Add subsystem density matrix snapshots to qasm simulator

[chriseclectic]

Summary

Blocked by #712

• Adds support for the density matrix snapshot to return the reduced density matrix of specified qubits
• Adds density matrix snapshot support to the statevector method, but returning density matrix sampled from the average of statevectors for each shots

Details and comments

• Include subsystem density matrix snapshot tests
• Include statevector method density matrix snapshot tests
• Add release note

[atilag]

First round.
Will finish later!

[atilag]

Besides some suspicious using of std::move, there's something about the usage of qreg_.vector() that would be great to rethink in order to avoid a huge data copy.

[atilag]

I would pass reduced_state as a reference (const?) instead of moving it. Both are really references, but the move semantics only adds noise here.

[chriseclectic]

The data container has special functions for move semantics, so passing the std move here is needed to use that. Otherwise reduced_state will be copied (and it is potentially a very large matrix).

[atilag]

My point is that we don't need move semantics here because there's no need for transfer ownership and using the overloaded add_average_snapshot method that passes reduced_state as a const reference would avoid the copy and will be even faster than casting to rvalue.

[atilag]

Almost there!! :)

[atilag]

My point is that we don't need move semantics here because there's no need for transfer ownership and using the overloaded add_average_snapshot method that passes reduced_state as a const reference would avoid the copy and will be even faster than casting to rvalue.

[atilag]

template <typename floating_t>
cmatrix_t State<QV::QubitVectorThrust<floating_t>>::density_matrix(const reg_t &qubits) {
  return vec2density(qubits, BaseState::qreg_.vector());
}

We can do this because both specializations have the same implementation, so the compiler will derive using monomorphization (specialize double and float if they are used in the code at compile time).

[chriseclectic]

I tried this change but it resulted in compiler errors like:

error: nested name specifier 'State<QV::DensityMatrixThrust<floating_t> >::' for declaration does not refer into a class, class template or class template partial specialization
cmatrix_t State<QV::DensityMatrixThrust<floating_t>>::reduced_density_matrix(...

[atilag]

And these too

[chriseclectic]

This one is a reduction so for one you would have to define a custom reduction type for OMP here, and I think that would result in memory for the matrix being duplicated across threads. For these types of snapshots which can be very large in memory usage I think minimizing memory is more important than speed.