Computing Shor's algorithmic steps with classical light beams

• URL: http://arxiv.org/abs/2103.16226v3
• Date: Tue, 3 Jan 2023 11:21:28 GMT
• Title: Computing Shor's algorithmic steps with classical light beams
• Authors: Wei Wang, Ziyang You, Shuangpeng Wang, Zikang Tang, Hou Ian
• Abstract summary: We show that the parallelism featured in Shor's factoring algorithm is equivalent to the concurrent light-path propagation of an entangled beam or pulse train. A gedanken experiment is proposed for executing the key algorithmic steps of modulariation and Fourier transform on a target integer $N$. The multiplicative order associated with the sought-after integer factors is identified through a four-hole diffraction interference from sources obtained from the entangled beam profile.
• Score: 3.8768637546735456
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: When considered as orthogonal bases in distinct vector spaces, the unit vectors of polarization directions and the Laguerre-Gaussian modes of polarization amplitude are inseparable, constituting a so-called classical entangled light beam. Equating this classical entanglement to quantum entanglement necessary for computing purpose, we show that the parallelism featured in Shor's factoring algorithm is equivalent to the concurrent light-path propagation of an entangled beam or pulse train. A gedanken experiment is proposed for executing the key algorithmic steps of modular exponentiation and Fourier transform on a target integer $N$ using only classical manipulations on the amplitudes and polarization directions. The multiplicative order associated with the sought-after integer factors is identified through a four-hole diffraction interference from sources obtained from the entangled beam profile. The unique mapping from the fringe patterns to the computed order is demonstrated through simulations for the case $N=15$.

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