code: def _batched_partial_trace_nonrep_indices(density_matrix, indices):
      """Compute the reduced density matrix for autograd interface by tracing out the provided indices with the use
      of projectors as same subscripts indices are not supported in autograd backprop.
      """
      # Dimension and reshape
      batch_dim, dim = density_matrix.shape[:2]
      num_indices = int(np.log2(dim))
      rho_dim = 2 * num_indices
      density_matrix = np.reshape(
          density_matrix, [batch_dim] + [2] * 2 * num_indices
      )
  
      kraus = cast(np.eye(2), density_matrix.dtype)
  
      kraus = np.reshape(kraus, (2, 1, 2))
      kraus_dagger = np.asarray(
          [np.conj(np.transpose(k)) for k in kraus]
      )
  
      kraus = convert_like(kraus, density_matrix)
      kraus_dagger = convert_like(kraus_dagger, density_matrix)
      # For loop over wires
      for target_wire in indices:
          # Tensor indices of density matrix
          state_indices = ABC[1 : rho_dim + 1]
          # row indices of the quantum state affected by this operation
          row_wires_list = [target_wire + 1]
          row_indices = "".join(ABC_ARRAY[row_wires_list].tolist())
          # column indices are shifted by the number of wires
          col_wires_list = [w + num_indices for w in row_wires_list]
          col_indices = "".join(ABC_ARRAY[col_wires_list].tolist())
          # indices in einsum must be replaced with new ones
          num_partial_trace_wires = 1
          new_row_indices = ABC[
              rho_dim + 1 : rho_dim + num_partial_trace_wires + 1
          ]
          new_col_indices = ABC[
              rho_dim
              + num_partial_trace_wires
              + 1 : rho_dim
              + 2 * num_partial_trace_wires
              + 1
          ]
          # index for summation over Kraus operators
          kraus_index = ABC[
              rho_dim
              + 2 * num_partial_trace_wires
              + 1 : rho_dim
              + 2 * num_partial_trace_wires
              + 2
          ]
          # new state indices replace row and column indices with new ones
          new_state_indices = functools.reduce(
              lambda old_string, idx_pair: old_string.replace(
                  idx_pair[0], idx_pair[1]
              ),
              zip(
                  col_indices + row_indices,
                  new_col_indices + new_row_indices,
              ),
              state_indices,
          )
          # index mapping for einsum, e.g., 'iga,abcdef,idh->gbchef'
          einsum_indices = (
              f"{kraus_index}{new_row_indices}{row_indices}, a{state_indices},"
              f"{kraus_index}{col_indices}{new_col_indices}->a{new_state_indices}"
          )
          density_matrix = einsum(
              einsum_indices, kraus, density_matrix, kraus_dagger
          )
  
      number_wires_sub = num_indices - len(indices)
      reduced_density_matrix = np.reshape(
          density_matrix,
          (batch_dim, 2**number_wires_sub, 2**number_wires_sub),
      )
      return reduced_density_matrix
  
imports: import itertools
  import functools
  from string import ascii_letters
  from autoray import numpy
  from numpy import float64
  import pennylane
  from .None import single_dispatch
  from .multi_dispatch import diag, dot, scatter_element_add, einsum, get_interface
  from .utils import is_abstract, allclose, cast, convert_like, cast_like
  from .matrix_manipulation import _permute_dense_matrix
label_desc: Use image node_id 5 for calling a global function with example usage: _batched_partial_trace_nonrep_indices(density_matrix, indices) and returns: reduced_density_matrix