Fix warnings in estimator tests (#8523)

**Context:**
Cleaning up the warnings that were raised by pytest.

**Description of the Change:**
- Remove `np.matrix` dependance in the `FirstQuantization` class.
- Renamed some dummy classes created in the `test_estimate.py` file. 
- Fix a test for the `PauliRot` resource operator which was previously
skipped.

---------

Co-authored-by: soranjh <[email protected]>

Author: Jaybsoni

doc/releases/changelog-dev.md

@@ -168,6 +168,10 @@
   [(#8486)](https://github.com/PennyLaneAI/pennylane/pull/8486)
   [(#8495)](https://github.com/PennyLaneAI/pennylane/pull/8495)
 
+* The various private functions of the :class:`~pennylane.estimator.FirstQuantization` class have 
+  been modified to avoid using `numpy.matrix` as this function is deprecated.
+  [(#8523)](https://github.com/PennyLaneAI/pennylane/pull/8523)
+
 * The `ftqc` module now includes dummy transforms for several Catalyst/MLIR passes (`to-ppr`, `commute-ppr`, `merge-ppr-ppm`, `pprm-to-mbqc` 
   and `reduce-t-depth`), to allow them to be captured as primitives in PLxPR and mapped to the MLIR passes in Catalyst. This enables using the passes with the unified compiler and program capture.
   [(#8519)](https://github.com/PennyLaneAI/pennylane/pull/8519)
@@ -178,6 +182,7 @@
   :class:`~.TemporaryAND`, :class:`~.QSVT`, and :class:`~.SelectPauliRot`.
   [(#8490)](https://github.com/PennyLaneAI/pennylane/pull/8490)
 
+
 <h3>Documentation 📝</h3>
 
 <h3>Bug fixes 🐛</h3>

pennylane/estimator/qpe_resources/first_quantization.py

@@ -120,7 +120,7 @@ def __init__(
                 / self.omega
                 * np.array([np.cross(vectors[i], vectors[j]) for i, j in [(1, 2), (2, 0), (0, 1)]])
             )
-            bbt = np.matrix(recip_vectors) @ np.matrix(recip_vectors).T
+            bbt = recip_vectors @ recip_vectors.T
             self.cubic = np.linalg.norm(bbt - (recip_vectors**2).max() * np.identity(3)) < 1e-6
 
         self._lamb = self.norm(
@@ -731,7 +731,7 @@ def _norm_noncubic(
             * np.array([np.cross(vectors[i], vectors[j]) for i, j in [(1, 2), (2, 0), (0, 1)]])
         )
 
-        bbt = np.matrix(recip_vectors) @ np.matrix(recip_vectors).T
+        bbt = recip_vectors @ recip_vectors.T
 
         orthogonal = (
             np.linalg.norm(bbt - np.array([np.max(b**2) for b in recip_vectors]) * np.identity(3))
@@ -801,8 +801,7 @@ def _norm_noncubic(
         lambda_u_1 = lambda_u * lambda_nu_1 / lambda_nu
         lambda_v_1 = lambda_v * lambda_nu_1 / lambda_nu
 
-        b_mat = np.matrix(recip_vectors)
-        abs_sum = np.abs(b_mat @ b_mat.T).flatten().sum()
+        abs_sum = np.abs(recip_vectors @ recip_vectors.T).flatten().sum()
 
         # taken from Appendix I.1 of arXiv:2302.07981v1 (2023)
         if orthogonal:
@@ -918,7 +917,7 @@ def _qubit_cost_noncubic(n, eta, error, br, charge, vectors):
                 * np.pi
                 * eta
                 * 2 ** (2 * n_p - 2)
-                * np.abs(np.matrix(recip_vectors) @ np.matrix(recip_vectors).T).flatten().sum()
+                * np.abs(recip_vectors @ recip_vectors.T).flatten().sum()
                 / error_b
             )
         )
@@ -1013,7 +1012,7 @@ def _unitary_cost_noncubic(n, eta, error, br, charge, vectors):
                 * np.pi
                 * eta
                 * 2 ** (2 * n_p - 2)
-                * np.abs(np.matrix(recip_vectors) @ np.matrix(recip_vectors).T).flatten().sum()
+                * np.abs(recip_vectors @ recip_vectors.T).flatten().sum()
                 / error_b
             )
         )

tests/estimator/ops/test_estimator_parametric_multi_qubit.py

@@ -187,7 +187,7 @@ def test_resource_rep(self, pauli_string, precision):
 
     expected_h_count = (0, 4, 6, 6, 0)
     expected_s_count = (0, 1, 0, 1, 0)
-    params = zip(pauli_words, expected_h_count, expected_s_count)
+    params = tuple(zip(pauli_words, expected_h_count, expected_s_count))
 
     @pytest.mark.parametrize("precision", (None, 1e-3))
     @pytest.mark.parametrize("pauli_string, expected_h_count, expected_s_count", params)
@@ -225,16 +225,13 @@ def test_resources_empty_pauli_string(self):
     @pytest.mark.parametrize("pauli_string, expected_h_count, expected_s_count", params)
     def test_resources_from_rep(self, pauli_string, expected_h_count, expected_s_count):
         """Test that the resources can be computed from the compressed representation and params."""
-        op = qre.PauliRot(0.5, pauli_string, wires=range(len(pauli_string)))
+        op = qre.PauliRot(pauli_string, 0.5, wires=range(len(pauli_string)))
         active_wires = len(pauli_string.replace("I", ""))
 
         if set(pauli_string) == {"I"}:
             expected = [qre.GateCount(qre.GlobalPhase.resource_rep())]
         else:
-            expected = [
-                qre.GateCount(qre.RZ.resource_rep()),
-                qre.GateCount(qre.CNOT.resource_rep(), 2 * (active_wires - 1)),
-            ]
+            expected = []
 
             if expected_h_count:
                 expected.append(qre.GateCount(qre.Hadamard.resource_rep(), expected_h_count))
@@ -248,6 +245,9 @@ def test_resources_from_rep(self, pauli_string, expected_h_count, expected_s_cou
                     )
                 )
 
+            expected.append(qre.GateCount(qre.RZ.resource_rep(precision=0.5)))
+            expected.append(qre.GateCount(qre.CNOT.resource_rep(), 2 * (active_wires - 1)))
+
         op_compressed_rep = op.resource_rep_from_op()
         op_resource_type = op_compressed_rep.op_type
         op_resource_params = op_compressed_rep.params