Quantum Error-Correcting Codes for Qudit Amplitude Damping

• Published in: IEEE transactions on information theory Vol. 64; no. 6; pp. 4674 - 4685
• Main Authors: Grassl, Markus, Kong, Linghang, Wei, Zhaohui, Yin, Zhang-Qi, Zeng, Bei
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-06-2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptation models; Amplitude damping channel; Amplitudes; Binary system; Channels; Codes; Damping; Decay; Decoding; Depolarization; Energy dissipation; Error correcting codes; Error correction; Error correction & detection; Error correction codes; Markov processes; Photonics; Photons; quantum codes; Quantum mechanics; qudit
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2018.2790423

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 with Markovian bath 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 (e.g., the number of photons) 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. In addition, 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 <inline-formula> <tex-math notation="LaTeX">V </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\Lambda </tex-math></inline-formula> channels.