code: def _compute_num_cnots(U):
      r"""Compute the number of CNOTs required to implement a U in SU(4). This is based on
      the trace of
  
      .. math::
  
          \gamma(U) = (E^\dag U E) (E^\dag U E)^T,
  
      and follows the arguments of this paper: https://arxiv.org/abs/quant-ph/0308045.
      """
      u = math.dot(Edag, math.dot(U, E))
      gammaU = math.dot(u, math.T(u))
      trace = math.trace(gammaU)
  
      # Case: 0 CNOTs (tensor product), the trace is +/- 4
      # We need a tolerance of around 1e-7 here in order to work with the case where U
      # is specified with 8 decimal places.
      if math.allclose(trace, 4, atol=1e-7) or math.allclose(
          trace, -4, atol=1e-7
      ):
          return 0
  
      # To distinguish between 1/2 CNOT cases, we need to look at the eigenvalues
      evs = math.linalg.eigvals(gammaU)
  
      sorted_evs = math.sort(math.imag(evs))
  
      # Case: 1 CNOT, the trace is 0, and the eigenvalues of gammaU are [-1j, -1j, 1j, 1j]
      # Checking the eigenvalues is needed because of some special 2-CNOT cases that yield
      # a trace 0.
      if math.allclose(trace, 0j, atol=1e-7) and math.allclose(
          sorted_evs, [-1, -1, 1, 1]
      ):
          return 1
  
      # Case: 2 CNOTs, the trace has only a real part (or is 0)
      if math.allclose(math.imag(trace), 0.0, atol=1e-7):
          return 2
  
      # For the case with 3 CNOTs, the trace is a non-zero complex number
      # with both real and imaginary parts.
      return 3
  
file_path: pennylane/pennylane/ops/op_math/decompositions/two_qubit_unitary.py
imports: import numpy
  import pennylane
  from pennylane import math
  from .single_qubit_unitary import one_qubit_decomposition
label_desc: Use image node_id 2 for calling a global function with example usage: _compute_num_cnots(U) and returns: int, int, int, int