[QAOA] Small Changes to Cost Hamiltonians

[Lucaman99]

Context:

Part of the ongoing addition of QAOA functionality to PennyLane

Description of the Change:

Makes some small changes to the pennylane/qaoa/cost.py file. Instead of returning just a cost Hamiltonian, the functions corresponding to each optimization problem will also return a mixer Hamiltonian that is "recommended" for each problem. This is motivated by the fact that in some instances, using the "recommended mixer is actually crucial to the algorithms success. In addition, there are instances where the mixer Hamiltonian that should be used for an optimization problem is highly non-trivial to construct, and is specific to one optimization problem.

The user would obtain the cost and mixer Hamiltonians as follows:

from pennylane import qaoa
from networkx import Graph

graph = Graph([(0, 1), (1, 2)])
cost_h, mixer_h = qaoa.maxcut(graph)

[codecov]

Codecov Report

Merging #741 into master will increase coverage by 47.12%.
The diff coverage is 100.00%.

@@             Coverage Diff             @@
##           master     #741       +/-   ##
===========================================
+ Coverage   48.50%   95.62%   +47.12%     
===========================================
  Files         111      111               
  Lines        6944     6945        +1     
===========================================
+ Hits         3368     6641     +3273     
+ Misses       3576      304     -3272     

Impacted Files	Coverage Δ
pennylane/qaoa/cost.py	100.00% <100.00%> (+73.33%)	⬆️
...templates/subroutines/double_excitation_unitary.py	100.00% <0.00%> (+1.39%)	⬆️
pennylane/qnodes/passthru.py	83.78% <0.00%> (+2.70%)	⬆️
...templates/subroutines/single_excitation_unitary.py	100.00% <0.00%> (+2.94%)	⬆️
pennylane/numpy/wrapper.py	100.00% <0.00%> (+3.44%)	⬆️
pennylane/devices/default_qubit.py	98.31% <0.00%> (+5.88%)	⬆️
pennylane/templates/subroutines/uccsd.py	100.00% <0.00%> (+6.89%)	⬆️
pennylane/collections/map.py	100.00% <0.00%> (+8.00%)	⬆️
pennylane/vqe/vqe.py	78.26% <0.00%> (+8.69%)	⬆️
pennylane/ops/__init__.py	100.00% <0.00%> (+9.37%)	⬆️
... and 75 more

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[josh146]

I think this is a great improvement!