\([[6,1,3]]\) Six-qubit stabilizer code[1]
Description
One of two six-qubit distance-three codes that are unique up to equivalence [2], with the other code a trivial extension of the five-qubit code [1]. Stabilizer generators and logical Pauli operators are presented in Ref. [1].
Encoding
CNOT and Hadamard gates [1].
Gates
Logical CNOT gate [1].
Parents
- Qubit stabilizer code
- Six-qubit-tensor holographic code — The \([[6,1,3]]\) six-qubit stabilizer code is the smallest six-qubit-tensor holographic code. The encoding of more general SCF holographic codes is a holographic tensor network consisting of the encoding isometry for the \([[6,1,3]]\) six-qubit stabilizer code.
- Small-distance block quantum code
Cousins
- Subsystem qubit stabilizer code — The \([[6,1,3]]\) six-qubit code can be converted into a \([[6,1,1,3]]\) subsystem code that saturates the subsystem Singleton bound [1].
- Five-qubit perfect code — The \([[6,1,3]]\) six-qubit code is one of two six-qubit distance-three codes that are unique up to equivalence [2], with the other code a trivial extension of the five-qubit code [1].
References
- [1]
- B. Shaw et al., “Encoding one logical qubit into six physical qubits”, Physical Review A 78, (2008) arXiv:0803.1495 DOI
- [2]
- A. R. Calderbank et al., “Quantum Error Correction via Codes over GF(4)”, (1997) arXiv:quant-ph/9608006
Page edit log
- Victor V. Albert (2024-05-26) — most recent
- Matthew Steinberg (2024-05-26)
Cite as:
“\([[6,1,3]]\) Six-qubit stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/stab_6_1_3