Shor
class Shor(quantum_instance=None)
Bases: object
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 in polynomial time.
Adapted from https://github.com/ttlion/ShorAlgQiskit
See also https://arxiv.org/abs/quant-ph/0205095
Parameters
quantum_instance (Union[QuantumInstance, Backend, BaseBackend, None]) – Quantum Instance or Backend
Methods
construct_circuit
Shor.construct_circuit(N, a=2, measurement=False)
Construct quantum part of the algorithm.
Parameters
- N (
int) – The odd 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.
Return type
QuantumCircuit
Returns
Quantum circuit.
factor
Shor.factor(N, a=2)
Execute the algorithm.
The input integer 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 can also be supplied, which needs to be a co-prime smaller than .
Parameters
- N (
int) – The odd integer to be factored, has a min. value of 3. - a (
int) – Any integer that satisfies 1 < a < N and gcd(a, N) = 1.
Returns
results of the algorithm.
Return type
Raises
- ValueError – Invalid input
- AlgorithmError – If a quantum instance or backend has not been provided
modinv
static Shor.modinv(a, m)
Returns the modular multiplicative inverse of a with respect to the modulus m.
Return type
int
Attributes
quantum_instance
Returns quantum instance.
Return type
Optional[QuantumInstance]