Quantum Stabilizer Codes and Beyond

Ivan B. Djordjević

Ivan B. Djordjević

Andreas Klappenecker, Martin Roetteler

Knill introduced a generalization of stabilizer codes, in this note called Clifford codes. It remained unclear whether or not Clifford codes can be superior to stabilizer codes. We show that Clifford codes are stabilizer codes provided that the abstract error group has an abelian index group. In particular, if the errors are modelled by tensor products of Pauli matrices, then the associated Clifford codes are necessarily stabilizer codes.

Andreas Klappenecker, Martin Rötteler

For pt. I see ibid., vol.48, no.8, p.2392-95 (2002). Knill (1996) introduced a generalization of stabilizer codes, called Clifford codes. It remained unclear whether or not Clifford codes can be superior to stabilizer codes. We show that Clifford codes are stabilizer codes provided that the abstract error group has an Abelian index group. In particular, if the errors are modeled by tensor products of Pauli matrices, then the associated Clifford codes are necessarily stabilizer codes.

Andreas Klappenecker, Martin Roetteler

Knill introduced a generalization of stabilizer codes, in this note called Clifford codes. It remained unclear whether or not Clifford codes can be superior to stabilizer codes. We show that Clifford codes are stabilizer codes provided that the abstract error group is given by an extraspecial p-group. Suppose that the abstract error group has an abelian index group, then we show that a Clifford code can be derived from an abelian normal subgroup.

Alexey A. Kovalev, Ilya I. Dumer, Leonid P. Pryadko