Pauli-flow extraction from pattern

[thierry-martinez]

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Context

Theorems 1, 2 and 4 in Ref. ¹ prescribe how to recover an $XZ$-correction strategy (and therefore, an MBQC pattern) from a causal, g- or Pauli flow. The class XZCorrections has methods to_causal_flow and to_gflow which reverse this prescription to construct, respectively, CausalFlow and GFlow objects from a given set of $XZ$ corrections. However, the method to_pauli_flow is missing.

Extracting a Pauli flow from a deterministic $XZ$ correction strategy does not seem trivial, since the anachronical corrections do not appear in the pattern (compare Eq. in Theorem 2 vs Eq. in Theorem 4 in ¹).

Task

Implement a method XZCorrections.to_pauli_flow, and define a method extract_pauli_flow in Pattern that calls it for convenience (analogous to Pattern.extract_causal_flow and Pattern.extract_gflow).

Acceptance criteria

For the PR to be considered for review:

• It should pass the CI, including linting and type-checking.

• New functions should be tested and documented appropriately following numpy style.

• Unitary Hack AI use guidelines should be respected.

• Author should be ready to engage in a feedback loop.

• PR description should explicitly explain how the difficulty of dealing with anachronical corrections in the Pauli flow was tackled.

For the PR to be accepted:

• All provided feedback should have been implemented.

Footnotes

1. Browne, Kashefi, Mhalla and Perdrix, 2007 (arXiv:quant-ph/0702212). ↩ ↩²