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Nested space-filling designs are nested designs with attractive low-dimensional stratification. Such designs are gaining popularity in statistics, applied mathematics and engineering. Their applications include multi-fidelity computer…
Scalable quantum computation with linear optics was considered to be impossible due to the lack of efficient two-qubit logic gates, despite its ease of implementation of one-qubit gates. Two-qubit gates necessarily need a nonlinear…
Separation logic's compositionality and local reasoning properties have led to significant advances in scalable static analysis. But program analysis has new challenges -- many programs display computational effects and, orthogonally,…
Neural scaling laws have revolutionized the design and optimization of large-scale AI models by revealing predictable relationships between model size, dataset volume, and computational resources. Early research established power-law…
We present a scheme which offers a significant reduction in the resources required to implement linear optics quantum computing. The scheme is a variation of the proposal of Knill, Laflamme, and Milburn, and makes use of an incremental…
The need for accurate calculations on atoms and diatomic molecules is motivated by the opportunities and challenges of such studies. The most commonly-used approach for all-electron electronic structure calculations in general - the linear…
A brief review is presented of the scaling of complex fluids, polymers and polyelectrolytes in solution and in confined geometry, in thermodynamical, structural and rheology properties using equilibrium and nonequilibrium dissipative…
This contribution investigates the computational complexity of simulating linear ordinary differential equations (ODEs) on digital computers. We provide an exact characterization of the complexity blowup for a class of ODEs of arbitrary…
This short report focuses on the scalability challenges of the on-chip diffractive optical neural networks. It addresses an emerging gap in the literature, specifically around the limitations and challenges of scaling optical neural…
Atomic ensembles, comprising clouds of atoms addressed by laser fields, provide an attractive system for both the storage of quantum information, and the coherent conversion of quantum information between atomic and optical degrees of…
Many applications in computational physics involve approximating problems with microstructure, characterized by multiple spatial scales in their data. However, these numerical solutions are often computationally expensive due to the need to…
The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…
Simulating large quantum circuits on hardware with limited qubit counts is often attempted through methods like circuit knitting, which typically incur sample costs that grow exponentially with the number of connections cut. In this work,…
Quantum computing has shown great potential in various quantum chemical applications such as drug discovery, material design, and catalyst optimization. Although significant progress has been made in quantum simulation of simple molecules,…
A novel neural network (NN) approach is proposed for constrained optimization. The proposed method uses a specially designed NN architecture and training/optimization procedure called Neural Optimization Machine (NOM). The objective…
Quantum spatial search has been widely studied with most of the study focusing on quantum walk algorithms. We show that quantum walk algorithms are extremely sensitive to systematic errors. We present a recursive algorithm which offers…
The linked cell list algorithm is an essential part of molecular simulation software, both molecular dynamics and Monte Carlo. Though it scales linearly with the number of particles, there has been a constant interest in increasing its…
Recent years have witnessed the adoption of optical circuit switch (OCS) technology. How to design the physical topology, defined by the physical wiring between electrical switching equipments and the OCS, is fundamental to designing…
The linear programming method is applied to the space $\U_n(\C)$ of unitary matrices in order to obtain bounds for codes relative to the diversity sum and the diversity product. Theoretical and numerical results improving previously known…
It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular…