Adding Post Processing Standard Library for Gemini (#710)

In this PR I add some standard library functions that can be used to
standardize workflows for Gemini logical mode experiments.

Author: weinbe58

src/bloqade/gemini/logical/__init__.py

@@ -1,3 +1,4 @@
 from . import dialects as dialects
 from .group import kernel as kernel
+from .stdlib import default_post_processing as default_post_processing
 from .dialects.operations import terminal_measure as terminal_measure

src/bloqade/gemini/logical/stdlib/__init__.py

@@ -0,0 +1,5 @@
+from .post_processing import (
+    set_detector as set_detector,
+    set_observable as set_observable,
+    default_post_processing as default_post_processing,
+)

src/bloqade/gemini/logical/stdlib/post_processing.py

@@ -0,0 +1,43 @@
+from typing import Any
+
+from kirin.dialects import ilist
+
+from bloqade import squin, types
+
+from ..group import kernel
+from ..dialects import operations
+
+
+@kernel(aggressive_unroll=True, verify=False)
+def set_detector(meas: ilist.IList[types.MeasurementResult, Any]):
+    return ilist.IList(
+        [
+            squin.set_detector(
+                [meas[0], meas[1], meas[2], meas[3]], coordinates=[0, 0]
+            ),
+            squin.set_detector(
+                [meas[1], meas[2], meas[4], meas[5]], coordinates=[0, 1]
+            ),
+            squin.set_detector(
+                [meas[2], meas[3], meas[4], meas[6]], coordinates=[0, 2]
+            ),
+        ]
+    )
+
+
+@kernel(aggressive_unroll=True, verify=False)
+def set_observable(meas: ilist.IList[types.MeasurementResult, Any], index: int):
+    return squin.set_observable([meas[0], meas[1], meas[5]], index)
+
+
+@kernel(aggressive_unroll=True, verify=False)
+def default_post_processing(register: ilist.IList[types.Qubit, Any]):
+    measurements = operations.terminal_measure(register)
+
+    detectors = set_detector(measurements[0])
+    observables = ilist.IList([set_observable(measurements[0], 0)])
+    for i in range(1, len(register)):
+        detectors = detectors + set_detector(measurements[i])
+        observables = observables + [set_observable(measurements[i], i)]
+
+    return detectors, observables