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Graduate texts in physics

Quantum Error Correction and Quantum Cryptography

Masahito Hayashi, Satoshi Ishizaka, Akinori Kawachi, Gen Kimura, Tomohiro Ogawa

Published Aug 22, 2014• 0 citations
Publisher
DOI
10.1007/978-3-662-43502-1_9

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Realization of long distance quantum cryptography requires quantum error correction (QEC) of the errors introduced by noise on communication channels. This chapter begins with presenting common sources of errors in QEC. For quantum information processing qubits using photons, trapped ions, superconducting circuits and spins in semiconductors have been considered. Coherent quantum errors arise due to the errors associated with system controls and/or characterization where imprecise operation on the qubit introduces inaccurate Hamiltonian dynamics. The basic principle involved in classical error correction is to increase the number of bits more than is required for a given amount of information. Digitization of quantum errors makes it possible to correct any quantum error using the ability to correct a finite set of errors. The use of stabilizer codes to describe QEC codes is highly useful. It allows for easy synthesis of correction circuits and also shows how logical operations can be performed directly on encoded data.
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Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We propose a new technique based on the use of coding in order to detect and correct errors due to imperfect transmission lines in quantum cryptography or memories in quantum computers. We give a particular example of how to detect a decohered qubit in order to transmit or preserve with high fidelity the original qubit.