Fix Pauli measurement routine

[shinich1]

Before submitting, please check the following:

• Make sure you have tests for the new code and that test passes (run pytest)
• format added code and tests by black -l 120 <filename>
• If applicable, add a line to the [unreleased] part of CHANGELOG.md, following keep-a-changelog.

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Context (if applicable):

Description of the change:

1. Fixed bug in GraphState graph state simulator, specifically,
   • equivalent_graph_E2 method
   • bug in toggling 'loop' in s method
   • behaviour of measure_x and measure_z methods for isolated nodes
2. Fixed measure method of StatevectorBackend:
   • now we apply s and t signals by Clifford gate, not change of angles.
   • effect of vops in meas_op is now done by application of Clifford gate conjugation on measurement operator, instead of interchanging of measurement axes
3. Fixed pauli measurement preprocessing routine in pattern.py
   • we treat the signals by applying Clifford gates, not by the change of angles

Related issue:

62

(#56)

also see that checks (github actions) pass. If lint check keeps failing, try installing black==22.8.0 as behavior seems to vary across versions.

[masato-fuk]

@shinichi1 All changes appear to be good. By the way, I find vop makes the code a little complicated. As far as I understand, there shouldn't be any issues with merging vops into measurement angles and planes right after Pauli measurements(if my assumption is incorrect, please disregard this). I believe it would be better to do so because simple structure let users follow up easily. But, I think this modification should be done in another issue...

[masato-fuk]

I'll fix a bug in flow finding algorithm, so please wait a moment.

[shinich1]

By the way, I find vop makes the code a little complicated. As far as I understand, there shouldn't be any issues with merging vops into measurement angles and planes right after Pauli measurements(if my assumption is incorrect, please disregard this). I believe it would be better to do so because simple structure let users follow up easily. But, I think this modification should be done in another issue...

I agree, we will need to update angles as well as measurement planes, but that should be doable. I agree it would make things look much simpler. could you write up an issue for this?

[shinich1]

I'll fix a bug in flow finding algorithm, so please wait a moment.

let's do this in a separate issue.