LRE on hardware

[natestemen]

Description

Running Layerwise Richardson Extrapolation (LRE) on hardware.

Next steps

A first pass at this doesn't show great results, but the parameters we are running with LRE were basically chosen at random. Picking these more specifically, or doing a parameter sweep is a good place to start (first on simulator, and then hardware).

I chose the square heisenberg and qft circuits to run because since there are plenty of different sizes (number of qubits) available through benchpress. It might be nice to use that fact to test the performance as the system size grows.

@bdg221

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[b-goldsmith]

I have added the ideal and unmitigated results to the saved CSV file. The ideal results include a degree, fold_multiplier, num_chunks, and time as 0 (technically in the time column it appears as 0.0). For the mitigated results, the degree, fold_multiplier, and num_chunks are 0 with the time column set to 1.0.

square-heisenberg-4,aer_simulator_from(ibm_sherbrooke),1.0,0,0,0,0.0
square-heisenberg-4,aer_simulator_from(ibm_sherbrooke),0.626,0,0,0,1.0

The runs that result in an error due to the circuit being too large to obtain a determinate are also saved in the CSV file with an empty result.

square-heisenberg-4,aer_simulator_from(ibm_sherbrooke),,4,1,7,8.68698501586914

Also, I updated the number of shots to be 1000 even for the simulator, in order to match what will be done on hardware.