@@ -179,7 +179,21 @@ def Get_Rsl_matrix(Xsk_op_list, N_Qubits):
179179 return Rs_l_matrix
180180
181181
182- def SeqRot_linalg_Energy (anti_commuting_sets , S_key_dict , N_Qubits , atol = 1e-8 , rtol = 1e-05 , check_reduction = False ):
182+ def SeqRot_linalg_Energy_matrix (anti_commuting_sets , S_key_dict , N_Qubits , atol = 1e-8 , rtol = 1e-05 , check_reduction = False ):
183+ """
184+ Function giving ground state energy of Hamiltonian given as a dictionary of anti-commuting sets.
185+ Note this function builds up full matrix iteratively. See SeqRot_linalg_Energy for symbolic method.
186+
187+
188+ Args:
189+ anti_commuting_sets (dict): dictionary of int keys with list of anti commuting QubitOperators sets
190+ S_key_dict(dict): dictionary keys match that of anti_commuting_sets. Value gives index of P_s operator
191+ N_Qubits(int): number of qubits
192+
193+ returns:
194+ FCI_Energy(float): Ground state energy
195+
196+ """
183197 # TODO: could return reduced_H_matrix sparse matrix!
184198
185199 reduced_H_matrix = csc_matrix ((2 ** N_Qubits , 2 ** N_Qubits ), dtype = complex )
@@ -211,4 +225,85 @@ def SeqRot_linalg_Energy(anti_commuting_sets, S_key_dict, N_Qubits, atol=1e-8, r
211225 else :
212226 eig_values , eig_vectors = eigsh (reduced_H_matrix , k = 1 , which = 'SA' ) # < solves eigenvalue problem for a complex Hermitian matrix.
213227 FCI_Energy = min (eig_values )
228+ return FCI_Energy
229+
230+
231+
232+ def Get_Rsl_matrix_as_qubitops (Xsk_op_list ):
233+
234+ """
235+ Function that gives matrix of Rsl from a list of X_sk operators, theta_sks. This is the output from Get_Xsk_op_list function.
236+ X_sk operators from a given anti_commuting set and S_index
237+
238+ Args:
239+ X_sk_theta_sk_list(list): list of tuples containing X_sk QubitOperator and Theta_sk value
240+
241+ returns:
242+ R_S_q_ops (QubitOperator)
243+
244+ """
245+
246+ ### old SLOW method (exponentiated matrices)
247+ # R_sk_list = []
248+ # for X_sk_Op, theta_sk in Xsk_op_list:
249+ # pauliword_X_sk_MATRIX = qubit_operator_sparse(QubitOperator(list(X_sk_Op.terms.keys())[0], -1j),
250+ # n_qubits=N_Qubits)
251+ # const_X_sk = list(X_sk_Op.terms.values())[0]
252+
253+ # R_sk_list.append(expm(pauliword_X_sk_MATRIX * theta_sk / 2 * const_X_sk))
254+ # Rs_l_matrix = reduce(np.dot, R_sk_list[::-1]) # <- note reverse order!
255+
256+ ### new FAST method (symbolic application of rotation operators!)
257+ R_sk_list = []
258+ for X_sk_Op , theta_sk in Xsk_op_list :
259+ op = np .cos (theta_sk / 2 ) * QubitOperator ('' ) - 1j * np .sin (theta_sk / 2 ) * X_sk_Op
260+ R_sk_list .append (op )
261+
262+ R_S_q_ops = reduce (lambda x ,y : x * y , R_sk_list [::- 1 ]) # <- note reverse order!
263+ return R_S_q_ops
264+
265+
266+ from openfermion .utils import hermitian_conjugated
267+ def SeqRot_linalg_Energy (anti_commuting_sets , S_key_dict , N_Qubits , atol = 1e-8 , rtol = 1e-05 , check_reduction = False ):
268+ """
269+ Function giving ground state energy of Hamiltonian given as a dictionary of anti-commuting sets. Note this uses symbolic operators and only builds sparse matrix once.
270+
271+
272+ Args:
273+ anti_commuting_sets (dict): dictionary of int keys with list of anti commuting QubitOperators sets
274+ S_key_dict(dict): dictionary keys match that of anti_commuting_sets. Value gives index of P_s operator
275+ N_Qubits(int): number of qubits
276+
277+ returns:
278+ FCI_Energy(float): Ground state energy
279+
280+ """
281+ # TODO: could return reduced_H_matrix sparse matrix!
282+
283+
284+ H_single_terms = QubitOperator ()
285+ gammal_Rdag_P_R_terms = QubitOperator ()
286+ for key in anti_commuting_sets :
287+ AC_set = anti_commuting_sets [key ]
288+
289+ if len (AC_set ) < 2 :
290+ H_single_terms += AC_set [0 ]
291+ else :
292+ S_index = S_key_dict [key ]
293+
294+ X_sk_theta_sk_list , full_normalised_set , Ps , gamma_l = Get_Xsk_op_list (AC_set , S_index , N_Qubits , check_reduction = check_reduction , atol = atol , rtol = rtol )
295+
296+
297+ R_S = Get_Rsl_matrix_as_qubitops (X_sk_theta_sk_list )
298+ R_dag_P_R = hermitian_conjugated (R_S ) * Ps * R_S
299+ gammal_Rdag_P_R_terms += gamma_l * R_dag_P_R
300+
301+ all_symbolic_ops = H_single_terms + gammal_Rdag_P_R_terms
302+ reduced_H_matrix = qubit_operator_sparse (all_symbolic_ops , n_qubits = N_Qubits )
303+ # eig_values, eig_vectors = sparse_eigs(reduced_H_matrix)
304+ if reduced_H_matrix .shape [0 ]<= 64 :
305+ eig_values , eig_vectors = eigh (reduced_H_matrix .todense ()) # NOT sparse!
306+ else :
307+ eig_values , eig_vectors = eigsh (reduced_H_matrix , k = 1 , which = 'SA' ) # < solves eigenvalue problem for a complex Hermitian matrix.
308+ FCI_Energy = min (eig_values )
214309 return FCI_Energy
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