Add generate_samples() to lightning

[trevor-vincent]

Context:

generate_samples() performs most of the heavy lifting for the sample() function. Currently there is no lightning version of generate_samples().

Description of the Change:

This pr adds a lightning C++ version of the generate_samples function using the alias sampling method (https://en.wikipedia.org/wiki/Alias_method). This C++ function currently single-threaded only, however a parallel version is straight-forward (e.g. insert a openmp pragma above the for loop that computes samples while being mindful that the parallel random number generation and caching is thread-safe).

Benefits:

Lightning now has it's own version of generate_samples(), getting us closer to a complete independent lightning statistics module. For low numbers of shots, the single-threaded version is faster than default.qubit (which uses numpy.random.choice) on my machine:

This benchmark times the generate_samples() function for a randomly generated 10-qubit circuit (benchmarks were single-threaded for lightning, however numpy may be multi-threaded).

Possible Drawbacks:

At higher shots, we should likely switch to a parallel version.

Related GitHub Issues:

[github-actions]

Hello. You may have forgotten to update the changelog!
Please edit .github/CHANGELOG.md with:

• A one-to-two sentence description of the change. You may include a small working example for new features.
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[codecov]

Codecov Report

Merging #247 (c616693) into master (1c0a973) will not change coverage.
The diff coverage is 100.00%.

@@            Coverage Diff            @@
##            master      #247   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files            4         4           
  Lines          366       379   +13     
=========================================
+ Hits           366       379   +13     

Impacted Files	Coverage Δ
pennylane_lightning/_version.py	100.00% <100.00%> (ø)
pennylane_lightning/lightning_qubit.py	100.00% <100.00%> (ø)

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[github-actions]

Test Report (C++) on Ubuntu

       1 files  ±  0         1 suites  ±0   0s ⏱️ ±0s
   561 tests +  6     561 ✔️ +  6  0 💤 ±0  0 ❌ ±0 
2 299 runs  +10  2 299 ✔️ +10  0 💤 ±0  0 ❌ ±0 

Results for commit c616693. ± Comparison against base commit 1c0a973.

This pull request removes 4 and adds 10 tests. Note that renamed tests count towards both.

runner.global ‑ Variances/Testing list of operators defined by a matrix:
runner.global ‑ Variances/Testing list of operators defined by its name:
runner.global ‑ Variances/Testing single operation defined by a matrix:
runner.global ‑ Variances/Testing single operation defined by its name:

runner.global ‑ Sample - double/No wires provided:
runner.global ‑ Sample - float/No wires provided:
runner.global ‑ Variances - double/Testing list of operators defined by a matrix:
runner.global ‑ Variances - double/Testing list of operators defined by its name:
runner.global ‑ Variances - double/Testing single operation defined by a matrix:
runner.global ‑ Variances - double/Testing single operation defined by its name:
runner.global ‑ Variances - float/Testing list of operators defined by a matrix:
runner.global ‑ Variances - float/Testing list of operators defined by its name:
runner.global ‑ Variances - float/Testing single operation defined by a matrix:
runner.global ‑ Variances - float/Testing single operation defined by its name:

♻️ This comment has been updated with latest results.

[mlxd]

Thanks @trevor-vincent
I have a few comments and some suggestions

[maliasadi]

Thanks @trevor-vincent. Happy to approve!

[mlxd]

Great job @trevor-vincent
One suggestion below, but don't see any blocker otherwise. Happy to approve after this change!