Add API docs for QuantumCircuit methods (#1753)

* Add new doc for circuit method apis

* Remove QuantumCircuit description

---------

Co-authored-by: Hiroshi Horii <hhorii@users.noreply.github.com>

docs/apidocs/aer.rst

@@ -15,4 +15,5 @@ Qiskit Aer API Reference
     aer_pulse
     aer_utils
     aer_quantum_info
+    circuit
     parallel

docs/apidocs/circuit.rst

@@ -0,0 +1,50 @@
+.. _circuit:
+
+Additional circuit methods
+==========================
+
+.. currentmodule:: qiskit.circuit
+
+On import, Aer adds several simulation-specific methods to :class:`~qiskit.circuit.QuantumCircuit` for convenience.
+These methods are not available until Aer is imported (``import qiskit_aer``).
+
+Setting a custom simulator state
+--------------------------------
+
+The set instructions can also be added to circuits by using the
+following ``QuantumCircuit`` methods which are patched when importing Aer.
+
+.. automethod:: QuantumCircuit.set_density_matrix
+.. automethod:: QuantumCircuit.set_stabilizer
+.. automethod:: QuantumCircuit.set_unitary
+.. automethod:: QuantumCircuit.set_superop
+.. automethod:: QuantumCircuit.set_matrix_product_state
+
+Saving Simulator Data
+--------------------------------
+
+The save instructions can also be added to circuits by using the
+following ``QuantumCircuit`` methods which are patched when importing Aer.
+
+.. note ::
+  Each save method has a default label for accessing from the
+  circuit result data, however duplicate labels in results will result
+  in an exception being raised. If you use more than 1 instance of a
+  specific save instruction you must set a custom label for the
+  additional instructions.
+
+.. automethod:: QuantumCircuit.save_amplitudes
+.. automethod:: QuantumCircuit.save_amplitudes_squared
+.. automethod:: QuantumCircuit.save_clifford
+.. automethod:: QuantumCircuit.save_density_matrix
+.. automethod:: QuantumCircuit.save_expectation_value
+.. automethod:: QuantumCircuit.save_expectation_value_variance
+.. automethod:: QuantumCircuit.save_matrix_product_state
+.. automethod:: QuantumCircuit.save_probabilities
+.. automethod:: QuantumCircuit.save_probabilities_dict
+.. automethod:: QuantumCircuit.save_stabilizer
+.. automethod:: QuantumCircuit.save_state
+.. automethod:: QuantumCircuit.save_statevector
+.. automethod:: QuantumCircuit.save_statevector_dict
+.. automethod:: QuantumCircuit.save_superop
+.. automethod:: QuantumCircuit.save_unitary