qiskit.aqua.algorithms.Shor

class Shor(N=15, a=2, quantum_instance=None)

Shor’s factoring algorithm.

Shor’s Factoring algorithm is one of the most well-known quantum algorithms and finds the prime factors for input integer \(N\) in polynomial time.

The input integer \(N\) 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 \(a\) can also be supplied, which needs to be a co-prime smaller than \(N\) .

Adapted from https://github.com/ttlion/ShorAlgQiskit

See also https://arxiv.org/abs/quant-ph/0205095

Parameter

• N (int) – The integer to be factored, has a min. value of 3.

• a (int) – Any integer that satisfies 1 < a < N and gcd(a, N) = 1.

• quantum_instance (Union[QuantumInstance, Backend, BaseBackend, None]) –

  Quantum Instance or Backend

  Raises:

  ValueError: Invalid input

__init__(N=15, a=2, quantum_instance=None)

Parameter

• N (int) – The integer to be factored, has a min. value of 3.

• a (int) – Any integer that satisfies 1 < a < N and gcd(a, N) = 1.

• quantum_instance (Union[QuantumInstance, Backend, BaseBackend, None]) –

  Quantum Instance or Backend

  Raises:

  ValueError: Invalid input

Methods

__init__([N, a, quantum_instance])	type N int
construct_circuit([measurement])	Construct circuit.
modinv(a, m)	Returns the modular multiplicative inverse of a with respect to the modulus m.
run([quantum_instance])	Execute the algorithm with selected backend.
set_backend(backend, **kwargs)	Sets backend with configuration.

Attributes

backend	Returns backend.
quantum_instance	Returns quantum instance.
random	Return a numpy random.

property backend

Returns backend.

Rückgabetyp

Union[Backend, BaseBackend]

construct_circuit(measurement=False)

Construct circuit.

Parameter

measurement (bool) – Boolean flag to indicate if measurement should be included in the circuit.

Rückgabetyp

QuantumCircuit

Rückgabe

Quantum circuit.

static modinv(a, m)

Returns the modular multiplicative inverse of a with respect to the modulus m.

Rückgabetyp

int

property quantum_instance

Returns quantum instance.

Rückgabetyp

Optional[QuantumInstance]

property random

Return a numpy random.

run(quantum_instance=None, **kwargs)

Execute the algorithm with selected backend.

Parameter

• quantum_instance (Union[QuantumInstance, Backend, BaseBackend, None]) – the experimental setting.

• kwargs (dict) – kwargs

Rückgabe

results of an algorithm.

Rückgabetyp

dict

Verursacht

AquaError – If a quantum instance or backend has not been provided

set_backend(backend, **kwargs)

Sets backend with configuration.

Rückgabetyp

None