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Efficient Quantum Circuits for Non-Qubit Quantum Error-Correcting Codes

Markus Grassl·Martin Roetteler·Thomas Beth
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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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Markus Grassl, Martin Roetteler, Thomas Beth. 2002-11-04. Efficient Quantum Circuits for Non-Qubit Quantum Error-Correcting Codes. https://doi.org/10.1142/s0129054103002011

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