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Surface codes are promising for practical quantum error correction due to their high threshold and experimental feasibility. However, their performance under realistic noise conditions, particularly those involving correlated errors,…

Quantum Physics · Physics 2025-06-19 SiYing Wang , Yue Yan , ZhiXin Xia , Xiang-Bin Wang

Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…

Quantum Physics · Physics 2009-04-17 Daniel Gottesman

A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…

Quantum Physics · Physics 2018-02-01 P. Baireuther , T. E. O'Brien , B. Tarasinski , C. W. J. Beenakker

PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…

Quantum Physics · Physics 2018-02-06 Nikolas P. Breuckmann

Recently, operator quantum error-correcting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. This note introduces a natural construction of such codes in…

Quantum Physics · Physics 2007-07-13 Andreas Klappenecker , Pradeep Kiran Sarvepalli

Quantum error correction is essential for achieving fault-tolerant quantum computation. However, most typical quantum error-correcting codes are designed for generic noise models, which may fail to accurately capture the intricate noise…

Quantum Physics · Physics 2026-05-21 Yuguo Shao , Yong-Chang Li , Fuchuan Wei , Hao Zhan , Ben Wang , Zhaohui Wei , Lijian Zhang , Zhengwei Liu

Quantum error correcting codes have a distance parameter, conveying the minimum number of single spin errors that could cause error correction to fail. However, the success thresholds of finite per-qubit error rate that have been proven for…

Quantum Physics · Physics 2014-03-26 Alastair Kay

Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…

Quantum Physics · Physics 2015-04-13 Barbara M. Terhal

Quantum error correction is essential for the development of any scalable quantum computer. In this work we introduce a generalization of a quantum interleaving method for combating clusters of errors in toric quantum error-correcting…

We show how to obtain concrete constructions of homological quantum codes based on tilings of 2D surfaces with constant negative curvature (hyperbolic surfaces). This construction results in two-dimensional quantum codes whose tradeoff of…

Quantum Physics · Physics 2016-08-25 Nikolas P. Breuckmann , Barbara M. Terhal

The surface code is designed to suppress errors in quantum computing hardware and currently offers the most believable pathway to large-scale quantum computation. The surface code requires a 2-D array of nearest-neighbor coupled qubits that…

Quantum Physics · Physics 2013-10-04 Austin G. Fowler

Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…

Quantum computation and communication rely on the ability to manipulate quantum states robustly and with high fidelity. Thus, some form of error correction is needed to protect fragile quantum superposition states from corruption by…

Quantum error-correcting code for higher dimensional systems can, in general, be directly constructed from the codes for qubit systems. What remains unknown is whether there exist efficient code design techniques for higher dimensional…

Quantum Physics · Physics 2020-08-04 Ritajit Majumdar , Susmita Sur-Kolay

A theory for constructing quantum error correcting codes from Toric surfaces by the Calderbank-Shor-Steane method is presented. In particular we study the method on toric Hirzebruch surfaces. The results are obtained by constructing a…

Algebraic Geometry · Mathematics 2013-03-11 Johan P. Hansen

We study Algebraic Geometry codes producing quantum error-correcting codes by the CSS construction. We pay particular attention to the family of Castle codes. We show that many of the examples known in the literature in fact belong to this…

Information Theory · Computer Science 2016-06-30 Carlos Munuera , Wanderson Tenório , Fernando Torres

Quantum computers face significant challenges from quantum deviations or coherent noise, particularly during gate operations, which pose a complex threat to the efficacy of quantum error correction (QEC) protocols. In this study, we…

Quantum Physics · Physics 2025-03-11 Yuanchen Zhao , Dong E. Liu

The fragile nature of quantum information limits our ability to construct large quantities of quantum bits suitable for quantum computing. An important goal, therefore, is to minimize the amount of resources required to implement quantum…

Quantum Physics · Physics 2013-04-11 Adam Paetznick , Austin G. Fowler

A central challenge for the scaling of quantum computing systems is the need to control all qubits in the system without a large overhead. A solution for this problem in classical computing comes in the form of so called crossbar…

Quantum Physics · Physics 2018-03-28 Jonas Helsen , Mark Steudtner , Menno Veldhorst , Stephanie Wehner

The surface code is one the most promising alternatives for implementing fault-tolerant, large-scale quantum information processing. Its high threshold for single-qubit errors under stochastic noise is one of its most attrative features. We…

Quantum Physics · Physics 2014-10-29 Pejman Jouzdani , E. Novais , I. S. Tupitsyn , Eduardo R. Mucciolo