Add Qiskit addon API docs as a baseline (#2167)

We're in the process of adding six Qiskit addon API docs. This PR sets
up the initial projects so that it's easier for us to iterate on them,
such as running `npm run gen-api -- -a <path-to-html>` to see locally
how changes to Sphinx config impact the MDX pipeline.

The docs are _not_ ready to go live and they will not yet be synced by
closed source or deployed.

The quality issues will fixed in the project repositories, such as
Qiskit/qiskit-addon-obp#24.

## API naming scheme

We call the API by their full name, without their abbrevation. For
example, "Operator Backpropagation" rather than "OBP" or "Operator
Backpropagation (OBP)".

We do not explicitly mention "Qiskit addon" in the API name. It's
already evident these are addons by looking at the left ToC which shows
the full module path like `qiskit_addon_obp`.


![image_720](https://github.com/user-attachments/assets/fe664a69-a0a1-4058-92f2-34d03618db8f)

## URL scheme

Each package's URL matches their PyPI name, like `qiskit-addon-obp`.

Note that we may want to normalize the URLs for individual pages to
follow SEO best practices, e.g.
`/api/qiskit-addon-obp/qiskit_addon_obp.utils.simplify` would be
`/api/qiskit-addon-obp/qiskit-addon-obp-utils-simplify`. We would make
this change in a follow up PR.

docs/api/qiskit-addon-cutting/_package.json

@@ -0,0 +1,4 @@
+{
+  "name": "qiskit-addon-cutting",
+  "version": "0.9.0"
+}

docs/api/qiskit-addon-cutting/_toc.json

@@ -0,0 +1,155 @@
+{
+  "title": "Circuit Cutting",
+  "children": [
+    {
+      "title": "API index",
+      "url": "/api/qiskit-addon-cutting"
+    },
+    {
+      "title": "qiskit_addon_cutting",
+      "children": [
+        {
+          "title": "Module overview",
+          "url": "/api/qiskit-addon-cutting"
+        },
+        {
+          "title": "BaseQPDGate",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.qpd.BaseQPDGate"
+        },
+        {
+          "title": "bit_count",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.utils.bitwise.bit_count"
+        },
+        {
+          "title": "CommutingObservableGroup",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.utils.observable_grouping.CommutingObservableGroup"
+        },
+        {
+          "title": "ConsolidateResets",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.utils.transpiler_passes.ConsolidateResets"
+        },
+        {
+          "title": "cut_gates",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.cut_gates"
+        },
+        {
+          "title": "cut_wires",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.cut_wires"
+        },
+        {
+          "title": "CutWire",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.instructions.CutWire"
+        },
+        {
+          "title": "decompose_qpd_instructions",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.qpd.decompose_qpd_instructions"
+        },
+        {
+          "title": "DeviceConstraints",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.DeviceConstraints"
+        },
+        {
+          "title": "ExactSampler",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.utils.simulation.ExactSampler"
+        },
+        {
+          "title": "expand_observables",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.expand_observables"
+        },
+        {
+          "title": "find_cuts",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.find_cuts"
+        },
+        {
+          "title": "generate_cutting_experiments",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.generate_cutting_experiments"
+        },
+        {
+          "title": "generate_qpd_weights",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.qpd.generate_qpd_weights"
+        },
+        {
+          "title": "Move",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.instructions.Move"
+        },
+        {
+          "title": "ObservableCollection",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.utils.observable_grouping.ObservableCollection"
+        },
+        {
+          "title": "observables_restricted_to_subsystem",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.utils.observable_grouping.observables_restricted_to_subsystem"
+        },
+        {
+          "title": "OptimizationParameters",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.OptimizationParameters"
+        },
+        {
+          "title": "partition_circuit_qubits",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.partition_circuit_qubits"
+        },
+        {
+          "title": "partition_problem",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.partition_problem"
+        },
+        {
+          "title": "PartitionedCuttingProblem",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.PartitionedCuttingProblem"
+        },
+        {
+          "title": "QPDBasis",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.qpd.QPDBasis"
+        },
+        {
+          "title": "qpdbasis_from_instruction",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.qpd.qpdbasis_from_instruction"
+        },
+        {
+          "title": "reconstruct_expectation_values",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.reconstruct_expectation_values"
+        },
+        {
+          "title": "RemoveFinalReset",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.utils.transpiler_passes.RemoveFinalReset"
+        },
+        {
+          "title": "separate_circuit",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.utils.transforms.separate_circuit"
+        },
+        {
+          "title": "SeparatedCircuits",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.utils.transforms.SeparatedCircuits"
+        },
+        {
+          "title": "simulate_statevector_outcomes",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.utils.simulation.simulate_statevector_outcomes"
+        },
+        {
+          "title": "SingleQubitQPDGate",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.qpd.SingleQubitQPDGate"
+        },
+        {
+          "title": "TwoQubitQPDGate",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.qpd.TwoQubitQPDGate"
+        },
+        {
+          "title": "unique_by_eq",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.utils.iteration.unique_by_eq"
+        },
+        {
+          "title": "unique_by_id",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.utils.iteration.unique_by_id"
+        },
+        {
+          "title": "WeightType",
+          "url": "/api/qiskit-addon-cutting/qiskit_addon_cutting.qpd.WeightType"
+        }
+      ]
+    },
+    {
+      "title": "Release notes",
+      "url": "/api/qiskit-addon-cutting/release-notes"
+    }
+  ],
+  "collapsed": true
+}