qiskit.algorithms.Shor

class Shor(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.

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

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

Parâmetros

quantum_instance (Union[Backend, BaseBackend, QuantumInstance, None]) – Quantum Instance or Backend

__init__(quantum_instance=None)

Parâmetros

quantum_instance (Union[Backend, BaseBackend, QuantumInstance, None]) – Quantum Instance or Backend

Methods

__init__([quantum_instance])	type quantum_instance Union[Backend, BaseBackend, QuantumInstance, None]
construct_circuit(N[, a, measurement])	Construct circuit.
factor(N[, a])	Execute the algorithm.
modinv(a, m)	Returns the modular multiplicative inverse of a with respect to the modulus m.

Attributes

quantum_instance

Returns quantum instance.

construct_circuit(N, a=2, measurement=False)

Construct circuit.

Parâmetros

• 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.

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

Tipo de retorno

QuantumCircuit

Retorna

Quantum circuit.

Levanta

ValueError – Invalid N

factor(N, a=2)

Execute the algorithm.

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 \(N\) .

Parâmetros

• 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.

Retorna

results of the algorithm.

Tipo de retorno

ShorResult

Levanta

• ValueError – Invalid input

• AlgorithmError – If a quantum instance or backend has not been provided

static modinv(a, m)

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

Tipo de retorno

int

property quantum_instance

Returns quantum instance.

Tipo de retorno

Optional[QuantumInstance]