No More Perfect Codes: Classification of Perfect Quantum Codes
Zhuo Li, Lijuan Xing
TL;DR
This paper classifies perfect quantum codes and proves that the only nontrivial ones are those with specific parameters, establishing their uniqueness in quantum error correction.
Contribution
It provides a complete classification of perfect quantum codes, showing no other nontrivial codes exist beyond the known parameters.
Findings
Only known nontrivial perfect quantum codes are those with specific parameters.
No other nontrivial perfect quantum codes exist.
The classification resolves a long-standing problem in quantum coding theory.
Abstract
We solve the problem of the classification of perfect quantum codes. We prove that the only nontrivial perfect quantum codes are those with the parameters . There exist no other nontrivial perfect quantum codes.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Quantum-Dot Cellular Automata