Vortrag
eSeminar: Good Stabilizer Codes from Quasi-Cyclic Codes
Vortrag von Dr. Buket Özkaya
Datum: 06.05.20 Zeit: 09.00 - 10.00 Raum:
(**This eSeminar will take place on Zoom, using same meeting details as previous seminars. If you do not have meeting details, please contact karan.khathuria@math.uzh.ch **)
Lisonek and Singh proposed an interesting modification to the construction of qubit stabilizer codes by relaxing the Hermitian self-orthogonality requirement. Their framework, inspired by Construction X in the classical setup, yielded a number of better qubit codes than the previous best-known. These better codes came from applying their construction to specifically chosen quaternary cyclic codes. Construction X for qubit codes generalizes naturally to q-ary quantum codes.
This work uses self-orthogonal or nearly self-orthogonal quasi-cyclic codes over F4 and F9 as ingredients in the quantum Construction X to derive good qubit and qutrit (3-ary quantum) codes. We consider quasi-cyclic codes with large Hermitian hulls, which can be easily produced using their Chinese Remainder Theorem decomposition. Such codes have a good chance to be implemented in actual quantum processors. We exhibit quantum codes with parameters that strictly improve on the currently best-known ones and list those that match the best-known ones in performance.