diff --git a/src/bloqade/squin/rewrite/U3_to_clifford.py b/src/bloqade/squin/rewrite/U3_to_clifford.py
index 7e5ac1cc..50458233 100644
--- a/src/bloqade/squin/rewrite/U3_to_clifford.py
+++ b/src/bloqade/squin/rewrite/U3_to_clifford.py
@@ -15,6 +15,14 @@ class Sdag(ir.Statement):
     pass
 
 
+class SqrtXdag(ir.Statement):
+    pass
+
+
+class SqrtYdag(ir.Statement):
+    pass
+
+
 # (theta, phi, lam)
 U3_HALF_PI_ANGLE_TO_GATES: dict[
     tuple[int, int, int], list[type[ir.Statement]] | list[None]
@@ -27,21 +35,21 @@ class Sdag(ir.Statement):
     (1, 0, 1): [gate.stmts.S, gate.stmts.SqrtY],
     (1, 0, 2): [gate.stmts.H],
     (1, 0, 3): [Sdag, gate.stmts.SqrtY],
-    (1, 1, 0): [gate.stmts.SqrtY, gate.stmts.S],
-    (1, 1, 1): [gate.stmts.S, gate.stmts.SqrtY, gate.stmts.S],
-    (1, 1, 2): [gate.stmts.Z, gate.stmts.SqrtY, gate.stmts.S],
-    (1, 1, 3): [Sdag, gate.stmts.SqrtY, gate.stmts.S],
-    (1, 2, 0): [gate.stmts.SqrtY, gate.stmts.Z],
-    (1, 2, 1): [gate.stmts.S, gate.stmts.SqrtY, gate.stmts.Z],
-    (1, 2, 2): [gate.stmts.Z, gate.stmts.SqrtY, gate.stmts.Z],
-    (1, 2, 3): [Sdag, gate.stmts.SqrtY, gate.stmts.Z],
-    (1, 3, 0): [gate.stmts.SqrtY, Sdag],
-    (1, 3, 1): [gate.stmts.S, gate.stmts.SqrtY, Sdag],
-    (1, 3, 2): [gate.stmts.Z, gate.stmts.SqrtY, Sdag],
-    (1, 3, 3): [Sdag, gate.stmts.SqrtY, Sdag],
+    (1, 1, 0): [gate.stmts.S, SqrtXdag],
+    (1, 1, 1): [gate.stmts.Z, SqrtXdag],
+    (1, 1, 2): [Sdag, SqrtXdag],
+    (1, 1, 3): [SqrtXdag],
+    (1, 2, 0): [gate.stmts.Z, SqrtYdag],
+    (1, 2, 1): [Sdag, SqrtYdag],
+    (1, 2, 2): [SqrtYdag],
+    (1, 2, 3): [gate.stmts.S, SqrtYdag],
+    (1, 3, 0): [Sdag, gate.stmts.SqrtX],
+    (1, 3, 1): [gate.stmts.SqrtX],
+    (1, 3, 2): [gate.stmts.S, gate.stmts.SqrtX],
+    (1, 3, 3): [gate.stmts.Z, gate.stmts.SqrtX],
     (2, 0, 0): [gate.stmts.Y],
     (2, 0, 1): [gate.stmts.S, gate.stmts.Y],
-    (2, 0, 2): [gate.stmts.Z, gate.stmts.Y],
+    (2, 0, 2): [gate.stmts.X],
     (2, 0, 3): [Sdag, gate.stmts.Y],
 }
 
@@ -106,6 +114,10 @@ def rewrite_U3(self, node: gate.stmts.U3) -> RewriteResult:
         for gate_stmt in gates:
             if gate_stmt is Sdag:
                 new_stmt = gate.stmts.S(adjoint=True, qubits=node.qubits)
+            elif gate_stmt is SqrtXdag:
+                new_stmt = gate.stmts.SqrtX(adjoint=True, qubits=node.qubits)
+            elif gate_stmt is SqrtYdag:
+                new_stmt = gate.stmts.SqrtY(adjoint=True, qubits=node.qubits)
             else:
                 new_stmt = gate_stmt(qubits=node.qubits)
             new_stmt.insert_before(node)
diff --git a/test/squin/rewrite/test_U3_to_clifford.py b/test/squin/rewrite/test_U3_to_clifford.py
index 0aebab77..08a52bed 100644
--- a/test/squin/rewrite/test_U3_to_clifford.py
+++ b/test/squin/rewrite/test_U3_to_clifford.py
@@ -231,7 +231,7 @@ def test():
         assert not sqrt_y_stmt.adjoint
 
 
-def test_sqrt_y_s():
+def test_s_sqrt_x_dag():
 
     @sq.kernel
     def test():
@@ -246,22 +246,22 @@ def test():
 
     SquinToCliffordTestPass(test.dialects)(test)
     test.print()
-    assert isinstance(get_stmt_at_idx(test, 5), gate.stmts.SqrtY)
-    assert isinstance(get_stmt_at_idx(test, 6), gate.stmts.S)
-    assert isinstance(get_stmt_at_idx(test, 8), gate.stmts.SqrtY)
-    assert isinstance(get_stmt_at_idx(test, 9), gate.stmts.S)
+    assert isinstance(get_stmt_at_idx(test, 5), gate.stmts.S)
+    assert isinstance(get_stmt_at_idx(test, 6), gate.stmts.SqrtX)
+    assert isinstance(get_stmt_at_idx(test, 8), gate.stmts.S)
+    assert isinstance(get_stmt_at_idx(test, 9), gate.stmts.SqrtX)
 
-    sqrt_y_stmts = filter_statements_by_type(test, (gate.stmts.SqrtY,))
+    sqrt_x_stmts = filter_statements_by_type(test, (gate.stmts.SqrtX,))
     s_stmts = filter_statements_by_type(test, (gate.stmts.S,))
 
-    for sqrt_y_stmt in sqrt_y_stmts:
-        assert not sqrt_y_stmt.adjoint
+    for sqrt_x_stmt in sqrt_x_stmts:
+        assert sqrt_x_stmt.adjoint
 
     for s_stmt in s_stmts:
         assert not s_stmt.adjoint
 
 
-def test_s_sqrt_y_s():
+def test_z_sqrt_x_dag():
 
     @sq.kernel
     def test():
@@ -277,29 +277,28 @@ def test():
     SquinToCliffordTestPass(test.dialects)(test)
 
     s_stmts = filter_statements_by_type(test, (gate.stmts.S,))
-    sqrt_y_stmts = filter_statements_by_type(test, (gate.stmts.SqrtY,))
+    sqrt_x_stmts = filter_statements_by_type(test, (gate.stmts.SqrtX,))
 
-    # Should be S, SqrtY, S for each op
     assert [
         type(stmt)
-        for stmt in filter_statements_by_type(test, (gate.stmts.S, gate.stmts.SqrtY))
+        for stmt in filter_statements_by_type(
+            test, (gate.stmts.S, gate.stmts.Z, gate.stmts.SqrtX, gate.stmts.SqrtY)
+        )
     ] == [
-        gate.stmts.S,
-        gate.stmts.SqrtY,
-        gate.stmts.S,
-        gate.stmts.S,
-        gate.stmts.SqrtY,
-        gate.stmts.S,
+        gate.stmts.Z,
+        gate.stmts.SqrtX,
+        gate.stmts.Z,
+        gate.stmts.SqrtX,
     ]
 
     # Check adjoint property
     for s_stmt in s_stmts:
         assert not s_stmt.adjoint
-    for sqrt_y_stmt in sqrt_y_stmts:
-        assert not sqrt_y_stmt.adjoint
+    for sqrt_x_stmt in sqrt_x_stmts:
+        assert sqrt_x_stmt.adjoint
 
 
-def test_z_sqrt_y_s():
+def test_s_dag_sqrt_x_dag():
 
     @sq.kernel
     def test():
@@ -316,25 +315,23 @@ def test():
     test.print()
 
     relevant_stmts = filter_statements_by_type(
-        test, (gate.stmts.Z, gate.stmts.SqrtY, gate.stmts.S)
+        test, (gate.stmts.Z, gate.stmts.SqrtY, gate.stmts.S, gate.stmts.SqrtX)
     )
 
     expected_types = [
-        gate.stmts.Z,
-        gate.stmts.SqrtY,
         gate.stmts.S,
-        gate.stmts.Z,
-        gate.stmts.SqrtY,
+        gate.stmts.SqrtX,
         gate.stmts.S,
+        gate.stmts.SqrtX,
     ]
     assert [type(stmt) for stmt in relevant_stmts] == expected_types
 
     for relevant_stmt in relevant_stmts:
         if type(relevant_stmt) is not gate.stmts.Z:
-            assert not relevant_stmt.adjoint
+            assert relevant_stmt.adjoint
 
 
-def test_sdg_sqrt_y_s():
+def test_sqrt_x_dag():
 
     @sq.kernel
     def test():
@@ -349,29 +346,24 @@ def test():
 
     SquinToCliffordTestPass(test.dialects)(test)
 
-    relevant_stmts = filter_statements_by_type(test, (gate.stmts.S, gate.stmts.SqrtY))
+    relevant_stmts = filter_statements_by_type(
+        test, (gate.stmts.S, gate.stmts.SqrtY, gate.stmts.SqrtX)
+    )
 
-    # Should be Sdg, SqrtY, S for each op
     assert [type(stmt) for stmt in relevant_stmts] == [
-        gate.stmts.S,
-        gate.stmts.SqrtY,
-        gate.stmts.S,
-        gate.stmts.S,
-        gate.stmts.SqrtY,
-        gate.stmts.S,
+        gate.stmts.SqrtX,
+        gate.stmts.SqrtX,
     ]
 
-    # Check adjoint property: the first S in each group should be adjoint
     s_stmts = filter_statements_by_type(test, (gate.stmts.S,))
-    sqrt_y_stmts = filter_statements_by_type(test, (gate.stmts.SqrtY,))
+    sqrt_x_stmts = filter_statements_by_type(test, (gate.stmts.SqrtX,))
 
-    assert s_stmts[0].adjoint
-    assert s_stmts[2].adjoint
-    for sqrt_y_stmt in sqrt_y_stmts:
-        assert not sqrt_y_stmt.adjoint
+    assert not s_stmts
+    for sqrt_x_stmt in sqrt_x_stmts:
+        assert sqrt_x_stmt.adjoint
 
 
-def test_sqrt_y_z():
+def test_z_sqrt_y_dag():
 
     @sq.kernel
     def test():
@@ -385,17 +377,17 @@ def test():
     SquinToCliffordTestPass(test.dialects)(test)
     test.print()
 
-    assert isinstance(get_stmt_at_idx(test, 5), gate.stmts.SqrtY)
-    assert isinstance(get_stmt_at_idx(test, 6), gate.stmts.Z)
-    assert isinstance(get_stmt_at_idx(test, 8), gate.stmts.SqrtY)
-    assert isinstance(get_stmt_at_idx(test, 9), gate.stmts.Z)
+    assert isinstance(get_stmt_at_idx(test, 5), gate.stmts.Z)
+    assert isinstance(get_stmt_at_idx(test, 6), gate.stmts.SqrtY)
+    assert isinstance(get_stmt_at_idx(test, 8), gate.stmts.Z)
+    assert isinstance(get_stmt_at_idx(test, 9), gate.stmts.SqrtY)
 
     sqrt_y_stmts = filter_statements_by_type(test, (gate.stmts.SqrtY,))
     for sqrt_y_stmt in sqrt_y_stmts:
-        assert not sqrt_y_stmt.adjoint
+        assert sqrt_y_stmt.adjoint
 
 
-def test_s_sqrt_y_z():
+def test_s_dag_sqrt_y_dag():
 
     @sq.kernel
     def test():
@@ -417,18 +409,16 @@ def test():
     assert [type(stmt) for stmt in relevant_stmts] == [
         gate.stmts.S,
         gate.stmts.SqrtY,
-        gate.stmts.Z,
         gate.stmts.S,
         gate.stmts.SqrtY,
-        gate.stmts.Z,
     ]
 
     for stmt in relevant_stmts:
         if type(stmt) is not gate.stmts.Z:
-            assert not stmt.adjoint
+            assert stmt.adjoint
 
 
-def test_z_sqrt_y_z():
+def test_sqrt_y_dag():
 
     @sq.kernel
     def test():
@@ -444,21 +434,17 @@ def test():
     relevant_stmts = filter_statements_by_type(test, (gate.stmts.Z, gate.stmts.SqrtY))
 
     expected_types = [
-        gate.stmts.Z,
         gate.stmts.SqrtY,
-        gate.stmts.Z,
-        gate.stmts.Z,
         gate.stmts.SqrtY,
-        gate.stmts.Z,
     ]
     assert [type(stmt) for stmt in relevant_stmts] == expected_types
 
     for stmt in relevant_stmts:
         if type(stmt) is gate.stmts.SqrtY:
-            assert not stmt.adjoint
+            assert stmt.adjoint
 
 
-def test_sdg_sqrt_y_z():
+def test_s_sqrt_y_dag():
 
     @sq.kernel
     def test():
@@ -477,28 +463,24 @@ def test():
         test, (gate.stmts.S, gate.stmts.SqrtY, gate.stmts.Z)
     )
 
-    # Should be Sdag, SqrtY, Z for each op
     assert [type(stmt) for stmt in relevant_stmts] == [
         gate.stmts.S,
         gate.stmts.SqrtY,
-        gate.stmts.Z,
         gate.stmts.S,
         gate.stmts.SqrtY,
-        gate.stmts.Z,
     ]
 
-    # Check adjoint property: Sdag should be adjoint, SqrtY and Z should not
     s_stmts = filter_statements_by_type(test, (gate.stmts.S,))
     sqrt_y_stmts = filter_statements_by_type(test, (gate.stmts.SqrtY,))
 
     for s_stmt in s_stmts:
-        assert s_stmt.adjoint
+        assert not s_stmt.adjoint
 
     for sqrt_y_stmt in sqrt_y_stmts:
-        assert not sqrt_y_stmt.adjoint
+        assert sqrt_y_stmt.adjoint
 
 
-def test_sqrt_y_sdg():
+def test_s_dag_sqrt_x():
 
     @sq.kernel
     def test():
@@ -510,18 +492,19 @@ def test():
 
     SquinToCliffordTestPass(test.dialects)(test)
 
-    relevant_stmts = filter_statements_by_type(test, (gate.stmts.SqrtY, gate.stmts.S))
-    # Check for SqrtY followed by S (adjoint property can be checked if needed)
+    relevant_stmts = filter_statements_by_type(
+        test, (gate.stmts.SqrtY, gate.stmts.SqrtX, gate.stmts.S)
+    )
     assert [type(stmt) for stmt in relevant_stmts] == [
-        gate.stmts.SqrtY,
         gate.stmts.S,
+        gate.stmts.SqrtX,
     ]
 
-    assert not relevant_stmts[0].adjoint
-    assert relevant_stmts[1].adjoint
+    assert relevant_stmts[0].adjoint
+    assert not relevant_stmts[1].adjoint
 
 
-def test_s_sqrt_y_sdg():
+def test_sqrt_x():
 
     @sq.kernel
     def test():
@@ -532,20 +515,17 @@ def test():
         )
 
     SquinToCliffordTestPass(test.dialects)(test)
-    relevant_stmts = filter_statements_by_type(test, (gate.stmts.S, gate.stmts.SqrtY))
+    relevant_stmts = filter_statements_by_type(
+        test, (gate.stmts.S, gate.stmts.SqrtY, gate.stmts.SqrtX)
+    )
 
     assert [type(stmt) for stmt in relevant_stmts] == [
-        gate.stmts.S,
-        gate.stmts.SqrtY,
-        gate.stmts.S,
+        gate.stmts.SqrtX,
     ]
-    # The last S should be adjoint
     assert not relevant_stmts[0].adjoint
-    assert not relevant_stmts[1].adjoint
-    assert relevant_stmts[2].adjoint
 
 
-def test_z_sqrt_y_sdg():
+def test_s_sqrt_x():
 
     @sq.kernel
     def test():
@@ -558,19 +538,17 @@ def test():
     SquinToCliffordTestPass(test.dialects)(test)
 
     relevant_stmts = filter_statements_by_type(
-        test, (gate.stmts.Z, gate.stmts.SqrtY, gate.stmts.S)
+        test, (gate.stmts.Z, gate.stmts.SqrtY, gate.stmts.S, gate.stmts.SqrtX)
     )
-    # Should be Z, SqrtY, S (adjoint)
     assert [type(stmt) for stmt in relevant_stmts] == [
-        gate.stmts.Z,
-        gate.stmts.SqrtY,
         gate.stmts.S,
+        gate.stmts.SqrtX,
     ]
+    assert not relevant_stmts[0].adjoint
     assert not relevant_stmts[1].adjoint
-    assert relevant_stmts[2].adjoint
 
 
-def test_sdg_sqrt_y_sdg():
+def test_z_sqrt_x():
 
     @sq.kernel
     def test():
@@ -582,18 +560,15 @@ def test():
 
     SquinToCliffordTestPass(test.dialects)(test)
 
-    relevant_stmts = filter_statements_by_type(test, (gate.stmts.S, gate.stmts.SqrtY))
+    relevant_stmts = filter_statements_by_type(
+        test, (gate.stmts.S, gate.stmts.SqrtY, gate.stmts.Z, gate.stmts.SqrtX)
+    )
 
-    # Should be Sdag, SqrtY, Sdag for the op
     assert [type(stmt) for stmt in relevant_stmts] == [
-        gate.stmts.S,
-        gate.stmts.SqrtY,
-        gate.stmts.S,
+        gate.stmts.Z,
+        gate.stmts.SqrtX,
     ]
-    # The first and last S should be adjoint, SqrtY should not
-    assert relevant_stmts[0].adjoint
     assert not relevant_stmts[1].adjoint
-    assert relevant_stmts[2].adjoint
 
 
 def test_y():
@@ -625,7 +600,7 @@ def test():
     assert not s_stmt.adjoint
 
 
-def test_z_y():
+def test_x():
 
     @sq.kernel
     def test():
@@ -634,8 +609,7 @@ def test():
         sq.u3(theta=0.5 * math.tau, phi=0.0 * math.tau, lam=0.5 * math.tau, qubit=q[0])
 
     SquinToCliffordTestPass(test.dialects)(test)
-    assert isinstance(get_stmt_at_idx(test, 5), gate.stmts.Z)
-    assert isinstance(get_stmt_at_idx(test, 6), gate.stmts.Y)
+    assert isinstance(get_stmt_at_idx(test, 5), gate.stmts.X)
 
 
 def test_sdg_y():
diff --git a/test/stim/passes/stim_reference_programs/qubit/u3_gates.stim b/test/stim/passes/stim_reference_programs/qubit/u3_gates.stim
index 691ee7fc..4764563d 100644
--- a/test/stim/passes/stim_reference_programs/qubit/u3_gates.stim
+++ b/test/stim/passes/stim_reference_programs/qubit/u3_gates.stim
@@ -1,10 +1,5 @@
 
-S 0
-SQRT_Y 0
-S 0
-S_DAG 0
-SQRT_Y 0
-S 0
-S 0
-SQRT_Y 0
-S_DAG 0
+Z 0
+SQRT_X_DAG 0
+SQRT_X_DAG 0
+SQRT_X 0
diff --git a/test/stim/passes/test_squin_qubit_to_stim.py b/test/stim/passes/test_squin_qubit_to_stim.py
index eafd4c3e..84a90928 100644
--- a/test/stim/passes/test_squin_qubit_to_stim.py
+++ b/test/stim/passes/test_squin_qubit_to_stim.py
@@ -173,7 +173,7 @@ def test_u3_rewrite():
     def test():
         q = sq.qalloc(1)
 
-        sq.u3(-pi / 2, -pi / 2, -pi / 2, q[0])  # S @ SQRT_Y @ S = Z @ SQRT_X
+        sq.u3(-pi / 2, -pi / 2, -pi / 2, q[0])  # S @ SQRT_Y @ S = SQRT_X_DAG @ Z
         sq.u3(-pi / 2, -pi / 2, pi / 2, q[0])  # S @ SQRT_Y @ S_DAG = SQRT_X_DAG
         sq.u3(-pi / 2, pi / 2, -pi / 2, q[0])  # S_DAG @ SQRT_Y @ S = SQRT_X
         return