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High-fidelity decoding of quantum error correction codes relies on an accurate experimental model of the physical errors occurring in the device. Because error probabilities can depend on the context of the applied operations, the error…
This paper studies the qualitative behavior and robustness of two variants of Minimal Random Code Learning (MIRACLE) used to compress variational Bayesian neural networks. MIRACLE implements a powerful, conditionally Gaussian variational…
While the proper orthogonal decomposition (POD) is optimal under certain norms it's also expensive to compute. For large matrix sizes, it is well known that the QR decomposition provides a tractable alternative. Under the assumption that it…
Recent experimental advances have made it possible to implement logical multi-qubit transversal gates on surface codes in a multitude of platforms. A transversal controlled-NOT (tCNOT) gate on two surface codes introduces correlated errors…
We propose a novel method to calculate logical error rates in surface codes, assuming independent and identically distributed physical errors. We show how to use our method to analyze hypothetical quantum computers with various…
Densest Subgraph Problem (DSP) is an important primitive problem with a wide range of applications, including fraud detection, community detection and DNA motif discovery. Edge-based density is one of the most common metrics in DSP.…
Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this…
Low-rank decomposition has emerged as an important problem in Large Language Model (LLM) fine-tuning and inference. Through Singular Value Decomposition (SVD), the weight matrix can be factorized into low-rank spaces optimally. Previously,…
In this paper we consider a Metzner-Kapturowski-like decoding algorithm for high-order interleaved sum-rank-metric codes, offering a novel perspective on the decoding process through the concept of an error code. The error code, defined as…
In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. Using this new concept, we derive properties of maximum rank distance (MRD) codes that parallel…
We investigate threshold-based multi-trial decoding of concatenated codes with an inner Maximum-Likelihood decoder and an outer error/erasure (L+1)/L-extended Bounded Distance decoder, i.e. a decoder which corrects e errors and t erasures…
We introduce surface ZZZY codes, a novel family of quantum error-correcting codes designed for asymmetric channels. Derived from standard surface codes through tailored modification of generators, ZZZY codes can be decoded by the minimum…
We consider error decoding of locally repairable codes (LRC) and partial MDS (PMDS) codes through interleaved decoding. For a specific class of LRCs we investigate the success probability of interleaved decoding. For PMDS codes we show that…
Recent research in decoding methods for Natural Language Generation (NLG) tasks has shown that MAP decoding is not optimal, because model probabilities do not always align with human preferences. Stronger decoding methods, including Quality…
We study the Maximum Cardinality Matching (MCM) and the Maximum Weight Matching (MWM) problems, on trees and on some special classes of graphs, in the Online Preemptive and the Incremental Dynamic Graph models. In the {\em Online…
In this paper, we propose two new algorithms for maximum-likelihood estimation (MLE) of high dimensional sparse covariance matrices. Unlike most of the state of-the-art methods, which either use regularization techniques or penalize the…
An algorithm is presented for error correction in the surface code quantum memory. This is shown to correct depolarizing noise up to a threshold error rate of 18.5%, exceeding previous results and coming close to the upper bound of 18.9%.…
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…
Large Language Models (LLMs) have become an indispensable part of natural language processing tasks. However, autoregressive sampling has become an efficiency bottleneck. Multi-Draft Speculative Decoding (MDSD) is a recent approach where,…
We propose improved exact and heuristic algorithms for solving the maximum weight clique problem, a well-known problem in graph theory with many applications. Our algorithms interleave successful techniques from related work with novel data…