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Deconstructing Shor's Algorithm Using Quantum Fourier Transform
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DOI：10.56042/ijpap.v64i4.27189.png)
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Abstract
En 中文
Shor's algorithm proved a significant milestone in quantum computing. Because it promises an exponential speedup over conventional algorithms for integer factorization, a problem critical to modern cryptography systems. This work covers implementation steps of Shor's algorithm and analyzes Quantum Fourier Transform (QFT) usage for extracting periodicity from quantum superpositions. Firstly, theoretical foundations of algorithm are illustrated concentrating on QFT construction and operation within the setting of the quantum circuit. Thereafter, each implementation step such as qubit optimization, modular exponentiation, and circuit design is discussed. Our findings validate the theoretical effectiveness of the QFT in solving the period-finding subroutine, while also highlighting the practical difficulties and scaling constraints presented by existing quantum hardware. The paper ends with a summary of possible advancements and future paths for error mitigation strategies and quantum algorithm design. For the benchmark case N = 15, (N denotes the composite integer to be factored) the implemented order-finding circuit exhibits a logical depth of approximately 10, increasing to about 20-25 layers after gate decomposition, highlighting the rapid depth scaling that constrains near-term quantum implementations.
Keywords:
Quantum fourier's transform
Shor's algorithm
Cryptography
Superposition
Journal
I
IF:
1.1
Papers:
65
Citations:
0