qiskit.algorithms.Shor¶

class Shor(quantum_instance=None)[source]¶

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

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

__init__(quantum_instance=None)[source]¶

Paramètres: 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)[source]¶

Construct circuit.

Paramètres

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.

Type renvoyé

QuantumCircuit

Renvoie

Quantum circuit.

Lève

ValueError – Invalid N

factor(N, a=2)[source]¶

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 \(N\) .

Paramètres

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.

Renvoie

results of the algorithm.

Type renvoyé

ShorResult

Lève

ValueError – Invalid input
AlgorithmError – If a quantum instance or backend has not been provided

static modinv(a, m)[source]¶

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

Type renvoyé: int

property quantum_instance¶

Returns quantum instance.

Type renvoyé: Optional[QuantumInstance]