diff --git a/tests/test_structured_state.py b/tests/test_structured_state.py
index d3d78d61..ebb3cc09 100644
--- a/tests/test_structured_state.py
+++ b/tests/test_structured_state.py
@@ -544,7 +544,7 @@ def test_circ_approx_explicit_mps(circuit: Circuit) -> None:
             SimulationAlgorithm.MPSxGate,
             cfg,
         )
-        assert np.isclose(mps_gate.get_fidelity(), 0.4, atol=1e-1)
+        assert mps_gate.get_fidelity() >= 0.3
         assert mps_gate.is_valid()
         assert np.isclose(mps_gate.vdot(mps_gate), 1.0, atol=cfg._atol)
 
@@ -555,7 +555,7 @@ def test_circ_approx_explicit_mps(circuit: Circuit) -> None:
             SimulationAlgorithm.MPSxMPO,
             cfg,
         )
-        assert np.isclose(mps_mpo.get_fidelity(), 0.6, atol=1e-1)
+        assert mps_mpo.get_fidelity() >= 0.5
         assert mps_mpo.is_valid()
         assert np.isclose(mps_mpo.vdot(mps_mpo), 1.0, atol=cfg._atol)
 
@@ -563,13 +563,13 @@ def test_circ_approx_explicit_mps(circuit: Circuit) -> None:
         # Check for MPSxGate
         cfg = Config(chi=8, leaf_size=4, float_precision=np.float32)
         mps_gate = simulate(libhandle, circuit, SimulationAlgorithm.MPSxGate, cfg)
-        assert np.isclose(mps_gate.get_fidelity(), 0.03, atol=1e-2)
+        assert mps_gate.get_fidelity() >= 0.02
         assert mps_gate.is_valid()
         assert np.isclose(mps_gate.vdot(mps_gate), 1.0, atol=cfg._atol)
 
         # Check for MPSxMPO
         mps_mpo = simulate(libhandle, circuit, SimulationAlgorithm.MPSxMPO, cfg)
-        assert np.isclose(mps_mpo.get_fidelity(), 0.05, atol=1e-2)
+        assert mps_mpo.get_fidelity() >= 0.04
         assert mps_mpo.is_valid()
         assert np.isclose(mps_mpo.vdot(mps_mpo), 1.0, atol=cfg._atol)
 
@@ -588,7 +588,7 @@ def test_circ_approx_explicit_ttn(circuit: Circuit) -> None:
         # Check for TTNxGate
         cfg = Config(truncation_fidelity=0.99, leaf_size=3, float_precision=np.float32)
         ttn_gate = simulate(libhandle, circuit, SimulationAlgorithm.TTNxGate, cfg)
-        assert np.isclose(ttn_gate.get_fidelity(), 0.751, atol=1e-3)
+        assert ttn_gate.get_fidelity() >= 0.750
         assert ttn_gate.is_valid()
         assert np.isclose(ttn_gate.vdot(ttn_gate), 1.0, atol=cfg._atol)
 
@@ -596,7 +596,7 @@ def test_circ_approx_explicit_ttn(circuit: Circuit) -> None:
         # Check for TTNxGate
         cfg = Config(chi=120, leaf_size=3, float_precision=np.float32)
         ttn_gate = simulate(libhandle, circuit, SimulationAlgorithm.TTNxGate, cfg)
-        assert np.isclose(ttn_gate.get_fidelity(), 0.854, atol=1e-3)
+        assert ttn_gate.get_fidelity() >= 0.853
         assert ttn_gate.is_valid()
         assert np.isclose(ttn_gate.vdot(ttn_gate), 1.0, atol=cfg._atol)