class_docstr: Test tensor variance measurements.
class_docstr_tok: ["Test","tensor","variance","measurements","."]
docstr: Test that a tensor product involving qml.Projector works correctly
code: def test_projector(self, device, tol, skip_if):
      """Test that a tensor product involving qml.Projector works correctly"""
      n_wires = 3
      dev = device(n_wires)
  
      if "Projector" not in dev.observables:
          pytest.skip(
              "Skipped because device does not support the Projector observable."
          )
  
      skip_if(dev, {"supports_tensor_observables": False})
  
      theta = 0.432
      phi = 0.123
      varphi = -0.543
  
      @qml.qnode(dev)
      def circuit(basis_state):
          qml.RX(theta, wires=[0])
          qml.RX(phi, wires=[1])
          qml.RX(varphi, wires=[2])
          qml.CNOT(wires=[0, 1])
          qml.CNOT(wires=[1, 2])
          return qml.var(
              qml.PauliZ(wires=[0])
              @ qml.Projector(basis_state, wires=[1, 2])
          )
  
      res_basis = circuit([0, 0])
      res_state = circuit([1, 0, 0, 0])
      expected = (
          (np.cos(varphi / 2) * np.cos(phi / 2) * np.cos(theta / 2))
          ** 2
          + (np.cos(varphi / 2) * np.sin(phi / 2) * np.sin(theta / 2))
          ** 2
      ) - (
          (np.cos(varphi / 2) * np.cos(phi / 2) * np.cos(theta / 2))
          ** 2
          - (np.cos(varphi / 2) * np.sin(phi / 2) * np.sin(theta / 2))
          ** 2
      ) ** 2
      assert np.allclose(res_basis, expected, atol=tol(dev.shots))
      assert np.allclose(res_state, expected, atol=tol(dev.shots))
  
      res_basis = circuit([0, 1])
      res_state = circuit([0, 1, 0, 0])
      expected = (
          (np.sin(varphi / 2) * np.cos(phi / 2) * np.cos(theta / 2))
          ** 2
          + (np.sin(varphi / 2) * np.sin(phi / 2) * np.sin(theta / 2))
          ** 2
      ) - (
          (np.sin(varphi / 2) * np.cos(phi / 2) * np.cos(theta / 2))
          ** 2
          - (np.sin(varphi / 2) * np.sin(phi / 2) * np.sin(theta / 2))
          ** 2
      ) ** 2
      assert np.allclose(res_basis, expected, atol=tol(dev.shots))
      assert np.allclose(res_state, expected, atol=tol(dev.shots))
  
      res_basis = circuit([1, 0])
      res_state = circuit([0, 0, 1, 0])
      expected = (
          (np.sin(varphi / 2) * np.sin(phi / 2) * np.cos(theta / 2))
          ** 2
          + (np.sin(varphi / 2) * np.cos(phi / 2) * np.sin(theta / 2))
          ** 2
      ) - (
          (np.sin(varphi / 2) * np.sin(phi / 2) * np.cos(theta / 2))
          ** 2
          - (np.sin(varphi / 2) * np.cos(phi / 2) * np.sin(theta / 2))
          ** 2
      ) ** 2
      assert np.allclose(res_basis, expected, atol=tol(dev.shots))
      assert np.allclose(res_state, expected, atol=tol(dev.shots))
  
      res_basis = circuit([1, 1])
      res_state = circuit([0, 0, 0, 1])
      expected = (
          (np.cos(varphi / 2) * np.sin(phi / 2) * np.cos(theta / 2))
          ** 2
          + (np.cos(varphi / 2) * np.cos(phi / 2) * np.sin(theta / 2))
          ** 2
      ) - (
          (np.cos(varphi / 2) * np.sin(phi / 2) * np.cos(theta / 2))
          ** 2
          - (np.cos(varphi / 2) * np.cos(phi / 2) * np.sin(theta / 2))
          ** 2
      ) ** 2
      assert np.allclose(res_basis, expected, atol=tol(dev.shots))
      assert np.allclose(res_state, expected, atol=tol(dev.shots))
  
      res = circuit(np.array([1, 0, 0, 1]) / np.sqrt(2))
      expected_mean = 0.5 * (
          (np.cos(theta / 2) * np.cos(phi / 2) * np.cos(varphi / 2))
          ** 2
          + (np.cos(theta / 2) * np.sin(phi / 2) * np.cos(varphi / 2))
          ** 2
          - (np.sin(theta / 2) * np.sin(phi / 2) * np.cos(varphi / 2))
          ** 2
          - (np.sin(theta / 2) * np.cos(phi / 2) * np.cos(varphi / 2))
          ** 2
      )
      expected_var = (
          0.5
          * (
              (np.cos(theta / 2) * np.cos(phi / 2) * np.cos(varphi / 2))
              ** 2
              + (
                  np.cos(theta / 2)
                  * np.sin(phi / 2)
                  * np.cos(varphi / 2)
              )
              ** 2
              + (
                  np.sin(theta / 2)
                  * np.sin(phi / 2)
                  * np.cos(varphi / 2)
              )
              ** 2
              + (
                  np.sin(theta / 2)
                  * np.cos(phi / 2)
                  * np.cos(varphi / 2)
              )
              ** 2
          )
          - expected_mean**2
      )
      assert np.allclose(res, expected_var, atol=tol(False))
  
imports: import pytest
  from flaky import flaky
  from scipy.sparse import csr_matrix
  import pennylane
  from pennylane import numpy
  from pennylane.measurements import ClassicalShadowMP, MeasurementTransform, SampleMeasurement, SampleMP, StateMeasurement, StateMP
label_desc: Use image node_id 6 for calling the TestTensorVar obj's underlying member method code with example usage: obj.test_projector(device, tol, skip_if) and returns: qml