def create_TFIM(n: int, h: float, J: float):
"""Creates a 1D Transverse Field Ising Model hamiltonian with
open boundary conditions, i.e., no interaction between the
first and last spin sites.
n: int
Number of lattice sites
h: float
Strength of magnetic field
j: float
Interaction strength
"""
TFIM = System()
TFIM.hamiltonian = qf.QubitOperator()
circuit = [(-h, f"Z_{i}") for i in range(n)]
circuit += [(-J, f"X_{i} X_{i+1}") for i in range(n-1)]
for coeff, op_str in circuit:
TFIM.hamiltonian.add(coeff, qf.build_circuit(op_str))
TFIM.hf_reference = [0] * n
return TFIM
def build_operator(Inputstr):
ops = qforte.QubitOperator()
sepstr = Inputstr.split(';')
for i in range(len(sepstr)):
inputterm = sepstr[i].split(',')
ops.add(complex(inputterm[0]), qforte.build_circuit(inputterm[1]))
return ops
def do_qite_step(self):
btot = self.build_b()
A = qf.QubitOperator()
if(self._sparseSb):
sp_idxs, S, btot = self.build_sparse_S_b(btot)
else:
S = self.build_S()
x = lstsq(S, btot)[0]
x = np.real(x)
# sing_vals = lstsq(S, btot)[3]
# print(np.abs(sing_vals[-1] / sing_vals[0]))
if(self._sparseSb):
for I, spI in enumerate(sp_idxs):
if np.abs(x[I]) > self._x_thresh:
A.add(-1.0j * self._db * x[I], self._sig.terms()[spI][1].terms()[0][1])
self._n_classical_params += 1
else:
for I, SigI in enumerate(self._sig.terms()):
if np.abs(x[I]) > self._x_thresh:
A.add(-1.0j * self._db * x[I], SigI[1].terms()[0][1])
self._n_classical_params += 1
if(self._verbose):
print('\nbtot:\n ', btot)
print('\n S: \n')
matprint(S)
print('\n x: \n')
print(x)
eiA_kb, phase1 = trotterize(A, trotter_number=self._trotter_number)
self._total_phase *= phase1
self._Uqite.add(eiA_kb)
self._qc.apply_circuit(eiA_kb)
self._Ekb.append(np.real(self._qc.direct_op_exp_val(self._qb_ham)))
self._n_cnot += eiA_kb.get_num_cnots()
if(self._verbose):
qf.smart_print(self._qc)
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_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 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 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 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