Shor's algorithm can factor large integers with a certain success probability in polynomial time, making it one of the most significant quantum algorithms. However, its practical implementation requires an impractically large number of qubits in the current noisy intermediate-scale quantum era, posing major technological challenges. In this work, we present a classical optical scheme for implementing Shor's factorization algorithm. In our approach, the two core components of the algorithm—modular exponentiation and the quantum Fourier transform—are realized using classical coherent optical circuits. The number of required optical elements remains polynomial, matching the resource scaling of the quantum version. Importantly, this scheme avoids the decoherence issues inherent to quantum systems and is readily implementable with existing optical technologies. Using this method, we successfully factored $N=15$ and 21, with experimental results in excellent agreement with theoretical predictions. This work provides a practical classical pathway for simulating quantum algorithms and highlights the potential of classical optical computation for tackling complex computational problems.

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• Classical optics
• Optical coherence