Finalize the LM kernel

[chaeyeunpark]

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Context: This is the second part of adding a new gate implementation

Description of the Change:

• Add most of the gates in the LM kernel (including IsingXX, IsingYY, IsingZZ, as well as MultiRZ gates); still three-qubit gates are missing.
• Adjoint method now applies generators with DynamicDispatcher.
• Added tests for added gates and generators.
• Automated most of the tests for gates.
• Raise compile-time errors when the constants are not defined consistently.

Benefits: Adjoint method works for all gates.

Possible Drawbacks:

Related GitHub Issues:

As most of the +lines are from the test files (auto-generated using default.qubit), I hope that it will not make you fear...

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[chaeyeunpark]

Hi all, the benchmark of gate operations between kernels can be found here: https://github.com/PennyLaneAI/pennylane-lightning-compare-kernels. Even though the result is not that impressive for some gates, I see dramatic speed-up when parallelizing the new kernel gate operations (with OpenMP + loop unrolling). I will make a document on this when this PR is merged.

[maliasadi]

Great work on this 🥇 Do we know when it is likely to be merged?

[chaeyeunpark]

Hi @maliasadi, I want to merge this when @mlxd also approves this. I also thank you for reviewing this huge PR. As most of the components I wanted are settled, I will not make a vast PR anymore (at least for a while 😉 ).

[mlxd]

Amazing PR @chaeyeunpark !
Very happy to see this merged in. Though, for the record, is it possible to have a before and after comparison plot in the PR comments (Comparing v0.21 and this PR)?

Note, I expect this may also impact the external package work, but I think the sooner the better for this.

[mlxd]

This is a big one!

[chaeyeunpark]

Yes, I generated a test example using python. Still, if we are able to use constexpr JSON parser, it would be possible to define all test cases in a JSON file. That would be the best.

[chaeyeunpark]

This is the result from benchmark suite 1. Not as impressive as before, but still faster. More speed-up will come with OpenMP and SIMD kernels (that I am working on right now 😉).