def test_trotterization(self):
circ_vec = [Circuit(), build_circuit('Z_0')]
coef_vec = [-1.0j * 0.5, -1.0j * -0.04544288414432624]
# the operator to be exponentiated
minus_iH = QubitOperator()
for i in range(len(circ_vec)):
minus_iH.add(coef_vec[i], circ_vec[i])
# exponentiate the operator
Utrot, phase = trotterization.trotterize(minus_iH)
inital_state = np.zeros(2**4, dtype=complex)
inital_state[3] = np.sqrt(2 / 3)
inital_state[12] = -np.sqrt(1 / 3)
# initalize a quantum computer with above coeficients
# i.e. ca|1100> + cb|0011>
qc = Computer(4)
qc.set_coeff_vec(inital_state)
# apply the troterized minus_iH
qc.apply_circuit(Utrot)
qc.apply_constant(phase)
smart_print(qc)
coeffs = qc.get_coeff_vec()
assert np.real(coeffs[3]) == approx(0.6980209737879599, abs=1.0e-15)
assert np.imag(coeffs[3]) == approx(-0.423595782342996, abs=1.0e-15)
assert np.real(coeffs[12]) == approx(-0.5187235657531178, abs=1.0e-15)
assert np.imag(coeffs[12]) == approx(0.25349397560041553, abs=1.0e-15)
def test_qft(self):
trial_state = Computer(4)
trial_circ = build_circuit('X_0 X_1')
trial_state.apply_circuit(trial_circ)
# verify direct transformation
qft(trial_state, 0, 3)
a1_dag_a2 = build_operator('1.0, Z_0')
exp = trial_state.direct_op_exp_val(a1_dag_a2)
assert exp == approx(0, abs=1.0e-16)
# test unitarity
qft(trial_state, 0, 2)
rev_qft(trial_state, 0, 2)
a1_dag_a2 = build_operator('1.0, Z_0')
exp = trial_state.direct_op_exp_val(a1_dag_a2)
assert exp == approx(0, abs=1.0e-16)
# test reverse transformation
qft(trial_state, 0, 3)
a1_dag_a2 = build_operator('1.0, Z_0')
exp = trial_state.direct_op_exp_val(a1_dag_a2)
assert exp == approx(1.0, abs=1.0e-14)
def test_trotterization_with_controlled_U(self):
circ_vec = [build_circuit('Y_0 X_1'), build_circuit('X_0 Y_1')]
coef_vec = [-1.0719145972781818j, 1.0719145972781818j]
# the operator to be exponentiated
minus_iH = QubitOperator()
for i in range(len(circ_vec)):
minus_iH.add(coef_vec[i], circ_vec[i])
ancilla_idx = 2
# exponentiate the operator
Utrot, phase = trotterization.trotterize_w_cRz(minus_iH, ancilla_idx)
# Case 1: positive control
# initalize a quantum computer
qc = Computer(3)
# build HF state
qc.apply_gate(gate('X', 0, 0))
# put ancilla in |1> state
qc.apply_gate(gate('X', 2, 2))
# apply the troterized minus_iH
qc.apply_circuit(Utrot)
smart_print(qc)
coeffs = qc.get_coeff_vec()
assert coeffs[5] == approx(-0.5421829373021542, abs=1.0e-15)
assert coeffs[6] == approx(-0.8402604730072732, abs=1.0e-15)
# Case 2: negitive control
# initalize a quantum computer
qc = Computer(3)
# build HF state
qc.apply_gate(gate('X', 0, 0))
# apply the troterized minus_iH
qc.apply_circuit(Utrot)
smart_print(qc)
coeffs = qc.get_coeff_vec()
assert coeffs[1] == approx(1, abs=1.0e-15)
def test_op_exp_val_1(self):
# test direct expectation value measurement
trial_state = Computer(4)
trial_prep = [None] * 5
trial_prep[0] = gate('H', 0, 0)
trial_prep[1] = gate('H', 1, 1)
trial_prep[2] = gate('H', 2, 2)
trial_prep[3] = gate('H', 3, 3)
trial_prep[4] = gate('cX', 0, 1)
trial_circ = Circuit()
#prepare the circuit
for gate_ in trial_prep:
trial_circ.add(gate_)
# use circuit to prepare trial state
trial_state.apply_circuit(trial_circ)
# gates needed for [a1^ a2] operator
X1 = gate('X', 1, 1)
X2 = gate('X', 2, 2)
Y1 = gate('Y', 1, 1)
Y2 = gate('Y', 2, 2)
# initialize circuits to make operator
circ1 = Circuit()
circ1.add(X2)
circ1.add(Y1)
circ2 = Circuit()
circ2.add(Y2)
circ2.add(Y1)
circ3 = Circuit()
circ3.add(X2)
circ3.add(X1)
circ4 = Circuit()
circ4.add(Y2)
circ4.add(X1)
#build the quantum operator for [a1^ a2]
a1_dag_a2 = QubitOperator()
a1_dag_a2.add(0.0 - 0.25j, circ1)
a1_dag_a2.add(0.25, circ2)
a1_dag_a2.add(0.25, circ3)
a1_dag_a2.add(0.0 + 0.25j, circ4)
#get direct expectatoin value
exp = trial_state.direct_op_exp_val(a1_dag_a2)
assert exp == approx(0.25, abs=2.0e-16)
def test_io_simplified(self):
# test direct expectation value measurement
trial_state = Computer(4)
trial_circ = build_circuit('H_0 H_1 H_2 H_3 cX_0_1')
# use circuit to prepare trial state
trial_state.apply_circuit(trial_circ)
#build the quantum operator for [a1^ a2]
a1_dag_a2 = build_operator('0.0-0.25j, X_2 Y_1; 0.25, Y_2 Y_1; \
0.25, X_2 X_1; 0.0+0.25j, Y_2 X_1')
#get direct expectatoin value
exp = trial_state.direct_op_exp_val(a1_dag_a2)
assert exp == approx(0.25, abs=2.0e-16)
def test_circuit(self):
print('\n')
num_qubits = 10
qc1 = Computer(num_qubits)
qc2 = Computer(num_qubits)
prep_circ = Circuit()
circ = Circuit()
for i in range(num_qubits):
prep_circ.add(gate('H', i, i))
for i in range(num_qubits):
prep_circ.add(gate('cR', i, i + 1, 1.116 / (i + 1.0)))
for i in range(num_qubits - 1):
circ.add(gate('cX', i, i + 1))
circ.add(gate('cX', i + 1, i))
circ.add(gate('cY', i, i + 1))
circ.add(gate('cY', i + 1, i))
circ.add(gate('cZ', i, i + 1))
circ.add(gate('cZ', i + 1, i))
circ.add(gate('cR', i, i + 1, 3.14159 / (i + 1.0)))
circ.add(gate('cR', i + 1, i, 2.17284 / (i + 1.0)))
qc1.apply_circuit_safe(prep_circ)
qc2.apply_circuit_safe(prep_circ)
qc1.apply_circuit_safe(circ)
qc2.apply_circuit(circ)
C1 = qc1.get_coeff_vec()
C2 = qc2.get_coeff_vec()
diff_vec = [(C1[i] - C2[i]) * np.conj(C1[i] - C2[i])
for i in range(len(C1))]
diff_norm = np.sum(diff_vec)
print('\nNorm of diff vec |C - Csafe|')
print('-----------------------------')
print(' ', diff_norm)
assert diff_norm == approx(0, abs=1.0e-16)
def test_advanced_gates(self):
print('\n')
trial_state = Computer(4)
trial_circ = build_circuit('X_0 X_1')
trial_state.apply_circuit(trial_circ)
# verify Toffoli gate
T_circ = Toffoli(0, 1, 2)
print(T_circ.str())
trial_state.apply_circuit(T_circ) # This should turn the state to 1110
a1_dag_a2 = build_operator('1.0, Z_2')
exp = trial_state.direct_op_exp_val(a1_dag_a2)
assert exp == approx(-1, abs=9e-16) # Measure qubit 2 should give -1
# verify Fredkin gate
F_circ = Fredkin(1, 2, 3)
print(F_circ.str())
trial_state.apply_circuit(F_circ) # This should turn the state to 1101
# trial_state.apply_circuit_safe(F_circ) # This should turn the state to 1101
a1_dag_a2 = build_operator('1.0, Z_2')
exp = trial_state.direct_op_exp_val(a1_dag_a2)
assert exp == approx(1, abs=9e-16) # Measure qubit 2 should give +1