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相关论文: On the Construction of New Toric Quantum Codes and…

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Toric codes are error-correcting codes that are derived from toric varieties, which hold a unique correspondence to integral convex polytopes. In this paper, we focus on integral convex polytopes $P \subseteq \mathbb{R}^2$ and the toric…

代数几何 · 数学 2025-09-26 Amelia Gibbs , Eliza Hogan , Kelly Jabbusch , Jenna Plute , Nicholas Toloczko

Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a…

There have been various constructions of classical codes from polynomial valuations in literature \cite{ARC04, LNX01,LX04,XF04,XL00}. In this paper, we present a construction of classical codes based on polynomial construction again. One of…

信息论 · 计算机科学 2013-08-19 Lingfei Jin , Chaoping Xing

We present a construction of self-orthogonal codes using product codes. From the resulting codes, one can construct both block quantum error-correcting codes and quantum convolutional codes. We show that from the examples of convolutional…

量子物理 · 物理学 2009-05-24 Markus Grassl , Martin Roetteler

We construct $\mathbb{Z}_p$-lattices and $\mathbb{F}_q[\![t]\!]$-lattices from cyclic $(f,\sigma)$-codes over finite chain rings, employing quotients of natural nonassociative orders and principal left ideals in carefully chosen…

环与代数 · 数学 2025-01-22 Susanne Pumpluen

Quantum LDPC codes may provide a path to build low-overhead fault-tolerant quantum computers. However, as general LDPC codes lack geometric constraints, na\"ive layouts couple many distant qubits with crossing connections which could be…

量子物理 · 物理学 2022-08-17 Maxime A. Tremblay , Nicolas Delfosse , Michael E. Beverland

The hypergraph product (HGP) construction of quantum error-correcting codes (QECC) offers a general and explicit method for building a QECC from two classical codes, thereby paving the way for the discovery of good quantum low-density…

量子物理 · 物理学 2025-12-29 Yue Wu , Meng-Yuan Li , Chengshu Li , Hui Zhai

We investigate CSS and CSS-T quantum error-correcting codes from the point of view of their existence, rarity, and performance. We give a lower bound on the number of pairs of linear codes that give rise to a CSS code with good correction…

信息论 · 计算机科学 2024-05-29 Elena Berardini , Alessio Caminata , Alberto Ravagnani

We present new quantum codes with good parameters which are constructed from self-orthogonal algebraic geometry codes. Our method permits a wide class of curves to be used in the formation of these codes, which greatly extends the class of…

We propose a unifying paradigm for analyzing and constructing topological quantum error correcting codes as dynamical circuits of geometrically local channels and measurements. To this end, we relate such circuits to discrete fixed-point…

量子物理 · 物理学 2024-03-27 Andreas Bauer

In this paper, we explore the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds for scalable, fault-tolerant quantum computation. To circumvent the traditionally low thresholds of small…

量子物理 · 物理学 2022-12-15 Alexis T. E. Shaw , Michael J. Bremner , Alexandru Paler , Daniel Herr , Simon J. Devitt

In this paper, we construct the first families of asymmetric quantum convolutional codes (AQCC)'s. These new AQCC's are constructed by means of the CSS-type construction applied to suitable families of classical convolutional codes, which…

量子物理 · 物理学 2016-10-05 Giuliano G. La Guardia

We consider some questions related to codes constructed using various graphs, in particular focusing on graphs which are not lattices in two or three dimensions. We begin by considering Floquet codes which can be constructed using…

量子物理 · 物理学 2023-08-22 M. B. Hastings

Quantum error correction codes play a central role in the realisation of fault-tolerant quantum computing. Chamon model is a 3D generalization of the toric code. The error correction computation on this model has not been explored so far.…

量子物理 · 物理学 2023-03-10 Jian Zhao , Yu-Chun Wu , Guo-Ping Guo

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…

量子物理 · 物理学 2015-05-30 Jeonghwan Shin , Jun Heo , Todd A. Brun

Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…

This report surveys quantum error-correcting codes. As Preskill claimed, 21st century would be the golden age of quantum error correction. Quantum channels behave differently from classical channels, so researchers face difficulties in…

量子物理 · 物理学 2007-05-23 Hsun-Hsien Chang

Quantum error correction was invented to allow for fault-tolerant quantum computation. Systems with topological order turned out to give a natural physical realization of quantum error correcting codes (QECC) in their groundspaces. More…

量子物理 · 物理学 2019-09-17 Fernando G. S. L. Brandao , Elizabeth Crosson , M. Burak Şahinoğlu , John Bowen

Based on the group structure of a unitary Lie algebra, a scheme is provided to systematically and exhaustively generate quantum error correction codes, including the additive and nonadditive codes. The syndromes in the process of…

量子物理 · 物理学 2013-11-01 Ming-Chung Tsai , Po-Chung Chen , Kuan-Peng Chen , Zheng-Yao Su

Quantum error-correcting codes (QECC's) are needed to combat the inherent noise affecting quantum processes. Using ZX calculus, we represent QECC's in a form called a ZX diagram, consisting of a tensor network. In this paper, we present…

量子物理 · 物理学 2024-06-19 Andrey Boris Khesin , Alexander Li