Add initial qiskit-neko CI job (#1422)

In Qiskit/qiskit-neko#41 we're updating the default simulator backend
plugin used by qiskit-neko to rely on the fake backends provider in the
qiskit-ibm-runtime project. A key aspect of qiskit-neko is the
reciprocity of testing to maintain compatibility in the qiskit
ecosystem (see:
https://github.com/Qiskit/qiskit-neko?tab=readme-ov-file#downstream-usage-in-testing)
so to ensure this is maintainable and the interface remains compatible
for every project using neko this commit adds a corresponding job to
exercise the qiskit-ibm-runtime usage in the tests. However, this is
blocked until after Qiskit/qiskit-neko#41 merges as that is needed to
fix the test suite. A followup will be needed to add a backend selection
to the action configuration so that we can actually use a fake backend.

A longer term step we should investigate is adding a qiskit-neko plugin
to the repo which would enable using qiskit-ibm-runtime's backends and
primitives directly for integration testing with real backends. But that
is much longer term and isn't part of this

Co-authored-by: Elena Peña Tapia <[email protected]>

.github/workflows/neko.yml

@@ -0,0 +1,18 @@
+name: Qiskit Neko Integration Tests
+on:
+  push:
+  pull_request:
+    branches: ['main', 'stable/*']
+concurrency:
+  group: ${{ github.repository }}-${{ github.ref }}-${{ github.head_ref }}-${{ github.workflow }}
+  # Only cancel in PR mode.  In push mode, don't cancel so we don't see spurious test "failures".
+  cancel-in-progress: ${{ github.event_name == 'pull_request' }}
+jobs:
+  neko:
+    if: github.repository_owner == 'Qiskit'
+    name: Qiskit Neko Integration Tests
+    runs-on: ubuntu-latest
+    steps:
+      - uses: Qiskit/qiskit-neko@main
+        with:
+          test_selection: backend