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A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing…
Harmonic decomposition of surfaces, such as spherical and spheroidal harmonics, is used to analyze morphology, reconstruct, and generate surface inclusions of particulate microstructures. However, obtaining high-quality meshes of…
Compressed sensing is an image reconstruction technique to achieve high-quality results from limited amount of data. In order to achieve this, it utilizes prior knowledge about the samples that shall be reconstructed. Focusing on image…
Homogenization is a fundamental technique for estimating the macroscopic properties of materials with microscale heterogeneity. Among Homogenization methods, the FFT-based Homogenization algorithm has become widely used due to its…
Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the…
Homogenization in terms of multiscale limits transforms a multiscale problem with $n+1$ asymptotically separated microscales posed on a physical domain $D \subset \mathbb{R}^d$ into a one-scale problem posed on a product domain of dimension…
The reasoning abilities of Large Language Models (LLMs) can be improved by structurally denoising their weights, yet existing techniques primarily focus on denoising the feed-forward network (FFN) of the transformer block, and can not…
We describe a framework for controlling and improving the quality of high-order finite element meshes based on extensions of the Target-Matrix Optimization Paradigm (TMOP) of Knupp. This approach allows high-order applications to have a…
Quantum processing units boost entanglement at the level of hardware and enable physical simulations of highly correlated electron states in molecules and intermolecular chemical bonds. The variational quantum eigensolver provides a…
This paper describes a class of shape optimization problems for optical metamaterials comprised of periodic microscale inclusions composed of a dielectric, low-dimensional material suspended in a non-magnetic bulk dielectric. The shape…
This paper presents an efficient and compact MATLAB code for three-dimensional stress-based sensitivity analysis. The 146 lines code includes the finite element analysis and p-norm stress sensitivity analysis based on the adjoint method.…
The study of holographic bulk-boundary dualities has led to the construction of novel quantum error correcting codes. Although these codes have shed new light on conceptual aspects of these dualities, they have widely been believed to lack…
This paper demonstrates the computational design of soft elastomeric pneumatic actuators using nonlinear topology optimization. An existing density- and porohyperelasticity-based topology optimization framework was extended from 2D to 3D…
Topological quantum error correction is a milestone in the scaling roadmap of quantum computers, which targets circuits with trillions of gates that would allow running quantum algorithms for real-world problems. The square-lattice surface…
We present a novel characterization of the mapping of multiple parallelism forms (e.g. data and model parallelism) onto hierarchical accelerator systems that is hierarchy-aware and greatly reduces the space of software-to-hardware mapping.…
A crucial insight for practical quantum error correction is that different types of errors, such as single-qubit Pauli operators, typically occur with different probabilities. Finding an optimal quantum code under such biased noise is a…
We propose a versatile and efficient algorithmic framework for optimizing fermion-to-qubit mappings by generalizing the idea of randomized block coordinate descent. Our greedy approach, termed Randomized Subsystem Descent, iteratively…
We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…
We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…
Although stress-constrained topology optimization has been extensively studied in structural design, the development of optimization frameworks to enable the creation of metamaterials with optimal mechanical performance is still an open…