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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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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations

We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator as a weighted sum of Hamiltonian evolutions, thereby emulating a dissipative problem by mixing various time scales. We introduce an efficient encoding of the LCHS into a quantum circuit based on a simple coordinate transformation that turns the dependence on the summation index into a trigonometric function. Classically, this method is equivalent to the use of a highly accurate Fejér-Clenshaw-Curtis quadrature formula. Quantumly, this significantly simplifies block-encoding of a dissipative problem and allows one to perform an exponential number of Hamiltonian simulations by a single Quantum Signal Processing (QSP) circuit. The resulting LCHS circuit has high success probability and the selector scales logarithmically with the number of terms in the LCHS sum and linearly with time. Careful analysis of error convergence proves that this method is more efficient than other LCHS circuits that have recently appeared in the literature. We verify the quantum circuit and its scaling by simulating it on a digital emulator of fault-tolerant quantum computers and, as a test problem, solve the advection-diffusion equation. The proposed algorithm can be used for simulating a wide class of nonunitary initial-value problems including the Liouville equation with added dissipation and linear embeddings of nonlinear systems, such as the Koopman-von Neumann and Carleman embeddings.

Novikau, I [Lawrence Livermore National Laboratory↗
DOE OSTI2025

Computing Nonequilibrium Responses with Score-Shifted Stochastic Differential Equations

Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic dynamics. For nonequilibrium systems, perturbations cannot be interpreted simply by monitoring fluctuations in a conjugate observable and general response results rely on path ensemble averaging. Furthermore, these techniques do not apply to perturbations that affect the diffusion tensor in a stochastic system. Here, we introduce an “effective” physical process that represents the diffusion perturbed dynamics and enables accurate calculations of responses to a change in the diffusion. Interestingly, the effective dynamics contain an additional drift involving the instantaneous “score” of the system, and we leverage score matching algorithms to carry out nonequilibrium response calculations on systems for which the exact stationary distribution is unknown.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

The Differential Equations That Model Diseases

In this brief tutorial, I will describe the simplest way of modeling a deadly infectious disease, such as COVID-19. I will show that at early times, the disease grows exponentially, but at late times, falls off like a Bell curve. I will solve the equations numerically with Python. A common mathematical model is the so-called compartmental model, where diseases can move people between "categories" such as healthy, infectious, or truly sick. This is a large, well established field and there are many good resources on this topic. I started with the SIAM review article The mathematics of infectious diseases. However, there are many excellent textbooks and more modern reviews as well.

60 APPLIED LIFE SCIENCES↗