`TensorNetworkBackend` ignores the order of output nodes

[thierry-martinez]

TensorNetworkBackend ignores the order of output nodes. The current implementation of finalize is:

    def finalize(self, output_nodes) -> None:
        """Do nothing."""

This means that the resulting tensor network returns a state vector in an unexpected order, as demonstrated by the following test, which currently fails.

    @pytest.mark.parametrize(("nqubits", "jumps"), itertools.product(range(2, 6), range(1, 6)))
    def test_to_statevector_order(self, fx_bg: PCG64, nqubits: int, jumps: int, fx_rng: Generator) -> None:
        rng = Generator(fx_bg.jumped(jumps))
        circuit = rand_circuit(nqubits, 3, rng)
        pattern = circuit.transpile().pattern
        pattern.standardize()
        pattern.shift_signals()
        statevec_ref = circuit.simulate_statevector().statevec
        pattern.reorder_output_nodes(reversed(pattern.output_nodes))

        tn = pattern.simulate_pattern("tensornetwork", rng=fx_rng)
        statevec_tn = tn.to_statevector()

        inner_product = np.inner(statevec_tn, statevec_ref.flatten().conjugate())
        assert abs(inner_product) == pytest.approx(1)

[Abhinavintech]

Hello team, I would like to take this opportunity to work upon this issue, could you assign it to me.

[thierry-martinez]

@Abhinavintech Thank you for offering your help. We can discuss at any time if you need, and feel free to open a PR if and when you have something to show.