Shor's Algorithm
Theoretical analysis of Shor's quantum factorization algorithm and its implications for modern cryptography and computational complexity
In-depth analysis of Shor's algorithm for integer factorization, focusing on the quantum order-finding subroutine and quantum phase estimation techniques. The study examines the classical reduction from factorization to the order-finding problem and details the quantum circuit implementation using controlled-unitary operations and the Quantum Fourier Transform. Performance analysis demonstrates the algorithm's polynomial-time complexity compared to the sub-exponential complexity of classical algorithms. The project explores real-world implementation challenges, including noise and error accumulation in current quantum hardware, and evaluates the cryptographic impact on RSA and ECC security. Includes computational benchmarks and complexity comparisons.
引用格式
Simone Pellegatta, Pietro Lanna (2025). Shor's Algorithm (https://it.mathworks.com/matlabcentral/fileexchange/182539-shor-s-algorithm), MATLAB Central File Exchange.
