add synthesis plugin docs

qiskit/transpiler/passes/synthesis/plugin.py

@@ -336,6 +336,161 @@ def run(self, high_level_object, coupling_map=None, target=None, qubits=None, **
    HighLevelSynthesisPlugin
    HighLevelSynthesisPluginManager
    high_level_synthesis_plugin_names
+
+Available Plugins
+=================
+
+Below are the synthesis plugin classes available in Qiskit. These classes should not be
+used directly, but instead should be used through the plugin interface documented
+above. The classes are listed here to ease finding the documentation for each of the
+included plugins and to ease the comparison between different synthesis methods for
+a given object.
+
+
+Unitary Synthesis Plugins
+-------------------------
+
+.. autosummary::
+   :toctree: ../stubs/
+
+   /qiskit/transpiler/passes/synthesis/unitary_synthesis/DefaultUnitarySynthesis
+   /qiskit/transpiler/passes/synthesis/solovay_kitaev_synthesis/SolovayKitaevSynthesis
+
+
+High Level Synthesis
+--------------------
+
+For each high-level object we give a table that lists all of its plugins available
+directly in Qiskit. We include the name of the plugin, the class of the plugin,
+the targeted connectivity map and optionally additional information. Recall the plugins
+should be used via the previously described :class:`.HLSConfig`, for example::
+
+    HLSConfig(permutation=["kms"])
+
+creates a high-level synthesis configuration that uses the ``kms`` plugin
+for synthesizing :class:`.PermutationGate` objects -- i.e. those with
+``name = "permutation"``. In this case, the plugin name is "kms", the plugin class
+is :class:`~.KMSSynthesisPermutation`. This particular synthesis algorithm created
+a circuit adhering to the linear nearest-neighbor connectivity.
+
+
+Clifford Synthesis
+''''''''''''''''''
+
+.. list-table:: Plugins for :class:`qiskit.quantum_info.Clifford` (key = "clifford")
+    :header-rows: 1
+
+    * - Plugin name
+      - Plugin class
+      - Targeted connectivity
+      - Description
+    * - "ag"
+      - :class:`~.AGSynthesisClifford`
+      - all-to-all
+      -
+    * - "bm"
+      - :class:`~.BMSynthesisClifford`
+      - all-to-all
+      -
+    * - "greedy"
+      - :class:`~.GreedySynthesisClifford`
+      - all-to-all
+      -
+    * - "layers"
+      - :class:`~.LayerSynthesisClifford`
+      - all-to-all
+      -
+    * - "lnn"
+      - :class:`~.LayerLnnSynthesisClifford`
+      - linear
+      -
+    * - "default"
+      - :class:`~.DefaultSynthesisClifford`
+      - all-to-all
+      -
+
+.. autosummary::
+   :toctree: ../stubs/
+
+   /qiskit/transpiler/passes/synthesis/high_level_synthesis/AGSynthesisClifford
+   /qiskit/transpiler/passes/synthesis/high_level_synthesis/BMSynthesisClifford
+   /qiskit/transpiler/passes/synthesis/high_level_synthesis/GreedySynthesisClifford
+   /qiskit/transpiler/passes/synthesis/high_level_synthesis/LayerSynthesisClifford
+   /qiskit/transpiler/passes/synthesis/high_level_synthesis/LayerLnnSynthesisClifford
+   /qiskit/transpiler/passes/synthesis/high_level_synthesis/DefaultSynthesisClifford
+
+
+Linear Function Synthesis
+'''''''''''''''''''''''''
+
+.. list-table:: Plugins for :class:`.LinearFunction` (key = "linear")
+    :header-rows: 1
+
+    * - Plugin name
+      - Plugin class
+      - Targeted connectivity
+      - Description
+    * - "kms"
+      - :class:`~.KMSSynthesisLinearFunction`
+      - linear
+      -
+    * - "pmh"
+      - :class:`~.PMHSynthesisLinearFunction`
+      - all-to-all
+      -
+    * - "default"
+      - :class:`~.DefaultSynthesisLinearFunction`
+      - all-to-all
+      -
+
+.. autosummary::
+   :toctree: ../stubs/
+
+   /qiskit/transpiler/passes/synthesis/high_level_synthesis/KMSSynthesisLinearFunction
+   /qiskit/transpiler/passes/synthesis/high_level_synthesis/PMHSynthesisLinearFunction
+   /qiskit/transpiler/passes/synthesis/high_level_synthesis/DefaultSynthesisLinearFunction
+
+
+Permutation Synthesis
+'''''''''''''''''''''
+
+.. list-table:: Plugins for :class:`.PermutationGate` (key = "permutation")
+    :header-rows: 1
+
+    * - Plugin name
+      - Plugin class
+      - Targeted connectivity
+      - Description
+    * - "basic"
+      - :class:`~.BasicSynthesisPermutation`
+      - all-to-all
+      - optimal swap count
+    * - "acg"
+      - :class:`~.ACGSynthesisPermutation`
+      - all-to-all
+      - swap depth of at most `2`
+    * - "kms"
+      - :class:`~.KMSSynthesisPermutation`
+      - linear
+      - swap depth of at most `n`
+    * - "token_swapper"
+      - :class:`~.TokenSwapperSynthesisPermutation`
+      - any
+      -
+    * - "default"
+      - :class:`~.BasicSynthesisPermutation`
+      - all-to-all
+      - same as "basic"
+
+.. autosummary::
+   :toctree: ../stubs/
+
+   /qiskit/transpiler/passes/synthesis/high_level_synthesis/BasicSynthesisPermutation
+   /qiskit/transpiler/passes/synthesis/high_level_synthesis/ACGSynthesisPermutation
+   /qiskit/transpiler/passes/synthesis/high_level_synthesis/KMSSynthesisPermutation
+   /qiskit/transpiler/passes/synthesis/high_level_synthesis/TokenSwapperSynthesisPermutation
+
+
 """
 
 import abc