Automorphism group computation

[dsvandet]

• Definition of the automorphism groups of subsystem stabilizer codes. There are multiple types of automorphism groups.
  • Wirthmüller, Automorphisms of stabilizer codes, https://arxiv.org/abs/1102.5715
  • Rains, Quantum codes of minimum distance two, https://arxiv.org/abs/quant-ph/9704043
• How does the definition differ for subspace and subsystem codes?

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Problem: Compute the automorphism group of a subsystem stabilizer code

Here is a paper with some SAGE examples:
Hao, Investigations on automorphism groups of quantum stabilizer codes, https://arxiv.org/abs/2109.12735

• What are the inputs and outputs?
• What algorithms exist?
• What is the computational complexity of this problem?

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Problem: Compute the set of single codeblock transversal gates of a subsystem stabilizer code

• These gates are contained in the automorphism group

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Problem: Compute the set of gates that can be enacted by qubit permutations

• These gates are contained in the automorphism group

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Problem: Compute the set of gates that can be enacted by a stabilizer group automorphism

• These gates are contained in the automorphism group

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