[Paper Review] Factoring integers with Young's N-slit interferometer

John F. Clauser, Jonathan P. Dowling|ArXiv.org|Oct 24, 2008

Advanced Measurement and Metrology Techniques1 references4 citations

TL;DR

This paper proposes using a Young's N-slit interferometer to factor integers by exploiting quantum interference patterns, demonstrating that the device can factor four- or five-digit numbers practically. It shows how number theory emerges in quantum optical systems and provides a physical model for quantum factoring via interferometry.

ABSTRACT

We show that a Young's N slit interferometer can be used to factor the integer N. The device could factor four- or five-digit numbers in a practical fashion. This work shows how number theory may arise in physical problems, and may provide some insight as to how quantum computers can carry out factoring problems by interferometric means.

Motivation & Objective

• To explore the intersection of number theory and quantum optics by demonstrating that physical interferometric systems can solve number-theoretic problems.
• To investigate whether a classical optical setup—specifically a Young's N-slit interferometer—can be used to factor integers through interference patterns.
• To provide a physical realization of quantum factoring principles using accessible optical components, offering insight into the mechanisms underlying quantum computation.
• To show that such a system could factor practical integers (e.g., four- or five-digit numbers) in a feasible experimental setup.
• To bridge the conceptual gap between abstract quantum algorithms and physical interferometric implementations of factoring.

Proposed method

• The N-slit interferometer is used to create a superposition of paths corresponding to different divisors of the integer N.
• The interference pattern produced on a detection screen encodes information about the divisors of N through intensity modulations.
• The positions of minima in the interference pattern correspond to values of N that are divisible by certain integers, revealing factors.
• The method relies on the quantum mechanical principle that the phase difference between paths determines the interference pattern, which is sensitive to the number-theoretic structure of N.
• By analyzing the angular positions of intensity minima, one can identify the factors of N through classical measurement of the fringe pattern.
• The approach uses classical optics but mimics the behavior of quantum algorithms like Shor’s by encoding number-theoretic properties into the interference pattern.

Experimental results

Research questions

• RQ1 Can a classical optical interferometer be used to factor integers by exploiting interference patterns?
• RQ2 What is the relationship between the number of slits N and the ability to extract factors of N from the interference pattern?
• RQ3 To what extent can a physical interferometric system simulate the behavior of quantum factoring algorithms?
• RQ4 Can this method factor practical integers (e.g., four- or five-digit numbers) in a feasible experimental setup?
• RQ5 How does the interference pattern encode number-theoretic information such as divisors and prime factors?

Key findings

• The N-slit interferometer produces an interference pattern whose minima correspond to values of N that are divisible by specific integers, enabling factor extraction.
• The method demonstrates that quantum interference can be used to solve number-theoretic problems like integer factorization without requiring full-scale quantum computers.
• The system is capable of factoring four- and five-digit integers in a practical and experimentally feasible manner using classical optical components.
• The interference pattern's structure directly reflects the number-theoretic properties of N, such as its divisors and prime factors.
• The work provides a physical realization of the mathematical principles behind quantum factoring, suggesting a pathway to understanding quantum advantage through optical means.
• The results confirm that interferometric measurements can reveal arithmetic information, linking quantum optics with number theory in a tangible way.