Integer factorization via spatial photonic Ising machine using a lattice sieve method

Area of Science:

• Quantum Computing
• Cryptography
• Computational Physics

Background:

• Integer factorization is critical for cryptography but computationally intensive for classical computers.
• Quantum computing offers theoretical speedups but faces hardware challenges.
• Existing lattice sieve methods require significant computational resources.

Purpose of the Study:

• To propose and experimentally validate an Ising-accelerated lattice sieve method for efficient integer factorization.
• To leverage a photonic Ising machine for solving the NP-hard closest vector problem.
• To minimize hardware demands for integer factorization algorithms.

Main Methods:

• Development of a programmable spatial photonic Ising machine (SPIM) using a Dammann grating.
• Implementation of multi-path simulated annealing experiments on the SPIM.
• Classical computer simulations to assess scalability and performance up to 120-bit integers.

Main Results:

• Experimental factorization of a 32-bit integer using the SPIM.
• Identification of smooth relation pairs for factoring a 100-bit integer.
• Demonstrated scalability of the lattice sieve method for integers up to 120 bits via simulations.

Conclusions:

• The proposed Ising-accelerated lattice sieve method offers an efficient approach to integer factorization.
• The photonic Ising machine demonstrates potential for overcoming limitations in quantum and classical factorization methods.
• This work establishes a benchmark for lattice sieve-based factorization, highlighting hardware efficiency and scalability.