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Analytical technique for simplification of the encoder-decoder circuit for a perfect five-qubit error correction

Jin-Yuan Hsieh·Che-Ming Li·Der-San Chuu
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Abstract

Simpler encoding and decoding networks are necessary for more reliable quantum error correcting codes (QECCs). The simplification of the encoder-decoder circuit for a perfect five-qubit QECC can be derived analytically if the QECC is converted from its equivalent one-way entanglement purification protocol (1-EPP). In this work, the analytical method to simplify the encoder-decoder circuit is introduced and a circuit that is as simple as the existent simplest circuits is presented as an example. The encoder-decoder circuit presented here involves nine single- and two-qubit unitary operations, only six of which are controlled-NOT (CNOT) gates.

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Jin-Yuan Hsieh, Che-Ming Li, Der-San Chuu. 2005-12-23. Analytical technique for simplification of the encoder-decoder circuit for a perfect five-qubit error correction. https://doi.org/10.1088/1367-2630%2F8%2F5%2F080

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