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The smallest quantum code that can correct all one-qubit errors is based on five qubits. We experimentally implemented the encoding, decoding and error-correction quantum networks using nuclear magnetic resonance on a five spin subsystem of…

Quantum Physics · Physics 2013-05-29 E. Knill , R. Laflamme , R. Martinez , C. Negrevergne

Quantum error correction is indispensable to achieving reliable quantum computation. When quantum information is encoded redundantly, a larger Hilbert space is constructed using multiple physical qubits, and the computation is performed…

Quantum Physics · Physics 2026-01-29 Hoshitaro Ohnishi , Hideo Mukai

Gottesman, Kitaev and Preskill have proposed a scheme to encode a qubit in a harmonic oscillator, which is called the GKP code. It is designed to be resistant to small shift errors contained in momentum and position quadratures. Thus…

Quantum Physics · Physics 2019-08-02 Yang Wang

Experimental realization of stabilizer-based quantum error correction (QEC) codes that would yield superior logical qubit performance is one of the formidable task for state-of-the-art quantum processors. A major obstacle towards realizing…

Quantum Physics · Physics 2022-03-14 I. A. Simakov , I. S. Besedin , A. V. Ustinov

Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…

Quantum Physics · Physics 2026-04-17 Nico Meyer , Christopher Mutschler , Dominik Seuß , Andreas Maier , Daniel D. Scherer

Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…

Quantum Physics · Physics 2008-02-03 Dorit Aharonov , Michael Ben-Or

Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of…

Quantum Physics · Physics 2008-12-18 Daniel Gottesman , Alexei Kitaev , John Preskill

We investigate the usage of highly efficient error correcting codes of multilevel systems to protect encoded quantum information from erasure errors and implementation to repetitively correct these errors. Our scheme makes use of quantum…

Quantum Physics · Physics 2017-01-23 Sreraman Muralidharan , Chang-Ling Zou , Linshu Li , Jianming Wen , Liang Jiang

Reliable quantum information processing in the face of errors is a major fundamental and technological challenge. Quantum error correction protects quantum states by encoding a logical quantum bit (qubit) in multiple physical qubits. To be…

It is important to protect quantum information against decoherence and operational errors, and quantum error-correcting (QEC) codes are the keys to solving this problem. Of course, just the existence of codes is not efficient. It is…

Quantum Physics · Physics 2007-05-23 Jumpei Niwa , Keiji Matsumoto , Hiroshi Imai

The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…

Quantum Physics · Physics 2007-05-23 A. M. Steane

In a recent paper ([1]=quant-ph/0606035) it is shown how the optimal recovery operation in an error correction scheme can be considered as a semidefinite program. As a possible future improvement it is noted that still better error…

Quantum Physics · Physics 2007-05-23 M. Reimpell , R. F. Werner , K. Audenaert

The implementation of practical error correction protocols is essential for deployment of quantum information technologies. Ways of exploiting high-spin nuclei, which have multi-level quantum resources, have attracted interest in this…

Quantum Physics · Physics 2025-11-11 Sumin Lim , Arzhang Ardavan

Quantum Error Correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding…

Quantum Physics · Physics 2009-01-23 Emanuel Knill , Raymond Laflamme

We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…

Quantum Physics · Physics 2016-09-08 H. Bombin , M. A. Martin-Delgado

We present an error correcting protocol that enhances the lifetime of stabilizer code based qubits which are susceptible to the creation of pairs of localized defects (due to string-like error operators) at finite temperature, such as the…

Quantum Physics · Physics 2017-07-19 C. Daniel Freeman , C. M. Herdman , K. B. Whaley

When sending quantum information over a channel, we want to ensure that the message remains intact. Quantum error correction and quantum authentication both aim to protect (quantum) information, but approach this task from two very…

Quantum Physics · Physics 2022-11-18 Yfke Dulek , Garazi Muguruza , Florian Speelman

We construct explicitly two infinite families of genuine nonadditive 1-error correcting quantum codes and prove that their coding subspaces are 50% larger than those of the optimal stabilizer codes of the same parameters via the linear…

Quantum Physics · Physics 2009-01-15 Sixia Yu , Qing Chen , C. H. Oh

Quantum computing promises to solve problems previously deemed infeasible. However, high error rates necessitate quantum error correction for practical applications. Seminal experiments with zoned neutral atom architectures have shown…

Quantum Physics · Physics 2025-06-03 Yannick Stade , Ludwig Schmid , Lukas Burgholzer , Robert Wille

We describe a class of "neighboring-blocks" stabilizer quantum error correction codes and demonstrate that such class of codes can be implemented in a resource-efficient manner using a single ancilla and circular near-neighbor qubit…

Quantum Physics · Physics 2023-03-07 A. V. Antipov , E. O. Kiktenko , A. K. Fedorov