Update cutting tutorials to send ISA circuits to Qiskit Runtime (#500) (

#512)

* Remove explicit `session.close()` calls inside context manager

These `close` calls are redundant since
Qiskit/qiskit-ibm-runtime#1139.

* Demonstrate transpiling circuits before sending to Runtime

... in cutting tutorials 1 and 3

* Update tutorial 2 (cutting for depth)

* Remove a comma

* black

* Rename `pm` -> `pass_manager` for clarity

(cherry picked from commit bf82d2d)

Co-authored-by: Jim Garrison <[email protected]>

docs/circuit_cutting/tutorials/01_gate_cutting_to_reduce_circuit_width.ipynb

@@ -283,21 +283,26 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "# from qiskit_ibm_runtime import Session, Options, Sampler\n",
+    "# from qiskit_ibm_runtime import Session, Options, Sampler, QiskitRuntimeService\n",
+    "# from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
     "#\n",
-    "# with Session(backend=\"ibmq_qasm_simulator\") as session:\n",
+    "# service = QiskitRuntimeService()\n",
+    "# backend = service.least_busy(operational=True, simulator=False)\n",
+    "#\n",
+    "# # Prepare transpiler for target backend\n",
+    "# pass_manager = generate_preset_pass_manager(optimization_level=1, backend=backend)\n",
+    "#\n",
+    "# with Session(backend=backend) as session:\n",
     "#     # Set up Qiskit Runtime Sampler primitives.\n",
     "#     samplers = {\n",
     "#         label: Sampler(Options(execution={\"shots\": 2**12})) for label in subexperiments.keys()\n",
     "#     }\n",
     "#\n",
     "#     # Retrieve results from each subexperiment\n",
     "#     results = {\n",
-    "#         label: sampler.run(subexperiments[label]).result()\n",
+    "#         label: sampler.run(pass_manager.run(subexperiments[label])).result()\n",
     "#         for label, sampler in samplers.items()\n",
-    "#     }\n",
-    "#\n",
-    "#     session.close()"
+    "#     }"
    ]
   },
   {