Computing Shor's algorithmic steps with interference patterns of classical light

Area of Science:

• Quantum optics
• Classical entanglement
• Optical computing

Background:

• Classical entanglement of light, specifically using orthogonal polarization and Laguerre-Gaussian modes, is explored.
• This classical entanglement is analogous to quantum entanglement required for quantum computation.

Purpose of the Study:

• To demonstrate that classical light entanglement can be utilized for quantum computing tasks.
• To propose a gedanken experiment for executing Shor's factoring algorithm using classical optical manipulations.

Main Methods:

• Classical entanglement of light beams using polarization and Laguerre-Gaussian modes.
• Mapping algorithmic steps of modular exponentiation and Fourier transform to classical optical manipulations.
• Utilizing four-hole diffraction interference patterns to identify multiplicative order.

Main Results:

• The parallelism in Shor's algorithm is shown to be equivalent to the propagation of entangled light beams.
• A method is proposed to perform key algorithmic steps using classical light properties.
• Simulations demonstrate a unique mapping from interference fringe patterns to computed order for factoring.

Conclusions:

• Classical optical entanglement provides a viable pathway for implementing quantum algorithms like Shor's.
• This approach bypasses the need for true quantum entanglement, offering a potentially simpler route to optical quantum computation.