def __init__(
self,
N: int = 15,
a: int = 2,
quantum_instance: Optional[Union[QuantumInstance, BaseBackend,
Backend]] = None
) -> None:
"""
Args:
N: The integer to be factored, has a min. value of 3.
a: Any integer that satisfies 1 < a < N and gcd(a, N) = 1.
quantum_instance: Quantum Instance or Backend
Raises:
ValueError: Invalid input
"""
validate_min('N', N, 3)
validate_min('a', a, 2)
super().__init__(quantum_instance)
self._n = None # type: Optional[int]
self._up_qreg = None
self._down_qreg = None # type: Optional[QuantumRegister]
self._aux_qreg = None # type: Optional[QuantumRegister]
# check the input integer
if N < 1 or N % 2 == 0:
raise ValueError(
'The input needs to be an odd integer greater than 1.')
self._N = N
if a >= N or math.gcd(a, self._N) != 1:
raise ValueError(
'The integer a needs to satisfy a < N and gcd(a, N) = 1.')
self._a = a
self._ret = AlgorithmResult({
"factors": [],
"total_counts": 0,
"successful_counts": 0
})
# check if the input integer is a power
tf, b, p = is_power(N, return_decomposition=True)
if tf:
logger.info('The input integer is a power: %s=%s^%s.', N, b, p)
self._ret['factors'].append(b)
self._qft = QFT(do_swaps=False).to_instruction()
self._iqft = self._qft.inverse()
self._phi_add_N = None # type: Optional[Gate]
self._iphi_add_N = None
def factor(
self,
N: int,
a: int = 2,
) -> 'ShorResult':
"""Execute the algorithm.
The input integer :math:`N` to be factored is expected to be odd and greater than 2.
Even though this implementation is general, its capability will be limited by the
capacity of the simulator/hardware. Another input integer :math:`a` can also be supplied,
which needs to be a co-prime smaller than :math:`N` .
Args:
N: The integer to be factored, has a min. value of 3.
a: Any integer that satisfies 1 < a < N and gcd(a, N) = 1.
Returns:
ShorResult: results of the algorithm.
Raises:
ValueError: Invalid input
AlgorithmError: If a quantum instance or backend has not been provided
"""
validate_min('N', N, 3)
validate_min('a', a, 2)
# check the input integer
if N < 1 or N % 2 == 0:
raise ValueError(
'The input needs to be an odd integer greater than 1.')
if a >= N or math.gcd(a, N) != 1:
raise ValueError(
'The integer a needs to satisfy a < N and gcd(a, N) = 1.')
if self.quantum_instance is None:
raise AlgorithmError(
"A QuantumInstance or Backend "
"must be supplied to run the quantum algorithm.")
result = ShorResult()
# check if the input integer is a power
tf, b, p = is_power(N, return_decomposition=True)
if tf:
logger.info('The input integer is a power: %s=%s^%s.', N, b, p)
result.factors.append(b)
if not result.factors:
logger.debug('Running with N=%s and a=%s.', N, a)
if self._quantum_instance.is_statevector:
circuit = self.construct_circuit(N=N, a=a, measurement=False)
logger.warning('The statevector_simulator might lead to '
'subsequent computation using too much memory.')
result = self._quantum_instance.execute(circuit)
complete_state_vec = result.get_statevector(circuit)
# TODO: this uses too much memory
up_qreg_density_mat = partial_trace(
complete_state_vec, range(2 * self._n, 4 * self._n + 2))
up_qreg_density_mat_diag = np.diag(up_qreg_density_mat)
counts = dict()
for i, v in enumerate(up_qreg_density_mat_diag):
if not v == 0:
counts[bin(int(i))[2:].zfill(2 * self._n)] = v**2
else:
circuit = self.construct_circuit(N=N, a=a, measurement=True)
counts = self._quantum_instance.execute(circuit).get_counts(
circuit)
result.total_counts = len(counts)
# For each simulation result, print proper info to user
# and try to calculate the factors of N
for measurement in list(counts.keys()):
# Get the x_final value from the final state qubits
logger.info("------> Analyzing result %s.", measurement)
factors = self._get_factors(N, a, measurement)
if factors:
logger.info('Found factors %s from measurement %s.',
factors, measurement)
result.successful_counts = result.successful_counts + 1
if factors not in result.factors:
result.factors.append(factors)
return result