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2021

Investigations on Automorphism Groups of Quantum Stabilizer Codes

Hao, Hanson

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The stabilizer formalism for quantum error-correcting codes has been, without doubt, the most successful at producing examples of quantum codes with strong error-correcting properties.

In this paper, we discuss strong automorphism groups of stabilizer codes, beginning with the analogous notion from the theory of classical codes.
Two weakenings of this concept, the weak automorphism group and Clifford-twisted automorphism group, are also discussed, along with many examples highlighting the possible relationships between the types of "automorphism groups".
In particular, we construct an example of a $[[10,0,4]]$ stabilizer code showing how the Clifford-twisted automorphism groups might be connected to the Mathieu groups.

Investigations on Automorphism Groups of Quantum Stabilizer Codes · Around

Built on

On the clifford collineation, transform and similarity groups. i
Beverley Bolt, T. G. Room, and G. E. Wall · 1961
Earlier work this paper cites.
On the clifford collineation, transform and similarity groups. ii
Beverley Bolt, T. G. Room, and G. E. Wall · 1961
Earlier work this paper cites.
Scheme for reducing decoherence in quantum computer memory
Peter W. Shor · 1995
Earlier work this paper cites.

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