Steane, A.: Multiple‐particle interference and quantum errorĬorrection. Steane, A.: Error correcting codes in quantum theory. Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. They anticipate that by leveraging on the theory of fault-tolerant quantum computation, their scheme can achieve a high QFI even with imperfect QEC operation. Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. This means quantum error-corrected telescopes are easier than error-corrected quantum computers. 2(1+) This is why 3 is needed for bit-flips. In general, an -qubit code, protecting against single-qubit bit-flips requires. This is why we can distinguish errors and correct them. MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error–Correcting So, there will be 4 orthogonal 2D subspaces (correct and 3 with errors), which all fit well into 8D Hilbert space. Kribs, D., Laflamme, R., Poulin, D.: Unified and generalized approach to Knill, E., Laflamme, R., Martinez, R., Negrevergne, C.: Benchmarking quantumĬomputers: the five-qubit error correcting code.

Knill, E., Laflamme, R.: Theory of quantum error‐correcting codes. Gottesman, D.: Stabilizer codes and quantum error correction, Gottesman, D.: Class of quantum error‐correcting codes saturating the quantum

Theory 44, 1369–1387 (1998)Ĭalderbank, A.R., Shor, P.W.: Good quantum error‐correcting codesĬhiaverini, J., Leibfried, D., Schaetz, T., Barrett, M.D., Blakestad, R.B.,īritton, J., Itano, W.M., Jost, J.D., Knill, E., Langer, C., Ozeri, R., Wineland, D.J.: Realization of quantum error correction. In: Proceedings of the 47th Symposium on Foundations of Computer Scienceīennett, C.H., DiVincenzo, D.P., Smolin, J.A., Wootters, W.K.: Mixed-stateĮntanglement and quantum error correction. Multiparty quantum computation with (only) a strict honest majority. This process is experimental and the keywords may be updated as the learning algorithm improves.īen-Or, M., Crépeau, C., Gottesman, D., Hassidim, A., Smith, A.: Secure These keywords were added by machine and not by the authors. Its effect is to randomly apply one of the. This quantum channel is called the depolarizing channel and depends on a parameter p. A basic channel is the quantum mechanical analog of the classical binary symmetric channel . For more information about quantum channels and quantum information in general, see . Quantum noise is usually modeled by the notion of a quantum channel which generalizes the classical case, and, in particular, includes scenarios for communication (space) and storage (time) of quantum information.

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The book introduces concepts gradually, starting from intuitive and basic. This noise problem threatens quantum computers and their great promise, namely to provide a computational advantage over classical computers for certain problems (see also the cross references in the Sect.“ Cross References”). Quantum Information Processing and Quantum Error Correction: An Engineering Approach 1st Edition by Ivan B. Readers not interested in quantum error correction can approach only the. Basic subjects as well as advanced theory and a survey of topics from cutting-edge research make this book invaluable both as a pedagogical introduction at the graduate level and as a reference for experts in quantum information science.Quantum systems can never be considered isolated from an environment which permanently causes disturbances of the state of the system. The book is not limited to a single approach, but reviews many different methods to control quantum errors, including topological codes, dynamical decoupling and decoherence-free subspaces. Distance of a quantum code, and elementary.

Fundamental criteria for error correction. This comprehensive text, written by leading experts in the field, focuses on quantum error correction and thoroughly covers the theory as well as experimental and practical issues. Basics of quantum error correction: Modeling errors on a quantum computer. Scalable quantum computers require a far-reaching theory of fault-tolerant quantum computation. To achieve large scale quantum computers and communication networks it is essential not only to overcome noise in stored quantum information, but also in general faulty quantum operations. Quantum computation and information is one of the most exciting developments in science and technology of the last twenty years.

Quantum error correction book