Kitaev, “Quantum computing: algorithms and error correction”, Russian Mathematical Surveys, to appear. QEC is based on three central ideas: digitization of noise, the manipulation of error operators and syndromes, and quantum error correcting code (QECC). Girvin These lecture notes from the 2019 Les Houches Summer School on Quantum Information Machines are intended to provide an introduction to classical and quantum error correction with bits and qubits, and with continuous variable systems (harmonic oscillators). Sloane, “The Theory of Error-Correcting Codes”, North-Holland, Amsterdam (1977).Ī. Introduction to Quantum Error Correction and Fault Tolerance Steven M. Shor, “Fault-tolerant quantum computation”, LANL e-print quantph/9605011, į. Sloane, “Quantum error correction and orthogonal geometry”, LANL e-print quant-ph/9605005, Wootters, “Mixed state entanglement and quantum error-correcting codes”, LANL e-print quantph/9604024, Ī. In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault. Zurek, “Perfect quantum error correction code,” LANL e-print quant-ph/9602019,Ĭ. The qubits are located on the edges the stabilizers comprise 2 types of local operators. Shor, “Good quantum error-correcting codes exist”, LANL e-print quant-ph/9512032, (to appear in Phys. The information is stored in a quantum error-correcting code, which is a subspace in a larger Hilbert space. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Quantum error correction is a set of methods to protect quantum information-that is, quantum states-from unwanted environmental interactions (decoherence) and other forms of noise. Steane, “Multiple particle interference and quantum error correction”, LANL e-print quant-ph/9601029, (submitted to Proc.
QUANTUM ERROR CORRECTION PDF PDF
Shor, “Scheme for reducing decoherence in quantum memory,” Phys. Pdf : quantum-error-correction.pdf Book Excerpt : This text presents an algebraic approach to the construction of several important families of quantum codes derived from classical codes by applying the well-known Calderbank-Shor-Steane (CSS), Hermitian, and Steane enlargement constructions to certain classes of classical codes. Shor, “Algorithms for quantum computation: discrete log and factoring”, Proceedings of the 35th Annual Symposium on the Foundations of Computer Science (IEEE Computer Society Press, Los Alamitos, CA, 1994), p.
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