Refactor gate operations and add a new kernel for single qubit gates

[chaeyeunpark]

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Context: Previous implementation of gate operations is not well-performing. Thus it has been discussed to add an alternative implementation. This PR proposes a possible way to do it.

Description of the Change: Now, one can add an alternative kernel (gate implementations) relatively easily. I have also added a kernel with less memory bandwidth, which is faster for most gates.

Benefits: Faster gates. One can also add alternative kernels rather easily.

Possible Drawbacks: Some parts of the code get a bit complicated. Especially, template metaprogramming was unavoidable at some points. I hope to replace some of them in C++20.

Related GitHub Issues:

Sorry for making this giant PR...

[github-actions]

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[codecov]

Codecov Report

Merging #202 (d729a74) into master (7515848) will increase coverage by 0.01%.
The diff coverage is 100.00%.

❗ Current head d729a74 differs from pull request most recent head baf81a0. Consider uploading reports for the commit baf81a0 to get more accurate results

@@            Coverage Diff             @@
##           master     #202      +/-   ##
==========================================
+ Coverage   99.64%   99.65%   +0.01%     
==========================================
  Files           4        4              
  Lines         278      293      +15     
==========================================
+ Hits          277      292      +15     
  Misses          1        1              

Impacted Files	Coverage Δ
pennylane_lightning/_serialize.py	100.00% <100.00%> (ø)
pennylane_lightning/lightning_qubit.py	99.51% <100.00%> (+0.02%)	⬆️

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[github-actions]

Test Report (C++) on Ubuntu

       1 files  ±    0         1 suites  ±0   0s ⏱️ ±0s
   294 tests  -   94     294 ✔️  -   94  0 💤 ±0  0 ❌ ±0 
2 677 runs  +430  2 677 ✔️ +430  0 💤 ±0  0 ❌ ±0 

Results for commit baf81a0. ± Comparison against base commit 7515848.

This pull request removes 287 and adds 193 tests. Note that renamed tests count towards both.

runner.global ‑ StateVector::StateVector - double/StateVector
runner.global ‑ StateVector::StateVector - double/StateVector<TestType> cross types
runner.global ‑ StateVector::StateVector - double/StateVector<TestType> {std::complex<TestType>, size_t}
runner.global ‑ StateVector::StateVector - double/StateVector<TestType> {}
runner.global ‑ StateVector::StateVector - float/StateVector
runner.global ‑ StateVector::StateVector - float/StateVector<TestType> cross types
runner.global ‑ StateVector::StateVector - float/StateVector<TestType> {std::complex<TestType>, size_t}
runner.global ‑ StateVector::StateVector - float/StateVector<TestType> {}
runner.global ‑ StateVector::applyCNOT - double/Apply directly
runner.global ‑ StateVector::applyCNOT - double/Apply using dispatcher
…

runner.global ‑ DynamicDispatcher::applyOperation - double
runner.global ‑ DynamicDispatcher::applyOperation - float
runner.global ‑ GateOperations::applyCNOT - GateOperationsLM<double>
runner.global ‑ GateOperations::applyCNOT - GateOperationsLM<float>
runner.global ‑ GateOperations::applyCNOT - GateOperationsPI<double>
runner.global ‑ GateOperations::applyCNOT - GateOperationsPI<float>
runner.global ‑ GateOperations::applyCRot - GateOperationsPI<double>/CRot0,1 |000> -> |000>
runner.global ‑ GateOperations::applyCRot - GateOperationsPI<double>/CRot0,1 |100> -> |1>(a|0>+b|1>)|0>
runner.global ‑ GateOperations::applyCRot - GateOperationsPI<float>/CRot0,1 |000> -> |000>
runner.global ‑ GateOperations::applyCRot - GateOperationsPI<float>/CRot0,1 |100> -> |1>(a|0>+b|1>)|0>
…

♻️ This comment has been updated with latest results.

[chaeyeunpark]

Hi all, I applied most of the changes from the code review. For a few remaining issues, check my comments.

[mlxd]

Great work again @chaeyeunpark

I'd love to see a graph dropped here with the performance comparison of this PR against the current master using the kernel tests, as well as some workflow tests.

I think this is pretty much ready to approve (given the above, and the last few comments I made). I reckon it will be worth updating the architecture images and discussion on the docs in a following PR to account for the new structure.

[mlxd]

For some reason, the docs do not generate the inheritance diagram https://pennylane-lightning--202.org.readthedocs.build/en/202/code/__init__.html#class-inheritance-diagram

I wonder if we need to explicitly install graphviz/dot or make some changes to the documentation build for this.

[chaeyeunpark]

Hi @mlxd, I added graphviz dependency explicitly in requirements.txt and confs.py, but nothing changed. In fact, this is a problem from v0.20.0 (https://pennylane-lightning.readthedocs.io/en/v0.20.0/code/__init__.html). It is wiered as the only change was the header (qhack to carnival). Moreover, it just works well locally...

[chaeyeunpark]

Aha. It was .readthedocs problem. I now fixed it.

[mlxd]

Aha. It was .readthedocs problem. I now fixed it.

Great work on finding this! Happy to see this merged from my side.

[maliasadi]

85 files reviewed 😄 nothing else to be added. Great job!

[mlxd]

Once again, great work on this @chaeyeunpark
I may request we hold off the merge until we have a chat at our meeting today.