Related papers: A framework for large-scale relativistic simulatio…
We incorporate a massless scalar field into a 3-dimensional code for the characteristic evolution of the gravitational field. The extended 3-dimensional code for the Einstein--Klein--Gordon system is calibrated to be second order…
In the Hamiltonian formulation, Quantum Field Theory calculations scale exponentially with spatial volume, making real-time simulations intractable on classical computers and motivating quantum computation approaches. In Hamiltonian…
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We…
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV…
The recently introduced Quantum Lego framework provides a powerful method for generating complex quantum error correcting codes (QECCs) out of simple ones. We gamify this process and unlock a new avenue for code design and discovery using…
We present a numerical framework for modeling extended hyperelastic bodies based on a Lagrangian formulation of general relativistic elasticity theory. We use finite element methods to discretize the body, then use the semi--discrete action…
The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are…
We study a quantum-algorithmic framework for parameterizing partial differential equations (PDEs). For a broad class of problems in which the discretized parameter field admits a diagonal representation, block-encodings of diagonal…
This work presents a novel methodology for deriving stationary and axially symmetric solutions to Einstein field equations using the 1+3 tetrad formalism. This approach reformulates the Einstein equations into first order scalar equations,…
Optimization-based samplers such as randomize-then-optimize (RTO) [2] provide an efficient and parallellizable approach to solving large-scale Bayesian inverse problems. These methods solve randomly perturbed optimization problems to draw…
We consider quantum computational models defined via a Lie-algebraic theory. In these models, specified initial states are acted on by Lie-algebraic quantum gates and the expectation values of Lie algebra elements are measured at the end.…
Quantum field theories provide fundamental models of complex interacting systems, from high-energy physics and cosmology to condensed matter. However, solving these models in non-perturbative and dynamical regimes is often extremely…
In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these…
Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment.…
The effective Hamiltonian serves as the conceptual pivot of quantum engineering, transforming physical complexity into programmable logic; yet, its construction remains compromised by the mathematical non-uniqueness of block…
We present a high-order scheme for solving the full non-linear Einstein equations on characteristic null hypersurfaces using the framework established by Bondi and Sachs. This formalism allows asymptotically flat spaces to be represented on…
Large Language Models (LLMs) have driven substantial progress in artificial intelligence in recent years, exhibiting impressive capabilities across a wide range of tasks, including mathematical problem-solving. Inspired by the success of…
Nonlinear stochastic differential equations (NSDEs) are a pillar of mathematical modeling for scientific and engineering applications. Accurate and efficient simulation of large-scale NSDEs is prohibitive on classical computers due to the…
Ellipsoid fitting is of general interest in machine vision, such as object detection and shape approximation. Most existing approaches rely on the least-squares fitting of quadrics, minimizing the algebraic or geometric distances, with…
We reexamine the relativistic 2+1 dimensional Lee model in light-front coordinates on flat space and on a space-time with a spatial section given by a compact manifold in the usual canonical formalism. The simpler 2+1 dimension is chosen…