Add Clifford decoration on output nodes of OpenGraph

[matulni]

This PR fixes two known (but unreported) issues concerning patterns in the LC fragement and open graphs.

Issue 1

Pattern.extract_opengraph ignores Clifford commands on measured nodes. Therefore, this method returns different open graphs depending on whether the pattern has been standardized first or not:

from graphix import Command, Clifford, Measurement, Pattern

p = Pattern(cmds=[Command.N(0), Command.C(0, Clifford.H), Command.M(0, Measurement.XY(0.3))])
og = p.extract_opengraph()
p.standardize()
og_std = p.extract_opengraph()

assert og.isclose(og_std) # fails

To ensure canonicality, extracting an open graph from a pattern should always proceed by standardizing the pattern first.

Issue 2

Pattern.extract_opengraph ignores Clifford commands on output nodes. Therefore, it does not preserve the semantics of the pattern:

from graphix import Command, Clifford, Pattern

p = Pattern(input_nodes=[0],
            cmds=[
                N(1),
                E((0, 1)),
                C(0, Clifford.H),
                M(0, -Measurement.Z),
                X(1, {0}),
                C(1, Clifford.H),
                C(1, Clifford.X),
            ])
p_test = p.extract_opengraph().to_pattern()

sv = p.simulate_pattern()
sv_test = p_test.simulate_pattern()

assert sv.isclose(sv_test) # fails

To guarantee the round trip Pattern -> OpenGraph -> Flow -> XZCorrections -> Pattern for patterns in the LC fragment:

1. Clifford commands on measured nodes should be absorbed into measurements via standardization (issue 1),

2. Open graphs should conserve a mapping between output nodes and Clifford operators.

Summary of changes

To fix issues above, we introduce a new attribute to the OpenGraph.output_cliffords mapping output nodes to Clifford operations. This corresponds to c_dict in StandardizedPattern. Further:

• Pattern.extract_opengraph standardizes the pattern first.
• XZCorrections.to_pattern applies Cliffords in OpenGraph.output_cliffords at the end of the pattern.
• OpenGraph.isclose and OpenGraph.is_equal_structurally check equality of OpenGraph.output_cliffords.
• OpenGraph.compose merges Clifford decorations with measurements or other Clifford decorations on outputs if required.
• .draw methods allow to show Clifford commands in the outputs.
• PauliFlow.extract_circuit raises NotImplementedError if the open graph has Clifford decorations. This will be left for a future PR to simplify the review.

Additionally, a minor bug in Pattern.compose and OpenGraph.compose which appeared when trying to compose single-node objects with an empty mapping is fixed, and the corresponding test added.

[codecov]

Codecov Report

❌ Patch coverage is 96.29630% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 88.85%. Comparing base (6de358c) to head (84f08e0).

Files with missing lines	Patch %	Lines
graphix/opengraph.py	96.00%	1 Missing ⚠️
graphix/visualization.py	80.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #510      +/-   ##
==========================================
+ Coverage   88.84%   88.85%   +0.01%     
==========================================
  Files          49       49              
  Lines        7127     7135       +8     
==========================================
+ Hits         6332     6340       +8     
  Misses        795      795              

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[thierry-martinez]

Looks nice! I've some minor comments.

[thierry-martinez]

I propose to implement the clifford method on all AbstractMeasurement instead: thierry-martinez@67b0ab1

[matulni]

Thanks for the suggestion. Much cleaner and general now

[thierry-martinez]

I believe it is better to rely on the Clifford map stored in the extracted open graph.

[matulni]

Fixed in 40841d3

[pranav97nair]

Nice work, Mateo! I just made a very minor comment.

[pranav97nair]

Is there a particular reason you specify is not None instead of just saying if vm and um...? If not I think it would be better to do the latter for improved readability.

[matulni]

Indeed we could do that, but I'm not sure if it improves readability.

When we test the truthiness of an object x, the Python interpreter checks for the x.__bool__ and the x.__len__ methods. When they are not implemented (as it is the case for AbstractMeasurement and children), it always assigns a truthy value so your suggestion would work.

However, someone reading the code would need to know or assume that AbstractMeasurement does not implement __bool__, and may wonder what is the truth value of 0-angle measurements. (In Python, the zero of any numeric type is False).

Checking against None is indeed more verbose, but less ambiguous imo.