Implement pyqrack methods for sqrtx and sqrty (#416)

Closes #352

Author: david-pl

src/bloqade/pyqrack/squin/op.py

@@ -1,3 +1,5 @@
+import math
+
 from kirin import interp
 
 from bloqade.squin import op
@@ -122,6 +124,18 @@ def operator(
     ) -> tuple[OperatorRuntimeABC]:
         return (OperatorRuntime(method_name=stmt.name.lower()),)
 
+    @interp.impl(op.stmts.SqrtX)
+    @interp.impl(op.stmts.SqrtY)
+    def sqrt(
+        self,
+        interp: PyQrackInterpreter,
+        frame: interp.Frame,
+        stmt: op.stmts.SqrtX | op.stmts.SqrtY,
+    ):
+        axis_name = "x" if isinstance(stmt, op.stmts.SqrtX) else "y"
+        axis = OperatorRuntime(method_name=axis_name)
+        return (RotRuntime(axis=axis, angle=-0.5 * math.pi),)
+
     @interp.impl(op.stmts.P0)
     @interp.impl(op.stmts.P1)
     def projector(

test/pyqrack/squin/test_kernel.py

@@ -59,14 +59,17 @@ def main():
         "h",
         "s",
         "t",
+        "sqrt_x",
+        "sqrt_y",
+        "sqrt_z",
     ],
 )
 def test_basic_ops(op_name: str):
     @squin.kernel
     def main():
         q = squin.qubit.new(1)
         op = getattr(squin.op, op_name)()
-        squin.qubit.apply(op, q)
+        squin.qubit.apply(op, q[0])
         return q
 
     target = PyQrack(1)