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Shor’s algorithms

Qiskit has an implementation of Shor’s algorithm.

As referências anteriores têm explicações detalhadas e a construção de circuitos, enquanto este notebook tem exemplos com os algoritmos pré-construídos no Qiskit que você pode usar para fins educativos e de experimentação.

import math
import numpy as np
from qiskit import Aer
from qiskit.utils import QuantumInstance
from qiskit.algorithms import Shor

Shor’s Factoring algorithm

Algoritmo de Fatoração de Shor é um dos algoritmos quânticos mais conhecidos e encontra os fatores primos para o valor inteiro de entrada \(N\) em tempo polinomial. A implementação do algoritmo no Qiskit é simplesmente fornecer um inteiro alvo a ser fatorado e executar, da seguinte forma:

N = 15
backend = Aer.get_backend('aer_simulator')
quantum_instance = QuantumInstance(backend, shots=1024)
shor = Shor(quantum_instance=quantum_instance)
result = shor.factor(N)
print(f"The list of factors of {N} as computed by the Shor's algorithm is {result.factors[0]}.")

The list of factors of 15 as computed by the Shor's algorithm is [3, 5].

Note: this implementation of Shor’s algorithm uses \(4n + 2\) qubits, where \(n\) is the number of bits representing the integer in binary. So in practice, for now, this implementation is restricted to factorizing small integers. Given the above value of N we compute \(4n +2\) below and confirm the size from the actual circuit.

print(f'Computed of qubits for circuit: {4 * math.ceil(math.log(N, 2)) + 2}')
print(f'Actual number of qubits of circuit: {shor.construct_circuit(N).num_qubits}')

Computed of qubits for circuit: 18
Actual number of qubits of circuit: 18

import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright

Version Information

Qiskit Software	Version
Qiskit	None
Terra	0.18.0.dev0+5920b66
Aer	0.9.0
Ignis	0.7.0.dev0+8195559
Aqua	None
IBM Q Provider	None
System information
Python	3.8.8 (default, Apr 13 2021, 12:59:45) [Clang 10.0.0 ]
OS	Darwin
CPUs	2
Memory (Gb)	12.0
Thu May 27 11:05:34 2021 EDT

This code is a part of Qiskit

© Copyright IBM 2017, 2021.

This code is licensed under the Apache License, Version 2.0. You may
obtain a copy of this license in the LICENSE.txt file in the root directory
of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.

Any modifications or derivative works of this code must retain this
copyright notice, and modified files need to carry a notice indicating
that they have been altered from the originals.