Extended stabilizer is not thread safe

[doichanj]

Informations

• Qiskit Aer version:　0.12.2
• Python version:
• Operating system:

What is the current behavior?

Extended stabilizer uses same random generator among multiple threads without considering thread safety in the parallel section as below

qiskit-aer/src/simulators/extended_stabilizer/extended_stabilizer_state.hpp

Lines 462 to 489 in 5e77fc8

	template <typename InputIterator>
	void State::apply_ops_parallel(InputIterator first, InputIterator last,
	ExperimentResult &result, RngEngine &rng) {
	const int_t NUM_STATES = BaseState::qreg_.get_num_states();
	#pragma omp parallel for if (BaseState::qreg_.check_omp_threshold() && \
	BaseState::threads_ > 1) \
	num_threads(BaseState::threads_)
	for (int_t i = 0; i < NUM_STATES; i++) {
	if (!BaseState::qreg_.check_eps(i)) {
	continue;
	}
	for (auto it = first; it != last; it++) {
	switch (it->type) {
	case Operations::OpType::gate:
	apply_gate(*it, rng, i);
	break;
	case Operations::OpType::barrier:
	case Operations::OpType::qerror_loc:
	break;
	default:
	throw std::invalid_argument("CH::State::apply_ops_parallel does not "
	"support operations of the type \'" +
	it->name + "\'.");
	break;
	}
	}
	}
	}

I think we can not reproduce the same results with the same random seed

Suggested solutions

To get the consistent resault with the same random seed, we have to allocate random generators for each states