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Related papers: Quantum error-correcting codes and their geometrie…

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It is shown that the noise process in quantum computation can be described by spatially correlated decoherence and dissipation. We demonstrate that the conventional quantum error correcting codes correcting for single-qubit errors are…

Quantum Physics · Physics 2007-05-23 Lu-Ming Duan , Guang-Can Guo

Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…

Quantum Physics · Physics 2025-02-07 Ilya. A. Simakov , Ilya. S. Besedin

We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing…

Quantum Physics · Physics 2007-05-23 Raymond Laflamme , Cesar Miquel , Juan Pablo Paz , Wojciech Hubert Zurek

Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…

Quantum Physics · Physics 2018-12-13 Ciarán Ryan-Anderson

We study the decoherence of a quantum computer in an environment which is inherently correlated in time and space. We first derive the nonunitary time evolution of the computer and environment in the presence of a stabilizer error…

Quantum Physics · Physics 2007-05-23 E. Novais , Harold U. Baranger

The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most…

Quantum Physics · Physics 2007-05-23 Dave Bacon , Andrea Casaccino

The noise in physical qubits is fundamentally asymmetric: in most devices, phase errors are much more probable than bit flips. We propose a quantum error correcting code which takes advantage of this asymmetry and shows good performance at…

Quantum Physics · Physics 2015-06-26 Lev Ioffe , Marc Mezard

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

Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…

Quantum Physics · Physics 2015-06-26 Mark S. Byrd , Daniel A. Lidar

Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit…

Quantum Physics · Physics 2013-04-24 Yuichiro Fujiwara

The recently introduced detected-jump correcting quantum codes are capable of stabilizing qubit-systems against spontaneous decay processes arising from couplings to statistically independent reservoirs. These embedded quantum codes exploit…

Quantum Physics · Physics 2011-03-31 G. Alber , Th. Beth , Ch. Charnes , A. Delgado , M. Grassl , M. Mussinger

Errors in quantum computers are of two kinds: sudden perturbations to isolated qubits, and slow random drifts of all the qubits. The latter may be reduced, but not eliminated, by means of symmetrization, namely by using many replicas of the…

Quantum Physics · Physics 2007-05-23 Asher Peres

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

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

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 convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…

Quantum Physics · Physics 2009-10-31 H. F. Chau

In this paper, we address the problem of state communication in finite-level quantum systems through noise-affected channels. Our approach is based on a self-consistent theory of decoding inner products associated with the code and error…

Quantum Physics · Physics 2025-06-06 Jorge R. Bolaños-Servín , Yuriko Pitones , Josué I. Rios-Cangas

This paper characterizes Goppa codes of certain maximal curves over finite fields defined by equations of the form $y^n = x^m + x$. We investigate Algebraic Geometric and quantum stabilizer codes associated with these maximal curves and…

Algebraic Geometry · Mathematics 2025-02-07 Vahid Nourozi

Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…

Quantum Physics · Physics 2024-03-21 Arijit Mondal , Keshab K. Parhi

This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…

Quantum Physics · Physics 2015-04-08 Keisuke Fujii