diff --git a/src/qailo/state_vector/fidelity.py b/src/qailo/state_vector/fidelity.py
index 517c14c..953298d 100644
--- a/src/qailo/state_vector/fidelity.py
+++ b/src/qailo/state_vector/fidelity.py
@@ -4,4 +4,4 @@
 def fidelity(v0, v1):
     v0 = v0 / np.linalg.norm(v0)
     v1 = v1 / np.linalg.norm(v1)
-    return np.abs(np.vdot(v0, v1))
+    return np.abs(np.vdot(v0, v1))**2
diff --git a/test/state_vector/test_apply_seq.py b/test/state_vector/test_apply_seq.py
index 2476abd..62f9788 100644
--- a/test/state_vector/test_apply_seq.py
+++ b/test/state_vector/test_apply_seq.py
@@ -16,5 +16,5 @@ def test_apply_seq():
         assert q.sv.fidelity(v1, v1) == approx(1)
         assert q.sv.fidelity(v2, v2) == approx(1)
         assert q.sv.fidelity(v1, v2) == approx(1)
-        assert q.sv.fidelity(v0, v1) == approx(1 / np.sqrt(2**n))
-        assert q.sv.fidelity(v0, v2) == approx(1 / np.sqrt(2**n))
+        assert q.sv.fidelity(v0, v1) == approx(1 / 2**n)
+        assert q.sv.fidelity(v0, v2) == approx(1 / 2**n)
diff --git a/test/state_vector/test_fidelity.py b/test/state_vector/test_fidelity.py
index 946c1fb..cbcab77 100644
--- a/test/state_vector/test_fidelity.py
+++ b/test/state_vector/test_fidelity.py
@@ -11,4 +11,4 @@ def test_fidelity():
             sv1 = q.sv.apply(sv1, q.op.h(), [i])
         assert q.sv.fidelity(sv0, sv0) == approx(1)
         assert q.sv.fidelity(sv1, sv1) == approx(1)
-        assert q.sv.fidelity(sv0, sv1) == approx(1 / np.sqrt(2**n))
+        assert q.sv.fidelity(sv0, sv1) == approx(1 / 2**n)