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5 changes: 5 additions & 0 deletions codes/quantum/qubits/stabilizer/rm/quantum_reed_muller.yml
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Non-CSS codes can be derived from such codes by modifying the \(X\)-type stabilizers \cite{arxiv:quant-ph/9608026}.

CSS codes formed from a single RM code are also possible: CSS\((\text{RM}(r,m), \text{RM}(r,m))\), valid whenever \(2r < m-1\) (so that \(\text{RM}(r,m) \subset \text{RM}(r,m)^{\perp} = \text{RM}(m-r-1,m)\)), has parameters \([[2^m, 2^m - 2\sum_{j=0}^{r} {m \choose j}, 2^{r+1}]]\).
Its distance \(2^{r+1}\) follows from the RM minimum-weight theorem \cite[Ch. 13]{preset:MacSlo}: \(X\)-type logicals are cosets of \(C \setminus C^{\perp}\), whose minimum weight is that of \(\text{RM}(m-r-1,m)\), i.e., \(2^{m-(m-r-1)} = 2^{r+1}\); \(Z\)-type logicals follow by symmetry.

protection: 'Detects errors on \(d-1\) qubits, corrects errors on \(\left\lfloor (d-1)/2 \right\rfloor\) qubits.'

features:
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_meta:
# Change log - most recent first
changelog:
- user_id: sdoygb
date: '2026-08-13'
- user_id: VictorVAlbert
date: '2026-06-08'
- user_id: VictorVAlbert
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5 changes: 5 additions & 0 deletions users/users_db.yml
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githubusername: LeonidPryadko
pageurl: "https://faculty.ucr.edu/~leonid/"
avatarurl: "builtinavatar:LeonidPryadko"

- user_id: sdoygb
name: 'Ouyang Guobin'
githubusername: sdoygb

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