majorana partial traces example

[williamesamuelson]

Wanted to see if the partial trace of a Majorana operator contained in $R$ could give a sign. It doesn't (and I think it can be proved).

Maybe this could be moved to a fermionic quantum info tutorial eventually (or to a test).

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 87.09%. Comparing base (c724c35) to head (9fba281).

Additional details and impacted files

@@           Coverage Diff           @@
##             main      #25   +/-   ##
=======================================
  Coverage   87.09%   87.09%           
=======================================
  Files          14       14           
  Lines        1240     1240           
=======================================
  Hits         1080     1080           
  Misses        160      160           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[cvsvensson]

I agree, it shouldn't give any signs, because the signs depend on the jordan-wigner ordering used to define the fock space. On the algebraic level, there should be no ambiguity.

Related to this, we should implement a function symbolic_representation(matrix, H) which converts a matrix to a representation with symbolic fermions. In #26, I'll introduce the type MajoranaHilbertSpace and then we can also have symbolic_representation(matrix, H::MajoranaHilbertSpace) which gives symbolic majoranas. Then we should implement partial_trace on the symbolic level as well.

Then what you show here could be adapted to tests/tutorials on this functionality.

[williamesamuelson]

Sounds great!