code: def _rccsd_state(ccsd_solver, tol=1e-15):
      r"""Construct a wavefunction from PySCF's ``RCCSD`` Solver object.
  
      The generated wavefunction is a dictionary where the keys represent a configuration, which
      corresponds to a Slater determinant, and the values are the CI coefficients of the Slater
      determinant. Each dictionary key is a tuple of two integers. The binary representation of these
      integers correspond to a specific configuration: the first number represents the
      configuration of the alpha electrons and the second number represents the configuration of the
      beta electrons. For instance, the Hartree-Fock state :math:`|1 1 0 0 \rangle` will be
      represented by the flipped binary string ``0011` which is split to ``01`` and ``01`` for
      the alpha and beta electrons. The integer corresponding to ``01`` is ``1`` and the dictionary
      representation of the Hartree-Fock state will be ``{(1, 1): 1.0}``. The dictionary
      representation of a state with ``0.99`` contribution from the Hartree-Fock state and ``0.01``
      contribution from the doubly-excited state, i.e., :math:`|0 0 1 1 \rangle`, will be
      ``{(1, 1): 0.99, (2, 2): 0.01}``.
  
      In the current version, the exponential ansatz :math:`\exp(\hat{T}_1 + \hat{T}_2) \ket{\text{HF}}`
      is expanded to second order, with only single and double excitation terms collected and kept.
      In the future this will be amended to also collect terms from higher order. The expansion gives
  
      .. math::
          \exp(\hat{T}_1 + \hat{T}_2) \ket{\text{HF}} = \left[ 1 + \hat{T}_1 +
          \left( \hat{T}_2 + 0.5 * \hat{T}_1^2 \right) \right] \ket{\text{HF}}
  
      The coefficients in this expansion are the CI coefficients used to build the wavefunction
      representation.
  
      Args:
          ccsd_solver (PySCF RCCSD Class instance): the class object representing the RCCSD calculation in PySCF
          tol (float): the tolerance for discarding Slater determinants with small coefficients
  
      Returns:
          dict: dictionary of the form ``{(int_a, int_b) :coeff}``, with integers ``int_a, int_b``
          having binary represention corresponding to the Fock occupation vector in alpha and beta
          spin sectors, respectively, and coeff being the CI coefficients of those configurations
  
      **Example**
  
      >>> from pyscf import gto, scf, cc
      >>> mol = gto.M(atom=[['Li', (0, 0, 0)], ['Li', (0,0,0.71)]], basis='sto6g', symmetry="d2h")
      >>> myhf = scf.RHF(mol).run()
      >>> mycc = cc.CCSD(myhf).run()
      >>> wf_ccsd = _rccsd_state(mycc, tol=1e-1)
      >>> print(wf_ccsd)
      {(7, 7): 0.8886969878256522, (11, 11): -0.30584590248164206,
      (19, 19): -0.30584590248164145, (35, 35): -0.14507552651170982}
      """
  
      mol = ccsd_solver.mol
  
      norb = mol.nao
      nelec = mol.nelectron
      nelec_a = int((nelec + mol.spin) / 2)
      nelec_b = int((nelec - mol.spin) / 2)
  
      nvir_a, nvir_b = norb - nelec_a, norb - nelec_b
  
      # build the full, unrestricted representation of the coupled cluster amplitudes
      t1a = ccsd_solver.t1
      t1b = t1a
      t2aa = ccsd_solver.t2 - ccsd_solver.t2.transpose(1, 0, 2, 3)
      t2ab = ccsd_solver.t2.transpose(0, 2, 1, 3)
      t2bb = t2aa
  
      # add in the disconnected part ( + 0.5 T_1^2) of double excitations
      t2aa = t2aa - 0.5 * np.kron(t1a, t1a).reshape(
          nelec_a, nvir_a, nelec_a, nvir_a
      ).transpose(0, 2, 1, 3)
      t2bb = t2bb - 0.5 * np.kron(t1b, t1b).reshape(
          nelec_b, nvir_b, nelec_b, nvir_b
      ).transpose(0, 2, 1, 3)
      # align the entries with how the excitations are ordered when generated by _excited_configurations()
      t2ab = t2ab - 0.5 * np.kron(t1a, t1b).reshape(
          nelec_a, nvir_a, nelec_b, nvir_b
      )
  
      # numbers representing the Hartree-Fock vector, e.g., bin(ref_a)[::-1] = 1111...10...0
      ref_a = int(2**nelec_a - 1)
      ref_b = int(2**nelec_b - 1)
  
      dict_fcimatr = dict(zip(list(zip([ref_a], [ref_b])), [1.0]))
  
      # alpha -> alpha excitations
      t1a_configs, t1a_signs = _excited_configurations(nelec_a, norb, 1)
      dict_fcimatr.update(
          dict(
              zip(
                  list(zip(t1a_configs, [ref_b] * len(t1a_configs))),
                  t1a.ravel() * t1a_signs,
              )
          )
      )
  
      # beta -> beta excitations
      t1b_configs, t1b_signs = _excited_configurations(nelec_b, norb, 1)
      dict_fcimatr.update(
          dict(
              zip(
                  list(zip([ref_a] * len(t1b_configs), t1b_configs)),
                  t1b.ravel() * t1b_signs,
              )
          )
      )
  
      # alpha, alpha -> alpha, alpha excitations
      if nelec_a > 1 and nvir_a > 1:
          t2aa_configs, t2aa_signs = _excited_configurations(
              nelec_a, norb, 2
          )
          # select only unique excitations, via lower triangle of matrix
          ooidx = np.tril_indices(nelec_a, -1)
          vvidx = np.tril_indices(nvir_a, -1)
          t2aa = t2aa[ooidx][:, vvidx[0], vvidx[1]]
          dict_fcimatr.update(
              dict(
                  zip(
                      list(
                          zip(t2aa_configs, [ref_b] * len(t2aa_configs))
                      ),
                      t2aa.ravel() * t2aa_signs,
                  )
              )
          )
  
      if nelec_b > 1 and nvir_b > 1:
          t2bb_configs, t2bb_signs = _excited_configurations(
              nelec_b, norb, 2
          )
          # select only unique excitations, via lower triangle of matrix
          ooidx = np.tril_indices(nelec_b, -1)
          vvidx = np.tril_indices(nvir_b, -1)
          t2bb = t2bb[ooidx][:, vvidx[0], vvidx[1]]
          dict_fcimatr.update(
              dict(
                  zip(
                      list(
                          zip([ref_a] * len(t2bb_configs), t2bb_configs)
                      ),
                      t2bb.ravel() * t2bb_signs,
                  )
              )
          )
  
      # alpha, beta -> alpha, beta excitations
      rowvals, colvals = np.array(
          list(product(t1a_configs, t1b_configs)), dtype=int
      ).T
      dict_fcimatr.update(
          dict(
              zip(
                  list(zip(rowvals, colvals)),
                  t2ab.ravel() * np.kron(t1a_signs, t1b_signs),
              )
          )
      )
  
      # renormalize, to get the HF coefficient (CC wavefunction not normalized)
      norm = np.sqrt(np.sum(np.array(list(dict_fcimatr.values())) ** 2))
      dict_fcimatr = {
          key: value / norm for (key, value) in dict_fcimatr.items()
      }
  
      # filter based on tolerance cutoff
      dict_fcimatr = {
          key: value
          for key, value in dict_fcimatr.items()
          if abs(value) > tol
      }
  
      return dict_fcimatr
  
imports: import warnings
  from itertools import product
  import numpy
  import pennylane
  from pennylane.operation import Tensor, active_new_opmath
  from pennylane.pauli import pauli_sentence
  from pennylane.wires import Wires
label_desc: Use image node_id 13 for calling a global function with example usage: _rccsd_state(ccsd_solver, tol) and returns: dict_fcimatr