Quantum codes, and especially the additive and symplectic constructions thereof, were one of the reasons for our initial interest in the Clifford- Weil group. General quantum codes behave in many ways like classical selforthogonal codes, and there are strong connections with the theory of self-dual codes. In particular, Theorems 11.1.12, 11.1.16, 11.1.26 and 11.1.32 of Chapter 11 are all based on phenomena first noticed for quantum codes (more precisely, for codes of Type 4H+, but as we will see, the two are extremely closely related). There is also a direct connection: the natural group of equivalences acting on a symplectic quantum code is exactly the complex Clifford group X m = C m (.(2II)) (cf. Theorem 6.2.1).
KeywordsHermitian Operator Partial Trace Quantum Code Additive Code Weight Enumerator
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