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We consolidate recent theoretical advances in Detector Error Model (DEM) estimation and formalize several algorithms to learn DEM parameters and structure from syndromes without using a decoder, demonstrating recovery of known DEMs from…
We propose a decoder for quantum low density parity check (LDPC) codes based on a beam search heuristic guided by belief propagation (BP). Our beam search decoder applies to all quantum LDPC codes and achieves different speed-accuracy…
Massive multiuser (MU) multiple-input multiple-output (MIMO) promises significant improvements in spectral efficiency compared to small-scale MIMO. Typical massive MU-MIMO base-station (BS) designs rely on centralized linear data detectors…
Quantum error-correcting codes (QECCs) are necessary for fault-tolerant quantum computation. Surface codes are a class of topological QECCs that have attracted significant attention due to their exceptional error-correcting capabilities and…
The 2D Least Median of Squares (LMS) is a popular tool in robust regression because of its high breakdown point: up to half of the input data can be contaminated with outliers without affecting the accuracy of the LMS estimator. The…
We present an approach to showing that a linear code is resilient to random errors. We use this approach to obtain decoding results for both transitive codes and Reed-Muller codes. We give three kinds of results about linear codes in…
We compare the performance of quantum error correcting codes when memory errors are unitary with the more familiar case of dephasing noise. For a wide range of codes we analytically compute the effective logical channel that results when…
Fault-tolerant quantum computing demands decoders that are fast, accurate, and adaptable to circuit structure and realistic noise. While machine learning (ML) decoders have demonstrated impressive performance for quantum memory, their use…
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…
Semi-supervised semantic segmentation (SSSS) aims to improve segmentation performance by utilizing large amounts of unlabeled data with limited labeled samples. Existing methods often suffer from coupling, where over-reliance on initial…
Fault-tolerant quantum computation demands extremely low logical error rates, yet superconducting qubit arrays are subject to radiation-induced correlated noise arising from cosmic-ray muon-generated quasiparticles. The quasiparticle…
With the development of quantum hardware bringing the error-corrected quantum circuits to the near future, the lack of an efficient polynomial-time decoding algorithms for logical circuits presents a critical bottleneck. While quantum…
Log parsing converts log messages into structured event templates, allowing for automated log analysis and reducing manual inspection effort. To select the most compatible parser for a specific system, multiple evaluation metrics are…
We suggest a technique for constructing lower (existence) bounds for the fault-tolerant threshold to scalable quantum computation applicable to degenerate quantum codes with sublinear distance scaling. We give explicit analytic expressions…
This paper presents a GPU-accelerated decoder for quantum low-density parity-check (QLDPC) codes that achieves sub-$63$ $\mu$s latency, below the surface code decoder's real-time threshold demonstrated on Google's Willow quantum processor.…
Homological product codes are a class of codes that can have improved distance while retaining relatively low stabilizer weight. We show how to build union-find decoders for these codes, using a union-find decoder for one of the codes in…
We prove a new version of the quantum threshold theorem that applies to concatenation of a quantum code that corrects only one error, and we use this theorem to derive a rigorous lower bound on the quantum accuracy threshold epsilon_0. Our…
In this paper, we present an improved union bound on the Linear Programming (LP) decoding performance of the binary linear codes transmitted over an additive white Gaussian noise channels. The bounding technique is based on the second-order…
Parameters of LDPC codes, such as minimum distance, stopping distance, stopping redundancy, girth of the Tanner graph, and their influence on the frame error rate performance of the BP, ML and near-ML decoding over a BEC and an AWGN channel…
Quantum error correcting (QEC) codes protect quantum information from decoherence, as long as error rates fall below critical error thresholds. In general, obtaining thresholds implies simulating the QEC procedure using, in general,…