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arXiv · 1509.06829

Quantum Error-Correcting Codes for Qudit Amplitude Damping

Markus Grassl·Linghang Kong·Zhaohui Wei·Zhang-Qi Yin·Bei Zeng
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Abstract

Traditional quantum error-correcting codes are designed for the depolarizing channel modeled by generalized Pauli errors occurring with equal probability. Amplitude damping channels model, in general, the decay process of a multilevel atom or energy dissipation of a bosonic system at zero temperature. We discuss quantum error-correcting codes adapted to amplitude damping channels for higher dimensional systems (qudits). For multi-level atoms, we consider a natural kind of decay process, and for bosonic systems,we consider the qudit amplitude damping channel obtained by truncating the Fock basis of the bosonic modes to a certain maximum occupation number. We construct families of single-error-correcting quantum codes that can be used for both cases. Our codes have larger code dimensions than the previously known single-error-correcting codes of the same lengths. Additionally, we present families of multi-error correcting codes for these two channels, as well as generalizations of our construction technique to error-correcting codes for the qutrit $V$ and $\Lambda$ channels.

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Markus Grassl, Linghang Kong, Zhaohui Wei, Zhang-Qi Yin, Bei Zeng. 2015-09-23. Quantum Error-Correcting Codes for Qudit Amplitude Damping. https://doi.org/10.1109/tit.2018.2790423

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