class_docstr: Tests for the variance return type
class_docstr_tok: ["Tests","for","the","variance","return","type"]
docstr: Tests if the samples of a Projector observable returned by sample have
  the correct values
code: def test_var_projector(self, device, tol):
      """Tests if the samples of a Projector observable returned by sample have
      the correct values
      """
      n_wires = 2
      dev = device(n_wires)
  
      if "Projector" not in dev.observables:
          pytest.skip(
              "Skipped because device does not support the Projector observable."
          )
  
      phi = 0.543
      theta = 0.654
  
      @qml.qnode(dev)
      def circuit(state):
          qml.RX(phi, wires=[0])
          qml.RY(theta, wires=[1])
          qml.CNOT(wires=[0, 1])
          return qml.var(qml.Projector(state, wires=[0, 1]))
  
      res_basis = circuit([0, 0])
      res_state = circuit([1, 0, 0, 0])
      expected = (np.cos(phi / 2) * np.cos(theta / 2)) ** 2 - (
          (np.cos(phi / 2) * np.cos(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.cos(phi / 2) * np.sin(theta / 2)) ** 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, 0])
      res_state = circuit([0, 0, 1, 0])
      expected = (np.sin(phi / 2) * np.sin(theta / 2)) ** 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, 1])
      res_state = circuit([0, 0, 0, 1])
      expected = (np.sin(phi / 2) * np.cos(theta / 2)) ** 2 - (
          (np.sin(phi / 2) * np.cos(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)) ** 2
          + (np.cos(theta / 2) * np.sin(phi / 2)) ** 2
      )
      expected_var = expected_mean - expected_mean**2
      assert np.allclose(res, expected_var, atol=tol(dev.shots))
  
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 3 for calling the TestVar obj's underlying member method code with example usage: obj.test_var_projector(device, tol) and returns: qml