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
See also https://arxiv.org/abs/quant-ph/0205095
- Parameters
quantum_instance (
Union[Backend,BaseBackend,QuantumInstance,None]) – Quantum Instance or Backend
-
__init__(quantum_instance=None)[source]¶ - Parameters
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
Returns quantum instance.
-
construct_circuit(N, a=2, measurement=False)[source]¶ Construct circuit.
- Parameters
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.
- Return type
QuantumCircuit- Returns
Quantum circuit.
- Raises
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 \(N\) .
- Parameters
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.
- Returns
results of the algorithm.
- Return type
- Raises
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.
- Return type
int
-
property
quantum_instance¶ Returns quantum instance.
- Return type
Optional[QuantumInstance]