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A quantum-inspired probabilistic prime factorization based on virtually connected Boltzmann machine and probabilistic

Hyundo Jung1, Hyunjin Kim2, Woojin Lee2

  • 1Korea University, Seoul, Korea. guseh7274@gmail.com.

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Summary

This study introduces a novel prime factorization machine using probabilistic computing, significantly reducing hardware needs and sampling operations for complex calculations. This advancement offers a more efficient approach to solving challenging computational problems.

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Area of Science:

  • * Computational science and engineering
  • * Emerging computing paradigms

Background:

  • * Probabilistic computing utilizes probabilistic bits (p-bits) for enhanced computational capabilities, particularly in non-deterministic polynomial searching.
  • * Previous p-bit implementations mimicked quantum computers, demanding excessive hardware resources and numerous sampling operations, thus limiting performance in Ising machines.
  • * Conventional simulated annealing schemes also suffered from performance degradation due to extensive sampling requirements.

Purpose of the Study:

  • * To develop a more efficient prime factorization machine with reduced hardware complexity and sampling operations.
  • * To overcome the limitations of existing probabilistic computing and simulated annealing methods for factorization tasks.

Main Methods:

  • * Introduction of a prime factorization machine employing a virtually connected Boltzmann machine.
  • * Utilization of a novel probabilistic annealing method designed for efficiency.
  • * Implementation of hardware designed for reduced complexity and sampling needs.

Main Results:

  • * Successful prime factorization of numbers from 10-bit to 64-bit.
  • * Achieved up to a 1.2 × 10^8 times improvement in the number of sampling operations compared to prior factorization machines.
  • * Demonstrated a 22-fold reduction in hardware resources required.

Conclusions:

  • * The developed prime factorization machine offers significant improvements in efficiency and hardware resource utilization.
  • * This work presents a viable and optimized approach for tackling complex factorization problems using probabilistic computing.
  • * The novel architecture and annealing method pave the way for more practical and scalable probabilistic computing applications.