Bug fix in the C++ simulator: density matrix and probabilities are sometimes erroneous

[yaelbh]

Thanks to Guy Szweigman and Mohammad Heeb, who noticed that the C++ simulator does not always display correct density matrix and probabilities vector.

This happens in the presence of an optimization, which applies to no-noise circuits where all measurements are located at the end. The optimization replaces the shots by a single shot + sampling. However in the calculation of the density matrix and probabilities vector there is a normalization by the number of shots. This results in a density matrix whose trace is 1/(number of shots), and a probabilities vector whose sum is 1/(number of shots).

Description

I fixed the number of shots when the optimization is applied.

Independently of this pull request, it should be revised whether it is correct to normalize by total_shots. Looks like there is an infrastructure to allow, in the future, that total_shots will be the accumulation of number of shots in executions on different engines. What happens if one of the engines does not support density_matrix?

Motivation and Context

How Has This Been Tested?

I updated test_qasm_simulator_cpp.py
Note: test__simulator_online_size in test_quantumprogram fails in the system.

Screenshots (if appropriate):

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)

Checklist:

• My code follows the code style of this project.
• My change requires a change to the documentation.
• I have updated the documentation accordingly.
• I have read the CONTRIBUTING document.
• I have added tests to cover my changes.
• All new and existing tests passed.
  test__simulator_online_size in test_quantumprogram fails in the system.

[chriseclectic]

Could you add a second comment line here: // We need to subtract the additional shots added by BaseEngine class

[chriseclectic]

@yaelbh thanks for catching and fixing this! It looks like you need to rebase against the master before this can be merged, but the fix looks good to me.

[yaelbh]

I added a comment requested by Chris and rebased against the master.