Refactor of flow tools - Flow from pattern

[matulni]

This PR introduces some tooling to extract a causal flow and a generalised flow from a pattern without running the extraction algorithms on the underlying open graph.

It directly addresses #306 and additionally solves #367.

Description of changes

• We introduce the following methods:

  • graphix.optimization.StandardizedPattern.extract_partial_order_layers

    • Constructs a partial order layering from the dependency domains of $M$, $X$ and $Z$ commands. The layering follows the convention of the partial_order_layers attribute of :class: PauliFlow and :class: XZCorrections objects :
      • Nodes in the same layer can be measured simultaneously.
      • Nodes in layer i must be measured after nodes in layer i + 1.
      • All output nodes (if any) are in the first layer.
      • There cannot be any empty layers.

  • graphix.optimization.StandardizedPattern.extract_causal_flow

    • Attempts to extract a causal flow from a standardized pattern. The algorithm goes as follows:
      • The correction function is constructed by reading out $X$ and $M$ commands. In particular, a command $X_j^i$ implies $c(i) = j$ in the correction function. Analogously, a command $M_j^{s=i}$ also contributes $c(i) = j$ to the correction function.
      • A partial order of the pattern is extracted with graphix.optimization.StandardizedPattern.extract_partial_order_layers.
      • A CausalFlow is constructed combining these you objects.
      • The wellformedness of the CausalFlow object is checked.

  • graphix.optimization.StandardizedPattern.extract_gflow

    • Attempts to extract a gflow from a standardized pattern. The algorithm is similar to that of the causal flow, but in addition we allow $c(i) = i$ if the node $i$ is measured in planes $XZ$ or $YZ$.

  • graphix.optimization.StandardizedPattern.extract_opengraph

    • Extracts an open graph from a standardized pattern.

  • graphix.pattern.Pattern.extract_partial_order_layers, graphix.pattern.Pattern.extract_causal_flow and graphix.pattern.Pattern.extract_gflow

    • Wrappers which standardize the pattern and call the corresponding extraction routine.

• We introduce the a new module graphix.flow._partial_order.py with the function :func: compute_topological_generations.

  • This function was used in the algebraic Pauli-flow finding routine and is now used to extract the partial order from the pattern.

  • In the future, we should drop the dependency of graphix.flow.core on nx.DiGraph objects and replace :func: graphix.flow.core._dag_to_partial_order_layers with this function.

• Dependencies of the module graphix.visualization.py on graphix.gflow.py are removed where possible, but the new flow API is not fully exploited. This is out of the scope of this PR.

[codecov]

Codecov Report

❌ Patch coverage is 98.73418% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 84.91%. Comparing base (feb0a07) to head (b177d34).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
graphix/optimization.py	97.10%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #393      +/-   ##
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- Coverage   86.10%   84.91%   -1.19%     
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  Files          45       46       +1     
  Lines        6576     6637      +61     
==========================================
- Hits         5662     5636      -26     
- Misses        914     1001      +87     

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[matulni]

CI is failing on the visualization example with Pauli presimulation. Should pass when #392 is merged.

[thierry-martinez]

Note that this change preserves bug #157, but I think fixing it would be outside the scope of this PR. Ideally, we would like cf = self.try_extract_causal_flow(), but this may cause some regressions: minimize_space will be correct in the sense that it will preserve runnability, but in some examples the minimized pattern may use more space than the current heuristics.

[matulni]

Agree, thanks for the remark.

[matulni]

Thanks a lot for the detailed review, @thierry-martinez. I applied all suggestions in 596ec4b and 975f7aa. I think it's ready for another round!

[thierry-martinez]

LGTM!

[mgarnier59]

Looks good, nothing to add. Thanks!