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Spectral Signatures of Prime Factorization.

Giuseppe Mussardo1,2, Andrea Trombettoni2,3

  • 1SISSA, Via Bonomea 265, 34136 Trieste, Italy.

Entropy (Basel, Switzerland)
|March 28, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a quantum measurement protocol for integer factorization up to a set limit. The method uses a specialized quantum device, requiring fewer steps for factorization based on the number of prime factors.

Keywords:
prime factorizationprojective measurementsquantum mechanics

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Area of Science:

  • Quantum Information Science
  • Number Theory
  • Computational Complexity

Background:

  • Integer factorization is a cornerstone of modern cryptography.
  • Current factorization algorithms face significant computational challenges for large numbers.
  • Quantum computing offers potential avenues for accelerating complex computations.

Purpose of the Study:

  • To propose a novel quantum measurement-based protocol for integer factorization.
  • To establish a theoretical framework for factoring integers below a defined threshold (Λ=2d).
  • To demonstrate a method decoupling device preparation from the factorization process.

Main Methods:

  • Utilizing quantum measurement theory to develop a factorization protocol.
  • Designing a single-purpose quantum device capable of specific spectral measurements.
  • Solving a set of differential equations for device construction, independent of the target integer.
  • Employing quantum computation for efficient device initialization.

Main Results:

  • A protocol for factoring integers N ≤ Λ in I steps, where I is the number of prime factors.
  • The factorization process involves a sequence of I quantum measurements.
  • Device construction requires solving approximately 2d differential equations.
  • Device initialization can be achieved in d quantum computational steps.

Conclusions:

  • The proposed quantum measurement protocol offers a new approach to integer factorization.
  • The method's efficiency is tied to the number of prime factors of the integer.
  • The decoupling of device preparation and factorization suggests a scalable quantum solution.