Variational Quantum Computation Integer Factorization Algorithm

The integer factorization problem is a major challenge in the field of computer science, and Shor’s algorithm provides a promising solution for this problem. However, Shor’s algorithm involves complex modular exponentiation computation, which leads to the construction of complicated quantum circuits...

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Bibliographic Details
Published in:International journal of theoretical physics Vol. 62; no. 11; p. 245
Main Authors: Zhang, Xinglan, Zhang, Feng
Format: Journal Article
Language:English
Published: New York Springer US 15.11.2023
Springer Nature B.V
Subjects:
Algorithms
Circuits
Complexity
Computers
Elementary Particles
Factorization
Integers
Machine learning
Mathematical and Computational Physics
Optimization techniques
Physics
Physics and Astronomy
Prime numbers
Quantum computing
Quantum Field Theory
Quantum Physics
Qubits (quantum computing)
Theoretical
Shor’s algorithm
Variational quantum algorithm
Variational quantum computation integer factorization algorithm
Integer factorization
Qiskit
ISSN:1572-9575, 0020-7748, 1572-9575
Online Access:Get full text
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Summary:The integer factorization problem is a major challenge in the field of computer science, and Shor’s algorithm provides a promising solution for this problem. However, Shor’s algorithm involves complex modular exponentiation computation, which leads to the construction of complicated quantum circuits. Moreover, the precision of continued fraction computations in Shor’s algorithm is influenced by the number of qubits, making it difficult to implement the algorithm on Noisy Intermediate-Scale Quantum (NISQ) computers. To address these issues, this paper proposes variational quantum computation integer factorization (VQCIF) algorithm based on variational quantum algorithm (VQA). Inspired by classical computing, this algorithm utilizes the parallelism of quantum computing to calculate the product of parameterized quantum states. Subsequently, the quantum multi-control gate is used to map the product satisfying p q = N onto an auxiliary qubit. Then the variational quantum circuit is adjusted by the optimizer, and it is possible to obtain a prime factor of the integer N with a high probability. While maintaining generality, VQCIF has a simple quantum circuit structure and requires only 2 n + 1 qubits. Furthermore, the time complexity is exponentially accelerated. VQCIF algorithm is implemented using the Qiskit framework, and tests are conducted on factorization instances to demonstrate its feasibility.
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ISSN:1572-9575
0020-7748
1572-9575
DOI:10.1007/s10773-023-05473-y