def _mul_with_qubits(self, qubits: Tuple['cirq.Qid', ...], other):
if isinstance(other, raw_types.Operation):
return other
if isinstance(other, (complex, float, int)):
from cirq.ops.pauli_string import PauliString
return PauliString(coefficient=other)
return NotImplemented
def __add__(self, other):
if not isinstance(other, (numbers.Complex, PauliString, PauliSum)):
if hasattr(other, 'gate') and isinstance(other.gate, identity.IdentityGate):
other = PauliString(other)
else:
return NotImplemented
result = self.copy()
result += other
return result
def __isub__(self, other):
if isinstance(other, numbers.Complex):
other = PauliSum.from_pauli_strings([PauliString(coefficient=other)])
if isinstance(other, PauliString):
other = PauliSum.from_pauli_strings([other])
if not isinstance(other, PauliSum):
return NotImplemented
self._linear_dict -= other._linear_dict
return self
def __iadd__(self, other):
if isinstance(other, (float, int, complex)):
other = PauliSum.from_pauli_strings(
[PauliString(coefficient=other)])
elif isinstance(other, PauliString):
other = PauliSum.from_pauli_strings([other])
if not isinstance(other, PauliSum):
return NotImplemented
self._linear_dict += other._linear_dict
return self
def from_boolean_expression(
cls, boolean_expr: Expr,
qubit_map: Dict[str, 'cirq.Qid']) -> 'PauliSum':
"""Builds the Hamiltonian representation of a Boolean expression.
This is based on "On the representation of Boolean and real functions as Hamiltonians for
quantum computing" by Stuart Hadfield, https://arxiv.org/abs/1804.09130
Args:
boolean_expr: A Sympy expression containing symbols and Boolean operations
qubit_map: map of string (boolean variable name) to qubit.
Return:
The PauliString that represents the Boolean expression.
Raises:
ValueError: If `boolean_expr` is of an unsupported type.
"""
if isinstance(boolean_expr, Symbol):
# In table 1, the entry for 'x' is '1/2.I - 1/2.Z'
return cls.from_pauli_strings([
PauliString({}, 0.5),
PauliString({qubit_map[boolean_expr.name]: pauli_gates.Z},
-0.5),
])
if isinstance(boolean_expr, (And, Not, Or, Xor)):
sub_pauli_sums = [
cls.from_boolean_expression(sub_boolean_expr, qubit_map)
for sub_boolean_expr in boolean_expr.args
]
# We apply the equalities of theorem 1.
if isinstance(boolean_expr, And):
pauli_sum = cls.from_pauli_strings(PauliString({}, 1.0))
for sub_pauli_sum in sub_pauli_sums:
pauli_sum = pauli_sum * sub_pauli_sum
elif isinstance(boolean_expr, Not):
assert len(sub_pauli_sums) == 1
pauli_sum = cls.from_pauli_strings(PauliString(
{}, 1.0)) - sub_pauli_sums[0]
elif isinstance(boolean_expr, Or):
pauli_sum = cls.from_pauli_strings(PauliString({}, 0.0))
for sub_pauli_sum in sub_pauli_sums:
pauli_sum = pauli_sum + sub_pauli_sum - pauli_sum * sub_pauli_sum
elif isinstance(boolean_expr, Xor):
pauli_sum = cls.from_pauli_strings(PauliString({}, 0.0))
for sub_pauli_sum in sub_pauli_sums:
pauli_sum = pauli_sum + sub_pauli_sum - 2.0 * pauli_sum * sub_pauli_sum
return pauli_sum
raise ValueError(f'Unsupported type: {type(boolean_expr)}')
def _pauli_string_from_unit(unit: UnitPauliStringT,
coefficient: Union[int, float, complex] = 1):
return PauliString(qubit_pauli_map=dict(unit), coefficient=coefficient)