Support arbitrary controlled operations in lightning.qubit

[vincentmr]

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---

Context:
Applying a gate such as qml.ControlledQubitUnitary(U, control_wires=range(5), wires=[5]) should be quite fast compared with qml.QubitUnitary(U, wires=range(6)) because the first requires applying a 2x2 matrix to 1/32th of all state vector entries and the second applying a 64x64 matrix to all entries. This also provides less control over the parametrization of U, which can be handy in adjoint-diff implementations.

Description of the Change:
Introduce three new kind of gates: controlled gates, controlled generators and controlled matrix ops. The new gates are analogous to the current gates, generators and matrix ops. The new gates accept arbitrary controls, for example LM::NCMultiQubitOp takes in std::vector<std::size_t> &controlled_wires in addition to the usual input of the other kernels. This extra input required modifying the dispatcher and all related definitions. The adjoint-diff classes also need to carry controlled_wires around. All new gate kernels are implemented in GateImplementationsLM.hpp. The Python layer also differentiate between ControlledQubitUnitary operations and others for now.

Benefits:

• Easier to add gate kernels in LM.
• More gate supported in forward/backward mode.
• Improved multi-controlled ops performance.

Possible Drawbacks:
Some gates might be slower, but benchmarks show that this is likely limited. For example, all non-controlled 1-qubit gates have the same performance.

Related GitHub Issues:

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[codecov]

Codecov Report

Attention: 7 lines in your changes are missing coverage. Please review.

Comparison is base (d165de1) 99.02% compared to head (7ef3bb7) 99.09%.

Files	Patch %	Lines
...rc/simulators/lightning_gpu/StateVectorCudaMPI.hpp	50.00%	2 Missing ⚠️
...imulators/lightning_gpu/StateVectorCudaManaged.hpp	50.00%	2 Missing ⚠️
...lators/lightning_qubit/gates/DynamicDispatcher.hpp	94.44%	2 Missing ⚠️
...ylane_lightning/lightning_qubit/lightning_qubit.py	96.87%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #516      +/-   ##
==========================================
+ Coverage   99.02%   99.09%   +0.06%     
==========================================
  Files         168      201      +33     
  Lines       23235    29202    +5967     
==========================================
+ Hits        23009    28937    +5928     
- Misses        226      265      +39     

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[AmintorDusko]

Nice job here! I left some comments and suggestions, but I think this is in very good shape.

[multiphaseCFD]

Looks good to me! Thanks @vincentmr for the nice work!

[AmintorDusko]

Nothing more to add! Great work!