def test_qubitop_to_paulisum_more_terms(self):
# Given
qubit_operator = (
QubitOperator("Z0 Z1 Z2", -1.5)
+ QubitOperator("X0", 2.5)
+ QubitOperator("Y1", 3.5)
)
expected_qubits = (LineQubit(0), LineQubit(5), LineQubit(8))
expected_paulisum = (
PauliSum()
+ (
PauliString(Z.on(expected_qubits[0]))
* PauliString(Z.on(expected_qubits[1]))
* PauliString(Z.on(expected_qubits[2]))
* -1.5
)
+ (PauliString(X.on(expected_qubits[0]) * 2.5))
+ (PauliString(Y.on(expected_qubits[1]) * 3.5))
)
# When
paulisum = qubitop_to_paulisum(qubit_operator, qubits=expected_qubits)
# Then
self.assertEqual(paulisum.qubits, expected_qubits)
self.assertEqual(paulisum, expected_paulisum)
def test_qubitop_to_paulisum_setting_qubits(self):
# Given
qubit_operator = QubitOperator("Z0 Z1", -1.5)
expected_qubits = (LineQubit(0), LineQubit(5))
expected_paulisum = (PauliSum() +
PauliString(Z.on(expected_qubits[0])) *
PauliString(Z.on(expected_qubits[1])) * -1.5)
# When
paulisum = qubitop_to_paulisum(qubit_operator, qubits=expected_qubits)
# Then
self.assertEqual(paulisum.qubits, expected_qubits)
self.assertEqual(paulisum, expected_paulisum)
def test_qubitop_to_paulisum_z0z1_operator(self):
# Given
qubit_operator = QubitOperator("Z0 Z1", -1.5)
expected_qubits = (GridQubit(0, 0), GridQubit(1, 0))
expected_paulisum = (PauliSum() +
PauliString(Z.on(expected_qubits[0])) *
PauliString(Z.on(expected_qubits[1])) * -1.5)
# When
paulisum = qubitop_to_paulisum(qubit_operator)
# Then
self.assertEqual(paulisum.qubits, expected_qubits)
self.assertEqual(paulisum, expected_paulisum)
def simplify_cirq_pauli_sum(cirq_pauli_sum):
"""
Simplifies the input CirqPauliSum object according to Pauli algebra rules
Parameters
----------
cirq_pauli_sum : (CirqPauliSum object) represents the objects that needs to be simplified according to
Pauli algebra rules
Returns
-------
CirqPauliSum object simplified according to Pauli algebra rules
"""
pauli_strings = []
identity_strings = []
for pauli_string in cirq_pauli_sum.pauli_strings:
if not pauli_string._qubit_pauli_map == {} and not np.isclose(pauli_string.coefficient, 0.0):
pauli_strings.append(pauli_string)
else:
identity_strings.append(pauli_string)
coeff = sum(i.coefficient for i in identity_strings)
if not np.isclose(coeff, 0.0):
total_identity_string = PauliString(
qubit_pauli_map={}, coefficient=coeff)
pauli_strings.append(total_identity_string)
return CirqPauliSum(pauli_strings)
def create_cost_operators(self):
"""
Creates family of phase separation operators that depend on the objective function to be optimized
Returns
-------
cost_operators : (list) cost clauses for the graph on which Maxcut needs to be solved
"""
cost_operators = []
for i, j in self.graph.edges():
qubit_map_i = {i: Pauli.by_index(2)}
qubit_map_j = {j: Pauli.by_index(2)}
pauli_z_term = PauliString(
qubit_map_i, coefficient=0.5) * PauliString(qubit_map_j)
pauli_identity_term = PauliString(coefficient=-0.5)
cost_pauli_sum = add_pauli_strings(
[pauli_z_term, pauli_identity_term])
cost_operators.append(cost_pauli_sum)
return cost_operators
def create_driver_operators(self):
"""
Creates family of mixing operators that depend on the domain of the problem and its structure
Returns
-------
driver_operators : (list) mixing clauses for the graph on which Maxcut needs to be solved
"""
driver_operators = []
for i in self.graph.nodes():
qubit_map_i = {i: Pauli.by_index(0)}
driver_operators.append(
CirqPauliSum([PauliString(qubit_map_i, coefficient=-1.0)]))
return driver_operators
def compute_characteristic_function(
pauli_string: cirq.PauliString, qubits: List[cirq.Qid], density_matrix: np.ndarray
):
n_qubits = len(qubits)
d = 2**n_qubits
qubit_map = dict(zip(qubits, range(n_qubits)))
# rho_i or sigma_i in https://arxiv.org/abs/1104.3835
trace = pauli_string.expectation_from_density_matrix(density_matrix, qubit_map)
assert np.isclose(trace.imag, 0.0, atol=1e-6)
trace = trace.real
prob = trace * trace / d # Pr(i) in https://arxiv.org/abs/1104.3835
return trace, prob
def circuit_for_expectation_value(
circuit: cirq.Circuit, pauli_string: cirq.PauliString) -> cirq.Circuit:
"""Sandwich a PauliString operator between a forwards and backwards
copy of a circuit.
This is a circuit representation of the expectation value of an operator
<A> = <psi|A|psi> = <0|U^dag A U|0>. You can either extract the 0..0
amplitude of the final state vector (assuming starting from the |0..0>
state or extract the [0, 0] entry of the unitary matrix of this combined
circuit.
"""
assert pauli_string.coefficient == 1
return cirq.Circuit([
circuit,
cirq.Moment(gate.on(q) for q, gate in pauli_string.items()),
cirq.inverse(circuit)
])
def _measure_in(circuit: cirq.Circuit, pauli: cirq.PauliString):
# Transform circuit to canonical qubit layout.
qubit_map = dict(
zip(
sorted(circuit.all_qubits()),
cirq.LineQubit.range(len(circuit.all_qubits())),
))
circuit = circuit.transform_qubits(lambda q: qubit_map[q])
# Measure the Paulis.
if not set(pauli).issubset(set(circuit.all_qubits())):
raise ValueError(
f"Qubit mismatch. The PauliString {self} acts on qubits "
f"{[q.x for q in pauli.qubits]} but the circuit has qubit "
f"indices {sorted([q.x for q in circuit.all_qubits()])}.")
measured = (circuit + pauli.to_z_basis_ops() +
cirq.measure(*pauli.qubits))
# Transform circuit back to original qubits.
reverse_qubit_map = dict(zip(qubit_map.values(), qubit_map.keys()))
return measured.transform_qubits(lambda q: reverse_qubit_map[q])
def _assert_pass_over(ops: List[cirq.Operation], before: cirq.PauliString,
after: cirq.PauliString):
assert before.pass_operations_over(ops[::-1]) == after
assert after.pass_operations_over(ops, after_to_before=True) == before
