\( \def\ket#1{{ \left| #1 \right> }} \def\bra#1{{ \left< #1 \right| }} \def\bracket#1{{ \left( #1 \right) }} \) \( \DeclareMathOperator{\tr}{tr} \) 1) Encoding into higher dimensional space In QEC, one needs to encode information into a higher dimensional Hilbert space, which can be a system of multiple qubits (like conventional repetition codes, Shor's code, Steane's code,...) or a $d$-level sy..
Physics Corner 2022. 7. 17. 11:37
\( \def\ket#1{{ \left| #1 \right> }} \def\bra#1{{ \left< #1 \right| }} \def\bracket#1{{ \left( #1 \right) }} \) \( \DeclareMathOperator{\tr}{tr} \) 1) Encoding into higher dimensional space In QEC, one needs to encode information into a higher dimensional Hilbert space, which can be a system of multiple qubits (like conventional repetition codes, Shor's code, Steane's code,...) or a $d$-level sy..
Physics Corner 2022. 7. 17. 10:59
\( \def\ket#1{{ \left| #1 \right> }} \) \( \def\bracket#1{{ \left( #1 \right) }} \) \( \def\bra#1{{ \left< #1 \right| }} \) $\left[7,1 \right]$ Steane code is an ubiquitous example of Calderbank-Shor-Steane (CSS) class of quantum error correction codes. Steane code was constructed from classical $\left[7,4,3 \right]$ Hamming code whose parity-check matrix takes the following form \begin{equation..