Related papers: Defect-Adaptive Lattice Surgery on Irregular Bound…
It is widely accepted that quantum error correction is essential for realizing large-scale fault-tolerant quantum computing. Recent experiments have demonstrated error correction codes operating below threshold, primarily using local planar…
This paper studies the lattice agreement problem in asynchronous systems and explores its application to building linearizable replicated state machines (RSM). First, we propose an algorithm to solve the lattice agreement problem in $O(\log…
In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…
The surface code is a promising platform for a quantum memory, but its threshold under coherent errors remains incompletely understood. We study maximum-likelihood decoding of the square-lattice surface code in the presence of single-qubit…
We present the first high performance compiler for very large scale quantum error correction: it translates an arbitrary quantum circuit to surface code operations based on lattice surgery. Our compiler offers an end to end error correction…
We propose a fault-tolerant quantum computation scheme that is broadly applicable to quantum low-density parity-check (qLDPC) codes. The scheme achieves constant qubit overhead and a time overhead of $O(d^{a+o(1)})$ for any $[[n,k,d]]$…
We introduce the ``Sequential Empirical Bayes Method'', an adaptive constrained-curve fitting procedure for extracting reliable priors. These are then used in standard augmented-$\chi^2$ fits on separate data. This better stabilizes fits to…
This paper addresses the overwhelming computational resources needed with standard numerical approaches to simulate architected materials. Those multiscale heterogeneous lattice structures gain intensive interest in conjunction with the…
The recently introduced tile codes are a promising alternative to surface codes, combining two-dimensional locality with higher encoding efficiency. While surface codes are well understood in terms of their logical operators and boundary…
We present new convergence analyses for parallel subspace correction methods for unconstrained semicoercive and nearly semicoercive convex optimization problems, generalizing the theory of singular and nearly singular linear problems to a…
We study various aspects of half-BPS surface defect operators in $\mathcal{N}=4$ SYM. For defects on generic points on the moduli space we use superconformal symmetry to fix the form of one-point and two-point functions of half-BPS…
This paper proposes some efficient and accurate adaptive two-grid (ATG) finite element algorithms for linear and nonlinear partial differential equations (PDEs). The main idea of these algorithms is to utilize the solutions on the $k$-th…
Automated program repair (APR) techniques are effective in fixing inevitable defects in software, enhancing development efficiency and software robustness. However, due to the difficulty of generating precise specifications, existing APR…
In this work, we consider adaptive linear programming (ALP) decoding of linear codes over the finite field $\mathbb{F}_p$ of size $p$ where $p$ is a prime. In particular, we provide a general construction of valid inequalities for the…
When binary linear error-correcting codes are used over symmetric channels, a relaxed version of the maximum likelihood decoding problem can be stated as a linear program (LP). This LP decoder can be used to decode error-correcting codes at…
We introduce a dilated coordinate method to address computational challenges in nuclear lattice effective field theory (NLEFT) for weakly-bound few-body systems. The approach employs adaptive mesh refinement via analytic coordinate…
Reliability is an important requirement for both communication and storage systems. Due to continuous scale down of technology multiple adjacent bits error probability increases. The data may be corrupted due soft errors. Error correction…
We consider spatially coupled low-density parity-check codes with finite smoothing parameters. A finite smoothing parameter is important for designing practical codes that are decoded using low-complexity windowed decoders. By optimizing…
Fault-tolerant quantum computation using two-dimensional topological quantum error correcting codes can benefit from multi-qubit long-range operations. By using simple commutation rules, a quantum circuit can be transpiled into a sequence…
We introduce a novel model-theoretic framework inspired from graph modification and based on the interplay between model theory and algorithmic graph minors. The core of our framework is a new compound logic operating with two types of…