, which leads to vulnerabilities and undesirable outcomes. The use of formal methods to characterize and prove system requirements removes ambiguity, increases automation, and provides high levels of assurance and reliability. In this paper, we contribute a methodology and a framework for the system-level verification of zero trust architecture requirements in operational technology environments. We define a formal specification for the core functionalities of operational technology environments, the corresponding invariants, and security proofs. Of particular note is our modular approach for the formal verification of asynchronous interactions in operational technology environments. The formal specification and the proofs have been mechanized using the interactive theorem proving environment Isabelle/HOL.

formal methods↗
DOE OSTI2026

From Quantum Time to Manifestly Covariant QFT: On the Need for a Quantum-Action-Based Quantization

In quantum time (QT) schemes, time is promoted to a degree of freedom, allowing Lorentz covariance to be made explicit for single particles. We ask whether this can be lifted to QFT so that Lorentz covariance becomes manifest at the Hilbert-space level, rather than being hidden as in the standard canonical formulation. We address this question by proposing a second-quantized approach in which the elementary particle is the QT particle itself, leading naturally to the notion of spacetime field algebras and of quantum action. We show, however, that a naive many-body construction runs into inconsistencies. To pinpoint their origin we introduce a classical counterpart of the second-quantized formalism, spacetime classical mechanics (SCM), and prove a no-go theorem: Dirac quantization of SCM collapses back to standard QFT and therefore hides covariance. We circumvent this problem by presenting a quantum-action-based quantization that yields a spacetime version of quantum mechanics (SQM), making covariance manifest for (interacting) QFTs. Finally, we show that this resolution is tied to a genuine spacetime generalization of the notion of a quantum state, required by causality and closely connected to recent “states over time” proposals and, in dS/CFT–motivated settings, to microscopic notions of timelike entanglement and emergent time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Quantum speed limit for the out-of-time-ordered correlator from an open-system perspective

Scrambling, the delocalization of initially localized quantum information, is commonly characterized by the out-of-time-ordered correlator (OTOC). Employing the OTOC–Renyi-2 entropy theorem, we derive a quantum speed limit for the OTOC, which sets a lower bound for the rate with which information can be scrambled. This bound becomes particularly tractable by describing the scrambling of information in a closed quantum system as an effective decoherence process of an open system interacting with an environment. We prove that decay of the OTOC can be bounded by the strength of the system-environment coupling and two-point environmental correlation functions. We validate our analytic bound numerically using the nonintegrable transverse field Ising model. Furthermore, our results provide a universal and model-agnostic quantitative framework for understanding the dynamical limits of information spreading across quantum many-body physics, condensed matter systems, and engineered quantum platforms.

Fermions↗
DOE OSTI2026

Quantum Routing and Entanglement Dynamics Through Bottlenecks

To implement arbitrary quantum circuits in architectures with restricted interactions, one may effectively simulate all-to-all connectivity by routing quantum information. We consider the entanglement dynamics and routing between two regions only connected through an intermediate “bottleneck” region with few qubits. In such systems, where the entanglement rate is restricted by a vertex boundary rather than an edge boundary of the underlying interaction graph, existing results such as the small incremental entangling theorem give only a trivial constant lower bound on the routing time (the minimum time to perform an arbitrary permutation). We significantly improve the lower bound on the routing time in systems with a vertex bottleneck. Specifically, for any system with two regions 𝐿,𝑅 with 𝑁 𝐿 ,𝑁 𝑅 qubits, respectively, coupled only through an intermediate region 𝐶 with 𝑁 𝐶 qubits, for any 𝛿 > 0 we show a lower bound of Ω⁢(𝑁$^{1−𝛿}_{𝑅}$/√𝑁 𝐿⁢ 𝑁 𝐶 ) on the Hamiltonian quantum routing time when using piecewise time-independent Hamiltonians, or time-dependent Hamiltonians subject to a smoothness condition. We also prove an upper bound on the average amount of bipartite entanglement between 𝐿 and 𝐶,𝑅 that can be generated in time 𝑡 by such architecture-respecting Hamiltonians in systems constrained by vertex bottlenecks, improving the scaling in the system size from 𝑂⁡(𝑁 𝐿⁢ 𝑡) to 𝑂⁡(√𝑁 𝐿⁢ 𝑡). As a special case, when applied to the star graph (i.e., one vertex connected to 𝑁 leaves), we obtain an Ω⁡(√𝑁 1−𝛿 ) lower bound on the routing time and on the time to prepare 𝑁/2 Bell pairs between the vertices. We also show that, in systems of free particles, we can route optimally on the star graph in time Θ⁡(√𝑁) using Hamiltonian quantum routing, obtaining a speedup over gate-based routing, which takes time Θ⁡(𝑁).

97 MATHEMATICS AND COMPUTING↗