Automatically set and save optimal OpenMP and fusion thresholds

[hhorii]

Summary

Adds basic profiling code to find suitable threshold values for OpenMP and gate fusion for backend options.
This is a revised version of #956.

Details and comments

This PR will add following into to #956.

• Save optimized parameters into settings.conf
• Optimize fusion_cost.N

[hhorii]

Once Qiskit/qiskit#5943 is merged, optimized parameters will be able to be store in user config around here:

qiskit-aer/qiskit/providers/aer/profile.py

Lines 68 to 69 in 9f7b832

	def _set_optimized_option(option_name, value):
	setattr(AerBackend, f'_{option_name}', value)

qiskit-aer/qiskit/providers/aer/profile.py

Lines 82 to 84 in 9f7b832

	def _clear_optimized_option(option_name):
	if hasattr(AerBackend, f'_{option_name}'):
	delattr(AerBackend, f'_{option_name}')

[chriseclectic]

Some changers needed here. I think it might be better to wait until after #1194 is merged and just use profiling for AerSimulator which provides a common interface to all simulation methods and makes it easier to check if using GPU or not since it has a separate device option.

[chriseclectic]

Lets remove this method from the provider for now and make it have to be run by importing the profiling functions

[chriseclectic]

Backend options is a deprecated argument. Typically the method will already be in the qobj config

[chriseclectic]

This should be handled as pat of the format qobj, and only add the profile option to the qobj config if they aren't present in options or run options

[chriseclectic]

This profile.py file should probably be moved into aer/utils/ and the user facing functions added to aer/utils/__init__.py

[hhorii]

Here are performance graphs (time_taken includes only transpilation + simulation and excludes interface overheads) with default and tuned configurations.

Configurations:

• Left: MacBook (2.6 GHz 6-Core Intel Core i7)
  • statevector_parallel_threshold=11
  • fusion_threshold=19
• Right: Xeon (Intel Xeon Gold 6140 CPU )
  • statevector_parallel_threshold=16
  • fusion_threshold=11

QuantumVolume:

IntegerComparator:

WeightedAdder:

QuadraticForm:

QFT:

RealAmplitudes with full entanglements

RealAmplitudes with linear entanglements

Red lines are expected the lowest. Because this profiling function uses QuantumVolume, tuned options do not work for others. However, I believe, these side-effects are acceptables.