class_docstr: Tests the _generalized_pauli_decompose via pauli_decompose function
docstr: Test differentiability for pauli_decompose
docstr_tok: ["Test","differentiability","for","pauli_decompose"]
code: def test_differentiability(self, matrices, check_hermitian):
      """Test differentiability for pauli_decompose"""
  
      import jax
      import torch
      import tensorflow as tf
  
      dev = qml.device("default.qubit", wires=2)
  
      @qml.qnode(dev)
      def circuit(A):
          coeffs, _ = qml.pauli_decompose(
              A, check_hermitian=check_hermitian
          ).terms()
          qml.RX(qml.math.real(coeffs[1]), 0)
          return qml.expval(qml.PauliZ(0))
  
      for matrix in matrices:
          # NumPy Interface
          grad_numpy = qml.grad(circuit)(qml.numpy.array(matrix))
  
          # Jax Interface
          grad_jax = jax.grad(circuit, argnums=(0))(
              jax.numpy.array(matrix)
          )
  
          # PyTorch Interface
          A = torch.tensor(matrix, requires_grad=True)
          result = circuit(A)
          result.backward()
          grad_torch = A.grad
  
          # Tensorflow Interface
          A = tf.Variable(qml.numpy.array(matrix))
          with tf.GradientTape() as tape:
              loss = circuit(A)
          grad_tflow = tape.gradient(loss, A)
  
          # Comparisons - note: https://github.com/google/jax/issues/9110
          assert qml.math.allclose(grad_numpy, grad_jax)
          assert qml.math.allclose(grad_torch, grad_tflow)
          assert qml.math.allclose(
              grad_numpy, qml.math.conjugate(grad_torch)
          )
  
imports: import pytest
  import numpy
  import pennylane
  from pennylane.operation import Tensor
  from pennylane.ops import Identity, PauliX, PauliY, PauliZ
  from pennylane.pauli import pauli_sentence, PauliWord, PauliSentence
  from pennylane.pauli.conversion import _generalized_pauli_decompose
label_desc: Use image node_id 14 for calling the TestPhasedDecomposition obj's underlying member method code with example usage: obj.test_differentiability(matrices, check_hermitian) and returns: qml