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In fault-tolerant quantum computing schemes, the overhead is often dominated by the cost of preparing codewords reliably. This cost generally increases quadratically with the block size of the underlying quantum error-correcting code. In…

Quantum Physics · Physics 2013-04-15 Adam Paetznick , Ben W. Reichardt

Entangled qubit can increase the capacity of quantum error correcting codes based on stabilizer codes. In addition, by using entanglement quantum stabilizer codes can be construct from classical linear codes that do not satisfy the…

Quantum Physics · Physics 2015-05-30 Jeonghwan Shin , Jun Heo , Todd A. Brun

A long standing open question is whether the distinguisher of high rate alternant codes or Goppa codes \cite{FGOPT11} can be turned into an algorithm recovering the algebraic structure of such codes from the mere knowledge of an arbitrary…

Information Theory · Computer Science 2023-05-30 Magali Bardet , Rocco Mora , Jean-Pierre Tillich

We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.

Quantum Physics · Physics 2007-05-23 D. Schlingemann

We examine general Gottesman-Kitaev-Preskill (GKP) codes for continuous-variable quantum error correction, including concatenated GKP codes, through the lens of lattice theory, in order to better understand the structure of this class of…

Quantum Physics · Physics 2022-02-14 Jonathan Conrad , Jens Eisert , Francesco Arzani

In this work, we define Generalized Monomial Cartesian Codes (GMCC), which constitute a natural extension of generalized Reed-Solomon codes. We describe how two different generalized Reed-Solomon codes can be combined to construct one GMCC.…

Information Theory · Computer Science 2025-12-19 Oisin Campion , Fernando Hernando , Gary McGuire

While reduced-order models (ROMs) have been popular for efficiently solving large systems of differential equations, the stability of reduced models over long-time integration is of present challenges. We present a greedy approach for ROM…

Numerical Analysis · Mathematics 2018-03-20 Babak Maboudi Afkham , Jan S. Hesthaven

Stabilizer codes obtained via CSS code construction and Steane's enlargement of subfield-subcodes and matrix-product codes coming from generalized Reed-Muller, hyperbolic and affine variety codes are studied. Stabilizer codes with good…

Information Theory · Computer Science 2024-05-01 Carlos Galindo , Fernando Hernando , Diego Ruano

Quantum error correction (QEC) is essential for scalable quantum computing, yet decoding errors via conventional algorithms result in limited accuracy (i.e., suppression of logical errors) and high overheads, both of which can be alleviated…

Quantum Physics · Physics 2025-10-09 Xiangjun Mi , Frank Mueller

We investigate quantum receiver architectures for demodulation $M$-ary Pulse Position Modulation under thermal noise and photon-starved conditions. Building on the greed receiver framework, we analyze it using jointly optimized…

Quantum Physics · Physics 2025-09-15 Leo Bia , Christos N. Gagatsos , Saikat Guha

Using the Weyl commutation relations over a finite field we introduce a family of error-correcting quantum stabilizer codes based on a class of symmetric matrices over the finite field satisfying certain natural conditions. When the field…

Quantum Physics · Physics 2007-05-23 V. Arvind , K. R. Parthasarathy

Guessing Random Additive Noise Decoding (GRAND) and its variants, known for their near-maximum likelihood performance, have been introduced in recent years. One such variant, Segmented GRAND, reduces decoding complexity by generating only…

Information Theory · Computer Science 2025-12-19 Lukas Rapp , Jiewei Feng , Muriel Médard , Ken R. Duffy

To produce an operable quantum computer that is made with imperfect hardware, we must design and test scalable quantum error correcting codes that are suited for the devices we can build and, in unison, develop decoding strategies that…

We apply quantum Construction X on quasi-cyclic codes with large Hermitian hulls over $\mathbb{F}_4$ and $\mathbb{F}_9$ to derive good qubit and qutrit stabilizer codes, respectively. In several occasions we obtain quantum codes with…

Information Theory · Computer Science 2020-04-28 Martianus Frederic Ezerman , San Ling , Buket Özkaya , Patrick Solé

Greedy algorithms are popular in compressive sensing for their high computational efficiency. But the performance of current greedy algorithms can be degenerated seriously by noise (both multiplicative noise and additive noise). A robust…

Information Theory · Computer Science 2014-02-10 Yurrit Avonds , Yipeng Liu , Sabine Van Huffel

We introduce \emph{stratified colimit codes}: stabiliser codes obtained by taking the degree-wise colimit $\mathcal C_\bullet(X):=\operatorname*{colim}_{\sigma\in X}F(\sigma)$ of a functor $F\colon X\to\mathbf{Ch}(R)$ from a finite poset…

Quantum Physics · Physics 2025-09-10 William Boone Samuels

Stabiliser codes with large weight measurements can be challenging to implement fault-tolerantly. To overcome this, we propose a Floquetification procedure which, given a stabiliser code, synthesises a novel Floquet code that only uses…

Quantum Physics · Physics 2024-12-17 Benjamin Rodatz , Boldizsár Poór , Aleks Kissinger

This paper introduces a new quantization scheme for real and complex Grassmannian sources. The proposed approach relies on a structured codebook based on a geometric construction of a collection of bent grids defined from an initial mesh on…

Information Theory · Computer Science 2016-10-27 Alexis Decurninge , Maxime Guillaud

Decoding sparse quantum codes can be accomplished by syndrome-based decoding using a belief propagation (BP) algorithm.We significantly improve this decoding scheme by developing a new feedback adjustment strategy for the standard BP…

Quantum Physics · Physics 2013-09-25 Yun-Jiang Wang , Barry C. Sanders , Bao-Ming Bai , Xin-Mei Wang

Graph Neural Networks are notorious for its memory consumption. A recent Transformer-based GNN called Graph Transformer is shown to obtain superior performances when long range dependencies exist. However, combining graph data and…

Machine Learning · Computer Science 2024-03-25 Eugene Ku