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IEEE International Symposium on Circuits and Systems proceedings

Quantum Circuits for Stabilizer Codes

Chien-Hsing Wu, Yan-Chr Tsai, Hwa-Long Tsai

Published Jul 27, 2005• 1 citation
Publisher

Abstract

Stabilizer codes constitute an important class of quantum error correction codes. This paper examines the sign-generation circuit based on controlled phase flip (Z) gates, and presents quantum circuits for efficient encoding and decoding of the [5,1,3] stabilizer code.
DOI
10.1109/iscas.2005.1465092

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Mapping the error syndromes to error operators is the core of quantum decoding network and the key step to realize quantum error correction. The definitions of the bit flip error syndrome matrix and the phase flip error syndrome matrix are presented, and then the error syndromes of Pauli errors are expressed in terms of the columns of the bit flip error syndrome matrix and the phase flip error syndrome matrix. It is also shown that the error syndrome matrix of a stabilizer code is determined by its check matrix, which is similar to the relationship between the classical error and the parity check matrix of classical codes. So, the techniques of error detection and error correction for classical linear codes can be applied to quantum stabilizer codes after some modifications. The error correction circuits are constructed based on the relationship between the error operator and error syndrom. The decoding circuit is constructed by reversing the encoding circuit because the encoding operators are unitary.
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