Define Hamiltonian.pauli_rep

[albi3ro]

In PR #5362 , I wanted to make ApproxTimeEvolution depend on the pauli_rep of the provided operator. Unfortunately, we never added to Hamiltonian because we didn't see the point in improving Hamiltonian. But not we are in the place where it needs to have similar behaviour to its replacement. So let's just add the pauli_rep property in.

[sc-58834]

[lillian542]

Such a small change, why didn't we just do it before 😅

[obliviateandsurrender]

Thanks for this, looking good!

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.64%. Comparing base (59b2078) to head (4e58d15).
Report is 1 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff            @@
##           master    #5377    +/-   ##
========================================
  Coverage   99.64%   99.64%            
========================================
  Files         401      398     -3     
  Lines       37264    36734   -530     
========================================
- Hits        37131    36603   -528     
+ Misses        133      131     -2     

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[Qottmann]

nice! 👌 thanks @albi3ro

[Qottmann]

Just noticed we lost some coverage in pennylane/pauli/conversion.py 😬

[Qottmann]

just re-approving after some additional changes 👍