Aer runtime api (from contrib) exposes the wrong sx operation

[aromanro]

Informations

• Qiskit Aer version:

0.13.0 - from VERSION.txt

• Python version:

3.11.4

• Operating system:

Windows 11

What is the current behavior?

Currently it's implemented with an rx operation like this:

// sqrt(NOT) gate
void aer_apply_sx(void *handler, uint_t qubit) {
  AER::AerState *state = reinterpret_cast<AER::AerState *>(handler);
  state->apply_mcrx({qubit}, -M_PI / 4.0);
};

This introduces a different global phase than the sx gate exposed to python (or described in qiskit documentation), for example. It's not a big issue, but I think it should have the same definition.

Steps to reproduce the problem

Compare results obtained with the normal qiskit sx gate and those obtained with using the aer runtime 'aer_apply_sx'.

What is the expected behavior?

Identical results.

Suggested solutions

Replace implementation with:

void aer_apply_sx(void *handler, uint_t qubit) {
  AER::AerState *state = reinterpret_cast<AER::AerState *>(handler);
  state->apply_unitary({ qubit }, AER::Linalg::Matrix::SX);
};

I'll make a pull request for this soon.