Efficient Quantum Circuits for Non-Qubit Quantum Error-Correcting Codes
<|reference_start|>Efficient Quantum Circuits for Non-Qubit Quantum Error-Correcting Codes: 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).<|reference_end|>
@article{grassl2002efficient,
    title={Efficient Quantum Circuits for Non-Qubit Quantum Error-Correcting Codes},
    author={Markus Grassl (1,2), Martin Roetteler (1), and Thomas Beth (1),
  (Universitaet Karlsruhe (1), The Mathematical Sciences Research Institute
  (2))},
    journal={International Journal of Foundations of Computer Science (IJFCS),
  Vol. 14, No. 5 (2003), pp. 757-775},
    year={2002},
    doi={10.1142/S0129054103002011},
    archivePrefix={arXiv},
    eprint={quant-ph/0211014},
    primaryClass={quant-ph cs.ET}
}