EFFICIENT QUANTUM CIRCUITS FOR NON-QUBIT QUANTUM ERROR-CORRECTING CODES

1 October 2003

journal article
Published by World Scientific Pub Co Pte Ltd in International Journal of Foundations of Computer Science

Vol. 14 (5) , 757-775
https://doi.org/10.1142/s0129054103002011

Abstract

We present two methods for the construction of quantum circuits for quantum error- correcting codes (QECC). The underlying quantum systems are tensor products of subsystems (qudits) of equal dimension which is a prime power. For a QECC encoding k qudits into n qudits, the resulting quantum circuit has O(n(n - k)) gates. The running time of the classical algorithm to compute the quantum circuit is O(n(n - k)²).

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Version 1, 2002-11-04, ArXiv

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