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Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively…

Protection of quantum information from noise is a massive challenge. One avenue people have begun to explore is reducing the number of particles needing to be protected from noise and instead use systems with more states, so called qudit…

Quantum Physics · Physics 2020-06-24 Lane G. Gunderman

We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…

Quantum Physics · Physics 2007-05-23 H. Ollivier , J. -P. Tillich

Recent advances in quantum error-correction (QEC) have shown that it is often beneficial to understand fault-tolerance as a dynamical process, a circuit with redundant measurements that help correct errors, rather than as a static code…

Quantum Physics · Physics 2025-09-30 Arthur Pesah , Austin K. Daniel , Ilan Tzitrin , Michael Vasmer

We propose a new scheme for quantum error correction using robust continuous variable probe modes, rather than fragile ancilla qubits, to detect errors without destroying data qubits. The use of such probe modes reduces the required number…

Quantum Physics · Physics 2009-11-11 Fumiko Yamaguchi , Kae Nemoto , William J. Munro

I give an overview of the basic concepts behind quantum error correction and quantum fault tolerance. This includes the quantum error correction conditions, stabilizer codes, CSS codes, transversal gates, fault-tolerant error correction,…

Quantum Physics · Physics 2007-11-16 Daniel Gottesman

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

Fault-tolerant operations based on stabilizer codes are the state of the art in suppressing error rates in quantum computations. Most such codes do not permit a straightforward implementation of non-Clifford logical operations, which are…

Quantum error correction (QEC) enables reliable computation on noisy hardware by encoding logical information across many physical qubits and periodically measuring parities to detect errors. A decoder is the classical algorithm that uses…

Programming Languages · Computer Science 2026-03-23 Abtin Molavi , Feras Saad , Aws Albarghouthi

We discuss two methods to encode one qubit into six physical qubits. Each of our two examples corrects an arbitrary single-qubit error. Our first example is a degenerate six-qubit quantum error-correcting code. We explicitly provide the…

Quantum Physics · Physics 2008-08-12 Bilal Shaw , Mark M. Wilde , Ognyan Oreshkov , Isaac Kremsky , Daniel A. Lidar

Quantum error correction (QEC) plays a critical role in preventing information loss in quantum systems and provides a framework for reliable quantum computation. Identifying quantum codes with nice code parameters for physically motivated…

Quantum Physics · Physics 2025-04-24 Sourav Dutta , Debjyoti Biswas , Prabha Mandayam

Scalable realisation of quantum computing is reliant on the development of fault tolerant devices. Analysis of quantum error correction protocols typically considers incoherent noise models or noise-free syndrome measurements. While this is…

Quantum Physics · Physics 2026-05-29 Ben Harper , Azar C. Nakhl , Martin Sevior , Muhammad Usman

We introduce the concept of generalized concatenated quantum codes. This generalized concatenation method provides a systematical way for constructing good quantum codes, both stabilizer codes and nonadditive codes. Using this method, we…

Quantum Physics · Physics 2009-05-24 Markus Grassl , Peter Shor , Graeme Smith , John Smolin , Bei Zeng

Up to now every good quantum error-correcting code discovered has had the structure of an eigenspace of an Abelian group generated by tensor products of Pauli matrices; such codes are known as stabilizer or additive codes. In this letter we…

Quantum Physics · Physics 2009-01-23 Eric M. Rains , R. H. Hardin , Peter W. Shor , N. J. A. Sloane

It is a standard result in the theory of quantum error-correcting codes that no code of length n can fix more than n/4 arbitrary errors, regardless of the dimension of the coding and encoded Hilbert spaces. However, this bound only applies…

Quantum Physics · Physics 2007-05-23 Claude Crepeau , Daniel Gottesman , Adam Smith

Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms.…

Quantum Physics · Physics 2026-05-13 Prithviraj Prabhu

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

Quantum error correcting (QEC) codes protect quantum information against environmental noise. Computational errors caused by the environment change the quantum state within the qubit subspace, whereas quantum erasures correspond to the loss…

Quantum Physics · Physics 2025-11-26 Luis Colmenarez , Seyong Kim , Markus Müller

A new class of error-correcting quantum codes is introduced capable of stabilizing qubits against spontaneous decay arising from couplings to statistically independent reservoirs. These quantum codes are based on the idea of using an…

Quantum Physics · Physics 2009-11-07 G. Alber , Th. Beth , Ch. Charnes , A. Delgado , M. Grassl , M. Mussinger

Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial…

Quantum Physics · Physics 2026-04-27 Nouédyn Baspin , Dominic Williamson