def Fredkin(i, j, k):
"""
builds a circuit to simulate a three-qubit Fredkin gate
(Controled-SWAP, CSWAP gate).
:param i: control qubit 1
:param j: swap qubit 1
:param k: swap qubit 2
"""
C12 = qforte.gate('cX', j, i)
C32 = qforte.gate('cX', j, k)
CV23 = qforte.gate('cV', k, j)
CV13 = qforte.gate('cV', k, i)
F_circ = qforte.Circuit()
F_circ.add(C32)
F_circ.add(CV23)
F_circ.add(CV13)
F_circ.add(C12)
F_circ.add(CV23.adjoint())
F_circ.add(C32)
F_circ.add(C12)
return F_circ
def build_classical_CI_mats(self):
"""Builds a classical configuration interaction out of single determinants.
"""
num_tot_basis = len(self._pre_sa_ref_lst)
h_CI = np.zeros((num_tot_basis,num_tot_basis), dtype=complex)
omega_lst = []
Homega_lst = []
for i, ref in enumerate(self._pre_sa_ref_lst):
# NOTE: do NOT use Uprep here (is determinant specific).
Un = qforte.Circuit()
for j in range(self._nqb):
if ref[j] == 1:
Un.add(qforte.gate('X', j, j))
QC = qforte.Computer(self._nqb)
QC.apply_circuit(Un)
omega_lst.append(np.asarray(QC.get_coeff_vec(), dtype=complex))
Homega = np.zeros((2**self._nqb), dtype=complex)
QC.apply_operator(self._qb_ham)
Homega_lst.append(np.asarray(QC.get_coeff_vec(), dtype=complex))
for j in range(len(omega_lst)):
h_CI[i][j] = np.vdot(omega_lst[i], Homega_lst[j])
h_CI[j][i] = np.conj(h_CI[i][j])
return h_CI
def build_Uprep(ref, state_prep_type):
Uprep = qforte.Circuit()
if state_prep_type == 'occupation_list':
for j in range(len(ref)):
if ref[j] == 1:
Uprep.add(qforte.gate('X', j, j))
else:
raise ValueError(
"Only 'occupation_list' supported as state preparation type")
return Uprep
def run(self,
beta=1.0,
db=0.2,
expansion_type='SD',
sparseSb=True,
b_thresh=1.0e-6,
x_thresh=1.0e-10,
do_lanczos=False,
lanczos_gap=2):
self._beta = beta
self._db = db
self._nbeta = int(beta/db)+1
self._expansion_type = expansion_type
self._sparseSb = sparseSb
self._total_phase = 1.0 + 0.0j
self._Uqite = qf.Circuit()
self._b_thresh = b_thresh
self._x_thresh = x_thresh
self._n_classical_params = 0
self._n_cnot = self._Uprep.get_num_cnots()
self._n_pauli_trm_measures = 0
self._do_lanczos = do_lanczos
self._lanczos_gap = lanczos_gap
qc_ref = qf.Computer(self._nqb)
qc_ref.apply_circuit(self._Uprep)
self._Ekb = [np.real(qc_ref.direct_op_exp_val(self._qb_ham))]
# Print options banner (should done for all algorithms).
self.print_options_banner()
# Build expansion pool.
self.build_expansion_pool()
# Do the imaginary time evolution.
self.evolve()
if (self._do_lanczos):
self.do_qlanczos()
# Print summary banner (should done for all algorithms).
self.print_summary_banner()
# verify that required attributes were defined
# (should done for all algorithms).
self.verify_run()
def trotterize(operator, factor=1.0, trotter_number=1, trotter_order=1):
"""
returns a circuit equivalent to an exponentiated QubitOperator
:param operator: (QubitOperator) the operator or state preparation ansatz
(represented as a sum of pauli terms) to be exponentiated
:param trotter_number: (int) for an operator A with terms A_i, the trotter_number
is the exponent (N) for to product of single term
exponentals e^A ~ ( Product_i(e^(A_i/N)) )^N
:param trotter_number: (int) the order of the trotterization approximation, can be 1 or 2
"""
total_phase = 1.0
trotterized_operator = qforte.Circuit()
if (trotter_number == 1) and (trotter_order == 1):
#loop over terms in operator
for term in operator.terms():
term_generator, phase = qforte.exponentiate_pauli_string(
factor * term[0], term[1])
for gate in term_generator.gates():
trotterized_operator.add(gate)
total_phase *= phase
else:
if (trotter_order > 1):
raise NotImplementedError(
"Higher order trotterization is not yet implemented.")
ho_op = qforte.QubitOperator()
for k in range(1, trotter_number + 1):
for term in operator.terms():
ho_op.add(factor * term[0] / float(trotter_number), term[1])
for trot_term in ho_op.terms():
term_generator, phase = qforte.exponentiate_pauli_string(
trot_term[0], trot_term[1])
for gate in term_generator.gates():
troterized_operator.add(gate)
total_phase *= phase
return (trotterized_operator, total_phase)
def build_circuit(Inputstr):
circ = qforte.Circuit()
sepstr = Inputstr.split() #Separate string to a list by space
for i in range(len(sepstr)):
inputgate = sepstr[i].split('_')
if len(inputgate) == 2:
circ.add(
qforte.gate(inputgate[0], int(inputgate[1]),
int(inputgate[1])))
else:
if 'R' in inputgate[0]:
circ.add(
qforte.gate(inputgate[0], int(inputgate[1]),
int(inputgate[1]), float(inputgate[2])))
else:
circ.add(
qforte.gate(inputgate[0], int(inputgate[1]),
int(inputgate[2])))
return circ
def build_expansion_pool(self):
print('\n==> Building expansion pool <==')
self._sig = qf.QubitOpPool()
if(self._expansion_type == 'complete_qubit'):
if (self._nqb > 6):
raise ValueError('Using complete qubits expansion will result in a very large number of terms!')
self._sig.fill_pool("complete_qubit", self._ref)
elif(self._expansion_type == 'cqoy'):
self._sig.fill_pool("cqoy", self._ref)
elif(self._expansion_type in {'SD', 'GSD', 'SDT', 'SDTQ', 'SDTQP', 'SDTQPH'}):
P = qf.SQOpPool()
P.set_orb_spaces(self._ref)
P.fill_pool(self._expansion_type)
sig_temp = P.get_qubit_operator("commuting_grp_lex", False)
# Filter the generated operators, so that only those with an odd number of Y gates are allowed.
# See section "Real Hamiltonians and states" in the SI of Motta for theoretical justification.
# Briefly, this method solves Ax=b, but all b elements with an odd number of Y gates are imaginary and
# thus vanish. This method will not be correct for non-real Hamiltonians or states.
for _, rho in sig_temp.terms():
nygates = 0
temp_rho = qf.Circuit()
for gate in rho.gates():
temp_rho.add(qf.gate(gate.gate_id(), gate.target(), gate.control()))
if (gate.gate_id() == "Y"):
nygates += 1
if (nygates % 2 == 1):
rho_op = qf.QubitOperator()
rho_op.add(1.0, temp_rho)
self._sig.add(1.0, rho_op)
else:
raise ValueError('Invalid expansion type specified.')
self._NI = len(self._sig.terms())
def get_dynamics_circ(self):
"""Generates controlled unitaries. Ancilla qubit n controls a Trotter
approximation to exp(-iHt*2^n).
Returns
-------
U : Circuit
A circuit approximating controlled application of e^-iHt.
"""
U = qforte.Circuit()
ancilla_idx = self._abegin
temp_op = qforte.QubitOperator()
scalar_terms = []
for scalar, operator in self._qb_ham.terms():
phase = -1.0j * scalar * self._t
if operator.size() == 0:
scalar_terms.append(scalar * self._t)
else:
# Strangely, the code seems to work even if this line is outside the else clause.
# TODO: Figure out how.
temp_op.add(phase, operator)
for n in range(self._n_ancilla):
tn = 2 ** n
expn_op, _ = trotterize_w_cRz(temp_op, ancilla_idx,
trotter_number=self._trotter_number)
# Rotation for the scalar Hamiltonian term
U.add(qforte.gate('R', ancilla_idx, ancilla_idx, -1.0 * np.sum(scalar_terms) * float(tn)))
for i in range(tn):
U.add_circuit(expn_op)
ancilla_idx += 1
return U
def get_qft_circuit(self, direct):
"""Generates a circuit for Quantum Fourier Transformation with no swapping
of bit positions.
Arguments
---------
self._abegin : int
The index of the begin qubit.
self._aend : int
The index of the end qubit.
direct : string
The direction of the Fourier Transform can be 'forward' or 'reverse.'
Returns
-------
qft_circ : Circuit
A circuit representing the Quantum Fourier Transform.
"""
qft_circ = qforte.Circuit()
lens = self._aend - self._abegin + 1
for j in range(lens):
qft_circ.add(qforte.gate('H', j+self._abegin))
for k in range(2, lens+1-j):
phase = 2.0*np.pi/(2**k)
qft_circ.add(qforte.gate('cR', j+self._abegin, j+k-1+self._abegin, phase))
if direct == 'forward':
return qft_circ
elif direct == 'reverse':
return qft_circ.adjoint()
else:
raise ValueError('QFT directions can only be "forward" or "reverse"')
def qft_circuit(na, nb, direct):
"""
generates a circuit for Quantum Fourier Transformation
:param na: (int) the begin qubit
:param nb: (int) the end qubit
:param direct: (string) the direction of the Fourier Transform
can be 'forward' or 'reverse'
"""
# Build qft circuit
qft_circ = qforte.Circuit()
lens = nb - na + 1
for j in range(lens):
qft_circ.add(qforte.gate('H', j + na, j + na))
for k in range(2, lens + 1 - j):
phase = 2.0 * numpy.pi / (2**k)
qft_circ.add(qforte.gate('cR', j + na, j + k - 1 + na, phase))
# Build reversing circuit
if lens % 2 == 0:
for i in range(int(lens / 2)):
qft_circ.add(qforte.gate('SWAP', i + na, lens - 1 - i + na))
else:
for i in range(int((lens - 1) / 2)):
qft_circ.add(qforte.gate('SWAP', i + na, lens - 1 - i + na))
if direct == 'forward':
return qft_circ
elif direct == 'reverse':
return qft_circ.adjoint()
else:
raise ValueError('QFT directions can only be "forward" or "reverse"')
return qft_circ
def Toffoli(i, j, k):
"""
builds a circuit to simulate a three-qubit Toffoli gate
(Control-Control-NOT, CCNOT gate).
:param i: control qubit 1
:param j: control qubit 2
:param k: target qubit
"""
T1 = qforte.gate('T', i, i)
T2 = qforte.gate('T', j, j)
T3 = qforte.gate('T', k, k)
C12 = qforte.gate('cX', j, i)
C13 = qforte.gate('cX', k, i)
C23 = qforte.gate('cX', k, j)
H3 = qforte.gate('H', k, k)
T_circ = qforte.Circuit()
T_circ.add(H3)
T_circ.add(C23)
T_circ.add(T3.adjoint())
T_circ.add(C13)
T_circ.add(T3)
T_circ.add(C23)
T_circ.add(T3.adjoint())
T_circ.add(C13)
T_circ.add(T2)
T_circ.add(T3)
T_circ.add(C12)
T_circ.add(H3)
T_circ.add(T1)
T_circ.add(T2.adjoint())
T_circ.add(C12)
return T_circ
def get_z_circuit(self):
"""Generates a circuit of Z gates for each quibit in the ancilla register.
Arguments
---------
self._abegin : int
The index of the begin qubit.
self._aend : int
The index of the end qubit.
Returns
-------
z_circ : Circuit
A circuit representing the the Z gates to be measured.
"""
Z_circ = qforte.Circuit()
for j in range(self._abegin, self._aend + 1):
Z_circ.add(qforte.gate('Z', j))
return Z_circ
def get_Uhad(self):
"""Generates a circuit which to puts all of the ancilla regester in
superpostion.
Arguments
---------
self._abegin : int
The index of the begin qubit.
self._aend : int
The index of the end qubit.
Returns
-------
qft_circ : Circuit
A circuit of consecutive Hadamard gates.
"""
Uhad = qforte.Circuit()
for j in range(self._abegin, self._aend + 1):
Uhad.add(qforte.gate('H', j))
return Uhad
def organizer_to_circuit(op_organizer):
"""Builds a Circuit from a operator orgainizer.
Parameters
----------
op_organizer : list
An object to organize what the coefficient and Pauli operators in terms
of the QubitOperator will be.
The orginzer is of the form
[[coeff_a, [ ("X", i), ("Z", j), ("Y", k), ... ] ], [...] ...]
where X, Y, Z are strings that indicate Pauli opterators;
i, j, k index qubits and coeff_a indicates the coefficient for the ath
term in the QubitOperator.
"""
operator = qforte.QubitOperator()
for coeff, word in op_organizer:
circ = qforte.Circuit()
for letter in word:
circ.add(qforte.gate(letter[0], letter[1], letter[1]))
operator.add(coeff, circ)
return operator
def build_sa_qk_mats(self):
"""Returns the QK effective hamiltonain and overlap matrices in a basis
of spin adapted references.
"""
num_tot_basis = len(self._sa_ref_lst) * self._nstates_per_ref
h_mat = np.zeros((num_tot_basis,num_tot_basis), dtype=complex)
s_mat = np.zeros((num_tot_basis,num_tot_basis), dtype=complex)
omega_lst = []
Homega_lst = []
for i, ref in enumerate(self._sa_ref_lst):
for m in range(self._nstates_per_ref):
Um = qforte.Circuit()
phase1 = 1.0
if(m>0):
fact = (0.0-1.0j) * m * self._mr_dt
expn_op1, phase1 = trotterize(self._qb_ham, factor=fact, trotter_number=self._trotter_number)
Um.add(expn_op1)
QC = qforte.Computer(self._nqb)
state_prep_lst = []
for term in ref:
coeff = term[0]
det = term[1]
idx = ref_to_basis_idx(det)
state = qforte.QubitBasis(idx)
state_prep_lst.append( (state, coeff) )
QC.set_state(state_prep_lst)
QC.apply_circuit(Um)
QC.apply_constant(phase1)
omega_lst.append(np.asarray(QC.get_coeff_vec(), dtype=complex))
QC.apply_operator(self._qb_ham)
Homega_lst.append(np.asarray(QC.get_coeff_vec(), dtype=complex))
if(self._diagonalize_each_step):
print('\n\n')
print(f"{'k(S)':>7}{'E(Npar)':>19}{'N(params)':>14}{'N(CNOT)':>18}{'N(measure)':>20}")
print('-------------------------------------------------------------------------------')
# TODO (opt): add this to previous loop
for p in range(num_tot_basis):
for q in range(p, num_tot_basis):
h_mat[p][q] = np.vdot(omega_lst[p], Homega_lst[q])
h_mat[q][p] = np.conj(h_mat[p][q])
s_mat[p][q] = np.vdot(omega_lst[p], omega_lst[q])
s_mat[q][p] = np.conj(s_mat[p][q])
if (self._diagonalize_each_step):
# TODO (cleanup): have this print to a separate file
evals, evecs = canonical_geig_solve(s_mat[0:p+1, 0:p+1],
h_mat[0:p+1, 0:p+1],
print_mats=False,
sort_ret_vals=True)
scond = np.linalg.cond(s_mat[0:p+1, 0:p+1])
cs_str = '{:.2e}'.format(scond)
k = p+1
self._n_classical_params = k
if(k==1):
self._n_cnot = self._srqk._n_cnot
else:
self._n_cnot = 2 * Um.get_num_cnots()
self._n_pauli_trm_measures = k * self._Nl + self._srqk._n_pauli_trm_measures
self._n_pauli_trm_measures += k * (k-1) * self._Nl
self._n_pauli_trm_measures += k * (k-1)
print(f' {scond:7.2e} {np.real(evals[self._target_root]):+15.9f} {self._n_classical_params:8} {self._n_cnot:10} {self._n_pauli_trm_measures:12}')
return s_mat, h_mat
def build_qk_mats(self):
"""Returns matrices S and H needed for the QK algorithm using the Trotterized
form of the unitary operators U_n = exp(-i n dt H)
The mathematical operations of this function are unphysical for a quantum
computer, but efficient for a simulator.
Returns
-------
s_mat : ndarray
A numpy array containing the elements S_mn = <Phi | Um^dag Un | Phi>.
_nstates by _nstates
h_mat : ndarray
A numpy array containing the elements H_mn = <Phi | Um^dag H Un | Phi>
_nstates by _nstates
"""
h_mat = np.zeros((self._nstates, self._nstates), dtype=complex)
s_mat = np.zeros((self._nstates, self._nstates), dtype=complex)
# Store these vectors for the aid of MRSQK
self._omega_lst = []
Homega_lst = []
if (self._diagonalize_each_step):
print('\n\n')
print(
f"{'k(S)':>7}{'E(Npar)':>19}{'N(params)':>14}{'N(CNOT)':>18}{'N(measure)':>20}"
)
print(
'-------------------------------------------------------------------------------'
)
if (self._print_summary_file):
f = open("summary.dat", "w+", buffering=1)
f.write(
f"#{'k(S)':>7}{'E(Npar)':>19}{'N(params)':>14}{'N(CNOT)':>18}{'N(measure)':>20}\n"
)
f.write(
'#-------------------------------------------------------------------------------\n'
)
for m in range(self._nstates):
# Compute U_m = exp(-i m dt H)
Um = qforte.Circuit()
Um.add(self._Uprep)
phase1 = 1.0
if (m > 0):
fact = (0.0 - 1.0j) * m * self._dt
expn_op1, phase1 = trotterize(
self._qb_ham,
factor=fact,
trotter_number=self._trotter_number)
Um.add(expn_op1)
# Compute U_m |φ>
QC = qforte.Computer(self._nqb)
QC.apply_circuit(Um)
QC.apply_constant(phase1)
self._omega_lst.append(
np.asarray(QC.get_coeff_vec(), dtype=complex))
# Compute H U_m |φ>
QC.apply_operator(self._qb_ham)
Homega_lst.append(np.asarray(QC.get_coeff_vec(), dtype=complex))
# Compute S_mn = <φ| U_m^\dagger U_n |φ> and H_mn = <φ| U_m^\dagger H U_n |φ>
for n in range(len(self._omega_lst)):
h_mat[m][n] = np.vdot(self._omega_lst[m], Homega_lst[n])
h_mat[n][m] = np.conj(h_mat[m][n])
s_mat[m][n] = np.vdot(self._omega_lst[m], self._omega_lst[n])
s_mat[n][m] = np.conj(s_mat[m][n])
if (self._diagonalize_each_step):
# TODO (cleanup): have this print to a separate file
k = m + 1
evals, evecs = canonical_geig_solve(s_mat[0:k, 0:k],
h_mat[0:k, 0:k],
print_mats=False,
sort_ret_vals=True)
scond = np.linalg.cond(s_mat[0:k, 0:k])
self._n_classical_params = k
self._n_cnot = 2 * Um.get_num_cnots()
self._n_pauli_trm_measures = k * self._Nl
self._n_pauli_trm_measures += k * (k - 1) * self._Nl
self._n_pauli_trm_measures += k * (k - 1)
print(
f' {scond:7.2e} {np.real(evals[self._target_root]):+15.9f} {self._n_classical_params:8} {self._n_cnot:10} {self._n_pauli_trm_measures:12}'
)
if (self._print_summary_file):
f.write(
f' {scond:7.2e} {np.real(evals[self._target_root]):+15.9f} {self._n_classical_params:8} {self._n_cnot:10} {self._n_pauli_trm_measures:12}\n'
)
if (self._diagonalize_each_step and self._print_summary_file):
f.close()
self._n_classical_params = self._nstates
self._n_cnot = 2 * Um.get_num_cnots()
# diagonal terms of Hbar
self._n_pauli_trm_measures = self._nstates * self._Nl
# off-diagonal of Hbar (<X> and <Y> of Hadamard test)
self._n_pauli_trm_measures += self._nstates * (self._nstates -
1) * self._Nl
# off-diagonal of S (<X> and <Y> of Hadamard test)
self._n_pauli_trm_measures += self._nstates * (self._nstates - 1)
return s_mat, h_mat
def build_qk_mats(self):
num_tot_basis = len(self._single_det_refs) * self._nstates_per_ref
h_mat = np.zeros((num_tot_basis,num_tot_basis), dtype=complex)
s_mat = np.zeros((num_tot_basis,num_tot_basis), dtype=complex)
# TODO (opt): make numpy arrays.
omega_lst = []
Homega_lst = []
for i, ref in enumerate(self._single_det_refs):
for m in range(self._nstates_per_ref):
# NOTE: do NOT use Uprep here (is determinant specific).
Um = qforte.Circuit()
for j in range(self._nqb):
if ref[j] == 1:
Um.add(qforte.gate('X', j, j))
phase1 = 1.0
if(m>0):
fact = (0.0-1.0j) * m * self._mr_dt
expn_op1, phase1 = trotterize(self._qb_ham, factor=fact, trotter_number=self._trotter_number)
Um.add(expn_op1)
QC = qforte.Computer(self._nqb)
QC.apply_circuit(Um)
QC.apply_constant(phase1)
omega_lst.append(np.asarray(QC.get_coeff_vec(), dtype=complex))
QC.apply_operator(self._qb_ham)
Homega_lst.append(np.asarray(QC.get_coeff_vec(), dtype=complex))
if(self._diagonalize_each_step):
print('\n\n')
print(f"{'k(S)':>7}{'E(Npar)':>19}{'N(params)':>14}{'N(CNOT)':>18}{'N(measure)':>20}")
print('-------------------------------------------------------------------------------')
for p in range(num_tot_basis):
for q in range(p, num_tot_basis):
h_mat[p][q] = np.vdot(omega_lst[p], Homega_lst[q])
h_mat[q][p] = np.conj(h_mat[p][q])
s_mat[p][q] = np.vdot(omega_lst[p], omega_lst[q])
s_mat[q][p] = np.conj(s_mat[p][q])
if (self._diagonalize_each_step):
# TODO (cleanup): have this print to a separate file
evals, evecs = canonical_geig_solve(s_mat[0:p+1, 0:p+1],
h_mat[0:p+1, 0:p+1],
print_mats=False,
sort_ret_vals=True)
scond = np.linalg.cond(s_mat[0:p+1, 0:p+1])
cs_str = '{:.2e}'.format(scond)
k = p+1
self._n_classical_params = k
if(k==1):
self._n_cnot = self._srqk._n_cnot
else:
self._n_cnot = 2 * Um.get_num_cnots()
self._n_pauli_trm_measures = k * self._Nl + self._srqk._n_pauli_trm_measures
self._n_pauli_trm_measures += k * (k-1) * self._Nl
self._n_pauli_trm_measures += k * (k-1)
print(f' {scond:7.2e} {np.real(evals[self._target_root]):+15.9f} {self._n_classical_params:8} {self._n_cnot:10} {self._n_pauli_trm_measures:12}')
return s_mat, h_mat
def matrix_element(self, m, n, use_op=False):
"""Returns a single matrix element M_mn based on the evolution of
two unitary operators Um = exp(-i * m * dt * H) and Un = exp(-i * n * dt * H)
on a reference state |Phi_o>, (optionally) with respect to an operator A.
Specifically, M_mn is given by <Phi_o| Um^dag Un | Phi_o> or
(optionally if A is specified) <Phi_o| Um^dag A Un | Phi_o>.
Arguments
---------
m : int
The number of time steps for the Um evolution.
n : int
The number of time steps for the Un evolution.
Returns
-------
value : complex
The outcome of measuring <X> and <Y> to determine <2*sigma_+>,
ultimately the value of the matrix elemet.
"""
value = 0.0
ancilla_idx = self._nqb
Uk = qforte.Circuit()
temp_op1 = qforte.QubitOperator()
# TODO (opt): move to C side.
for t in self._qb_ham.terms():
c, op = t
phase = -1.0j * n * self._dt * c
temp_op1.add(phase, op)
expn_op1, phase1 = trotterize_w_cRz(
temp_op1, ancilla_idx, trotter_number=self._trotter_number)
for gate in expn_op1.gates():
Uk.add(gate)
Ub = qforte.Circuit()
temp_op2 = qforte.QubitOperator()
for t in self._qb_ham.terms():
c, op = t
phase = -1.0j * m * self._dt * c
temp_op2.add(phase, op)
expn_op2, phase2 = trotterize_w_cRz(
temp_op2,
ancilla_idx,
trotter_number=self._trotter_number,
Use_open_cRz=False)
for gate in expn_op2.gates():
Ub.add(gate)
if not use_op:
# TODO (opt): use Uprep
cir = qforte.Circuit()
for j in range(self._nqb):
if self._ref[j] == 1:
cir.add(qforte.gate('X', j, j))
cir.add(qforte.gate('H', ancilla_idx, ancilla_idx))
cir.add(Uk)
cir.add(qforte.gate('X', ancilla_idx, ancilla_idx))
cir.add(Ub)
cir.add(qforte.gate('X', ancilla_idx, ancilla_idx))
X_op = qforte.QubitOperator()
x_circ = qforte.Circuit()
Y_op = qforte.QubitOperator()
y_circ = qforte.Circuit()
x_circ.add(qforte.gate('X', ancilla_idx, ancilla_idx))
y_circ.add(qforte.gate('Y', ancilla_idx, ancilla_idx))
X_op.add(1.0, x_circ)
Y_op.add(1.0, y_circ)
X_exp = qforte.Experiment(self._nqb + 1, cir, X_op, 100)
Y_exp = qforte.Experiment(self._nqb + 1, cir, Y_op, 100)
params = [1.0]
x_value = X_exp.perfect_experimental_avg(params)
y_value = Y_exp.perfect_experimental_avg(params)
value = (x_value + 1.0j * y_value) * phase1 * np.conj(phase2)
else:
value = 0.0
for t in self._qb_ham.terms():
c, V_l = t
# TODO (opt):
cV_l = qforte.Circuit()
for gate in V_l.gates():
gate_str = gate.gate_id()
target = gate.target()
control_gate_str = 'c' + gate_str
cV_l.add(qforte.gate(control_gate_str, target,
ancilla_idx))
cir = qforte.Circuit()
# TODO (opt): use Uprep
for j in range(self._nqb):
if self._ref[j] == 1:
cir.add(qforte.gate('X', j, j))
cir.add(qforte.gate('H', ancilla_idx, ancilla_idx))
cir.add(Uk)
cir.add(cV_l)
cir.add(qforte.gate('X', ancilla_idx, ancilla_idx))
cir.add(Ub)
cir.add(qforte.gate('X', ancilla_idx, ancilla_idx))
X_op = qforte.QubitOperator()
x_circ = qforte.Circuit()
Y_op = qforte.QubitOperator()
y_circ = qforte.Circuit()
x_circ.add(qforte.gate('X', ancilla_idx, ancilla_idx))
y_circ.add(qforte.gate('Y', ancilla_idx, ancilla_idx))
X_op.add(1.0, x_circ)
Y_op.add(1.0, y_circ)
X_exp = qforte.Experiment(self._nqb + 1, cir, X_op, 100)
Y_exp = qforte.Experiment(self._nqb + 1, cir, Y_op, 100)
# TODO (cleanup): Remove params as required arg (Nick)
params = [1.0]
x_value = X_exp.perfect_experimental_avg(params)
y_value = Y_exp.perfect_experimental_avg(params)
element = (x_value + 1.0j * y_value) * phase1 * np.conj(phase2)
value += c * element
return value
def trotterize_w_cRz(operator,
ancilla_qubit_idx,
factor=1.0,
Use_open_cRz=False,
trotter_number=1,
trotter_order=1):
"""
Returns a circuit equivalent to an exponentiated QubitOperator in which each term
in the trotterization exp(-i * theta_k ) only acts on the register if the ancilla
qubit is in the |1> state.
:param operator: (QubitOperator) the operator or state preparation ansatz
(represented as a sum of pauli terms) to be exponentiated
:param ancilla_qubit_idx: (int) the index of the ancilla qubit
:param Use_open_cRz: (bool) uses an open controlled Rz gate in exponentiation
(see Fig. 11 on page 185 of Nielson and Chung's
"Quantum Computation and Quantum Informatoin 10th Aniversary Ed.")
:param trotter_number: (int) for an operator A with terms A_i, the trotter_number
is the exponent (N) for to product of single term
exponentals e^A ~ ( Product_i(e^(A_i/N)) )^N
:param trotter_order: (int) the order of the trotterization approximation, can be 1 or 2
"""
total_phase = 1.0
trotterized_operator = qforte.Circuit()
if (trotter_number == 1) and (trotter_order == 1):
for term in operator.terms():
term_generator, phase = qforte.exponentiate_pauli_string(
factor * term[0],
term[1],
Use_cRz=True,
ancilla_idx=ancilla_qubit_idx,
Use_open_cRz=Use_open_cRz)
for gate in term_generator.gates():
trotterized_operator.add(gate)
total_phase *= phase
else:
if (trotter_order > 1):
raise NotImplementedError(
"Higher order trotterization is not yet implemented.")
ho_op = qforte.QubitOperator()
for k in range(1, trotter_number + 1):
k = float(k)
for term in operator.terms():
ho_op.add(factor * term[0] / float(trotter_number), term[1])
for trot_term in ho_op.terms():
term_generator, phase = qforte.exponentiate_pauli_string(
trot_term[0],
trot_term[1],
Use_cRz=True,
ancilla_idx=ancilla_qubit_idx,
Use_open_cRz=Use_open_cRz)
for gate in term_generator.gates():
trotterized_operator.add(gate)
total_phase *= phase
return (trotterized_operator, total_phase)
def run(self,
guess_energy: float,
t = 1.0,
nruns = 20,
success_prob = 0.5,
num_precise_bits = 4):
"""
guess_energy : A guess for the eigenvalue of the eigenspace with which |0>^(n)
has greatest overlap. You should be confident the ground state is within
t : A scaling parameter that controls the precision of the computation. You should
confident that the eigenvalue of interest is within +/- t of the guess energy.
"""
# float: evolution times
self._t = t
# int: number of times to sample the eigenvalue distribution
self._nruns = nruns
self._success_prob = success_prob
self._num_precise_bits = num_precise_bits
self._Uqpe = qforte.Circuit()
# int: The number of qubits needed to represent the state.
self._n_state_qubits = self._nqb
eps = 1 - success_prob
# int: The number of ancilla qubits used to hold eigenvalue information
self._n_ancilla = num_precise_bits + int(np.log2(2 + (1.0/eps)))
# int: The total number of qubits needed in the circuit
self._n_tot_qubits = self._n_state_qubits + self._n_ancilla
self._abegin = self._n_state_qubits
self._aend = self._n_tot_qubits - 1
self._n_classical_params = 0
self._n_pauli_trm_measures = nruns
self._guess_energy = guess_energy
self._guess_periods = round(self._t * guess_energy / (-2 * np.pi))
# Print options banner (should done for all algorithms).
self.print_options_banner()
######### QPE ########
# Apply Hadamard gates to all ancilla qubits
self._Uqpe.add(self.get_Uhad())
# Prepare the trial state on the non-ancilla qubits
self._Uqpe.add(self._Uprep)
# add controll e^-iHt circuit
self._Uqpe.add(self.get_dynamics_circ())
# add reverse QFT
self._Uqpe.add(self.get_qft_circuit('reverse'))
computer = qforte.Computer(self._n_tot_qubits)
computer.apply_circuit(self._Uqpe)
self._n_cnot = self._Uqpe.get_num_cnots()
if(self._fast):
z_readouts = computer.measure_z_readouts_fast(self._abegin, self._aend, self._nruns)
else:
Zcirc = self.get_z_circuit()
z_readouts = computer.measure_readouts(Zcirc, self._nruns)
self._phases = []
for readout in z_readouts:
val = sum(z / (2**i) for i, z in enumerate(readout, start=1))
self._phases.append(val)
# find final binary string of phase readouts:
final_readout = []
final_readout_aves = []
for i in range(self._n_ancilla):
iave = sum(readout[i] for readout in z_readouts) / nruns
final_readout_aves.append(iave)
final_readout.append(1 if iave > 0.5 else 0)
self._final_phase = sum(z / (2**i) for i, z in enumerate(final_readout, start=1))
E_u = -2 * np.pi * (self._final_phase + self._guess_periods - 1) / t
E_l = -2 * np.pi * (self._final_phase + self._guess_periods - 0) / t
E_qpe = E_l if abs(E_l - guess_energy) < abs(E_u - guess_energy) else E_u
res = stats.mode(np.asarray(self._phases))
self._mode_phase = res.mode[0]
E_u = -2 * np.pi * (self._mode_phase + self._guess_periods - 1) / t
E_l = -2 * np.pi * (self._mode_phase + self._guess_periods - 0) / t
self._mode_energy = E_l if abs(E_l - guess_energy) < abs(E_u - guess_energy) else E_u
print('\n ==> QPE readout averages <==')
print('------------------------------------------------')
for i, ave in enumerate(final_readout_aves):
print(' bit ', i, ': ', ave)
print('\n Final bit readout: ', final_readout)
######### QPE ########
# set Egs
self._Egs = E_qpe
# set Umaxdepth
self._Umaxdepth = self._Uqpe
# Print summary banner (should done for all algorithms).
self.print_summary_banner()
# verify that required attributes were defined
# (should done for all algorithms).
self.verify_run()
def exponentiate_pauli_string(coefficient,
term,
Use_cRz=False,
ancilla_idx=None,
Use_open_cRz=False):
"""
returns the exponential of an string of Pauli operators multiplied by an imaginary coefficient
exp(coefficient * term)
Parameters
----------
:param coefficient: complex
an imaginary coefficient that multiplies the Pauli string
:param term: Circuit
a Pauli string to be exponentiated
"""
# This function assumes that the factor is imaginary. The following tests for it.
if np.abs(np.real(coefficient)) > 1.0e-14:
raise ValueError(
f'exponentiate_pauli_string() called with a real coefficient {coefficient}'
)
# If the Pauli string has no terms this is just a phase factor times the identity circuit
if term.size() == 0:
return (qforte.Circuit(), np.exp(coefficient))
exponential = qforte.Circuit()
to_z = qforte.Circuit()
to_original = qforte.Circuit()
cX_circ = qforte.Circuit()
prev_target = None
max_target = None
for gate in term.gates():
id = gate.gate_id()
target = gate.target()
control = gate.control()
if (id == 'X'):
to_z.add(qforte.gate('H', target, control))
to_original.add(qforte.gate('H', target, control))
elif (id == 'Y'):
to_z.add(qforte.gate('Rzy', target, control))
to_original.add(qforte.gate('Rzy', target, control))
elif (id == 'I'):
continue
if (prev_target is not None):
cX_circ.add(qforte.gate('cX', target, prev_target))
prev_target = target
max_target = target
# Gate that actually contains the parameterization for the term
# TODO(Nick): investigate real/imaginary usage of 'factor' in below expression
if (Use_cRz):
z_rot = qforte.gate('cRz', max_target, ancilla_idx,
-2.0 * np.imag(coefficient))
else:
z_rot = qforte.gate('Rz', max_target, max_target,
-2.0 * np.imag(coefficient))
# Assemble the actual exponential
exponential.add(to_z)
exponential.add(cX_circ)
if (Use_open_cRz):
exponential.add(qforte.gate('X', ancilla_idx, ancilla_idx))
exponential.add(z_rot)
if (Use_open_cRz):
exponential.add(qforte.gate('X', ancilla_idx, ancilla_idx))
adj_cX_circ = cX_circ.adjoint()
exponential.add(adj_cX_circ)
adj_to_z = to_z.adjoint()
exponential.add(adj_to_z)
return (exponential, 1.0)