Related papers: Code generation for AMReX with applications to num…
We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…
This work develops a class of probabilistic algorithms for the numerical solution of nonlinear, time-dependent partial differential equations (PDEs). Current state-of-the-art PDE solvers treat the space- and time-dimensions separately,…
Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…
We present a Fortran 95 code for simulating the evolution of astrophysical systems using particles to represent the underlying fluid flow. The code is designed to be versatile, flexible and extensible, with modular options that can be…
Code generation is a core application of large language models (LLMs), yet LLMs still frequently fail on complex programming tasks. Given its success in mathematical reasoning, test-time scaling approaches such as Process Reward Model…
Additive codes and some nonadditive codes use the single and multiple invariant subspaces of the stabilizer G, respectively, to construct quantum codes, so the selection of the invariant subspaces is a key problem. In this paper, I provide…
A semi-implicit finite difference time domain (FDTD) numerical Maxwell solver is developed for full electromagnetic Particle-in-Cell (PIC) codes for the simulations of plasma-based acceleration. The solver projects the volumetric Yee…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
We have simulated the formation of a galaxy cluster in a $\Lambda$CDM universe using twelve different codes modeling only gravity and non-radiative hydrodynamics (\art, \arepo, \hydra\ and 9 incarnations of GADGET). This range of codes…
In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the problem of the identification of coefficients from some additional information. This work deals with the problem of…
A common task in astronomical research is to estimate the physical parameters (temperature, mass, density etc.) of a gas by using observed line emission. This often requires a calculation of how the radiation propagates via emission and…
Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular…
We present AsterX, a novel open-source, modular, GPU-accelerated, fully general relativistic magnetohydrodynamic (GRMHD) code designed for dynamic spacetimes in 3D Cartesian coordinates, and tailored for exascale computing. We utilize…
We have constructed new formulae for generation of solutions for the nonlinear heat equation and for the Burgers equation that are based on linearizing nonlocal transformations and on nonlocal symmetries of linear equations. Found nonlocal…
Due to their fast decoding algorithms, quantum generalizations of low-density parity check, or LDPC, codes have been investigated as a solution to the problem of decoherence in fragile quantum states. However, the additional twisted inner…
Random number generation is an enabling technology for fields as varied as Monte Carlo simulations and quantum information science. An important application is a secure quantum key distribution (QKD) system; here, we propose and demonstrate…
A new hybrid scheme for numerical relativity will be presented. The scheme will employ a 3-dimensional spacelike lattice to record the 3-metric while using the standard 3+1 ADM equations to evolve the lattice. Each time step will involve…
We present ADAM, a software system for designing and running child language learning experiments in Python. The system uses a virtual world to simulate a grounded language acquisition process in which the language learner utilizes…
Computational methods are essential to provide waveforms from coalescing black holes, which are expected to produce strong signals for the gravitational wave observatories being developed. Although partial simulations of the coalescence…
Cadabra is an open access program ideally suited to complex tensor commutations in General Relativity. Tensor expressions are written in LaTeX while an enhanced version of Python is used to control the computations. This tutorial assumes no…