Add AVX2/512 kernels

[chaeyeunpark]

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Test Report (Linux, Kokkos, and Kokkos Kernels) on Ubuntu

           1 files  ±       0             1 suites  ±0   2s ⏱️ ±0s
       956 tests  -      19         956 ✔️  -      19  0 💤 ±0  0 ❌ ±0 
234 969 runs  +5 689  234 969 ✔️ +5 689  0 💤 ±0  0 ❌ ±0 

Results for commit 740f4b2. ± Comparison against base commit e0768d6.

♻️ This comment has been updated with latest results.

[codecov]

Codecov Report

Merging #313 (740f4b2) into master (e0768d6) will decrease coverage by 0.05%.
The diff coverage is 99.48%.

@@            Coverage Diff             @@
##           master     #313      +/-   ##
==========================================
- Coverage   99.79%   99.74%   -0.06%     
==========================================
  Files          40       73      +33     
  Lines        3929     5108    +1179     
==========================================
+ Hits         3921     5095    +1174     
- Misses          8       13       +5     

Impacted Files	Coverage Δ
pennylane_lightning/src/gates/GateUtil.cpp	100.00% <ø> (ø)
pennylane_lightning/src/gates/GateUtil.hpp	100.00% <ø> (ø)
pennylane_lightning/src/util/IntegerInterval.hpp	100.00% <ø> (ø)
pennylane_lightning/src/util/Memory.hpp	100.00% <ø> (ø)
...nnylane_lightning/src/simulator/CPUMemoryModel.hpp	90.90% <87.50%> (-5.25%)	⬇️
...ennylane_lightning/src/simulator/KernelMap_X64.cpp	88.88% <88.88%> (ø)
...tning/src/gates/cpu_kernels/avx_common/AVXUtil.hpp	94.59% <94.59%> (ø)
pennylane_lightning/_version.py	100.00% <100.00%> (ø)
pennylane_lightning/lightning_qubit.py	99.62% <100.00%> (+<0.01%)	⬆️
...ylane_lightning/src/gates/RegisterKernels_AVX2.cpp	100.00% <100.00%> (ø)
... and 37 more

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[chaeyeunpark]

It seems like I need to refactor a code a little more. Still, I summarize here the benchmark results so far.

This is a result for the RX gate:

And the CZ gate:

We see a remarkable speedup for 10-18 qubits. For the RX gate with a single-precision, it is even up to 10 times faster. I suspect that AVX2/512 is less effective for a large number of qubits as the gate operation within packed data is faster than the operation between packed data. A similar result is observed for the CZ gate beside the fact that the speed-up is less compelling.

[chaeyeunpark]

One subtle point is that enabling -fma speeds up some gate operations of the AVX2 kernel by around 10%. Given that most CPUs supporting AVX2 also support FMA, we may compile AVX2 kernels always with FMA and enable them (in runtime) when both instruction sets are supported. Any idea?

[chaeyeunpark]

@mlxd I am still not so sure whether we want to exclude the AVX512 kernel from codecov.

[mlxd]

Great job putting this together @chaeyeunpark
It really helps out. I have some small suggestions, but nothing major.

Happy to give it another pass after this and call it done.

[chaeyeunpark]

Thanks all guys for the sincere reviews! CodeCov is not fully satisfying (it is still >99%), but I want to improve it in the following PRs. It is okay with you?

[mlxd]

@mlxd I am still not so sure whether we want to exclude the AVX512 kernel from codecov.

Yea, I think this may be sensible since we cannot guarantee what runner we will hit. Fine for me to exclude it completely for now.

[mlxd]

Awesome effort here @chaeyeunpark

[multiphaseCFD]

Thanks @Chae-Yeun! Great job!