Summary

In #13301, we introduced a synthesis plugin PauliEvolutionSynthesisRustiq for objects of type PauliEvolutionGate. At the time, the operator of a PauliEvolutionGate could be either a Pauli or a SparsePauliOp (or a list of such objects). Later, in #13836, we extended PauliEvolutionGate to also support operators of type SparseObservable, leading to impressive gains for the default synthesis plugin for PauliEvolutionGate. However, we forgot to extend PauliEvolutionSynthesisRustiq as well. As the result, the following code could run without raising any errors, but produced incorrect output circuits:

from qiskit.circuit.library import PauliEvolutionGate
from qiskit.quantum_info import SparseObservable, Operator
from qiskit.transpiler.passes.synthesis.hls_plugins import PauliEvolutionSynthesisRustiq

obs = SparseObservable.from_sparse_list([("1+XY", (0, 1, 2, 3), 1.5)], num_qubits=4)
evo = PauliEvolutionGate(obs, 1)
qct = PauliEvolutionSynthesisRustiq().run(evo)
assert Operator(qct) == Operator(evo)

This PR fixes the above problem by converting within the rustiq plugin SparseObservables to SparsePauliOps (note that this might exponentially increase the number of terms). In addition, the Qiskit Rust interface to rustiq has been extended to raise an error when the pauli input strings are invalid.