Local-dimension-invariant stabilizer codes
Protection of quantum information is a central challenge in building a quantum computer. Quantum error-correcting codes can correct for logical errors that occur in the system. A particularly well-studied category is stabilizer codes, such as the 9-qubit Shor code, as these are the quantum analogue of classical additive codes. Qudits (particles with local-dimension greater than 2) have more computational basis states per particle than qubits and retain this feature in stabilizer codes.
In this seminar I will briefly review stabilizer codes and their extension to qudits. Following this, I will go through my work extending stabilizer codes to local-dimension-invariant forms. While some examples of codes which happened to be local-dimension-invariant have been known since '97 [1,2], my work provides a broader framework for creating and proving the quality of these codes [3,4]. As such, I will provide some examples along the way. This framework allows for at least one family of codes to be used, with the distance of the code being preserved, regardless of the local-dimension of the underlying system [5].
This talk is aimed at those who have taken the quantum error-correction course or do research in the topic, although hopefully the broad ideas will be understandable for those who have taken QIC 710 (or equivalent).
References:
[1] Chau, H. F. "Five quantum register error correction code for higher spin systems." Physical Review A 56, no. 1 (1997): R1.
[2] Chau, H. F. "Correcting quantum errors in higher spin systems." Physical Review A 55, no. 2 (1997): R839.
[3] Gunderman, Lane G. "Local-dimension-invariant qudit stabilizer codes." Physical Review A 101, no. 5 (2020): 052343.
[4] Gunderman, Lane G. "Degenerate Local-dimension-invariant Stabilizer Codes and an Alternative Bound for the Distance Preservation Condition." arXiv preprint arXiv:2110.15274 (2021).
[5] Moorthy, Arun J., and Lane G. Gunderman. "Local-dimension-invariant Calderbank-Shor-Steane Codes with an Improved Distance Promise." arXiv preprint arXiv:2110.11510 (2021).
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Meeting link: IQC Student Seminar
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