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We present a quantum annealing method for prime factorization, a task difficult for classical computers. This approach uses a superconducting quantum circuit, demonstrating a viable alternative to Shor's algorithm for factoring numbers.

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Area of Science:

  • Quantum Computing
  • Number Theory
  • Superconducting Circuits

Background:

  • Prime factorization is computationally intensive for classical computers.
  • Shor's algorithm offers a quantum approach but requires error-correctable logical qubits.
  • Quantum annealing presents an alternative method for tackling prime factorization.

Purpose of the Study:

  • To describe and demonstrate a quantum annealing method for prime factorization.
  • To explore the theoretical and experimental aspects of a superconducting quantum circuit for factorization.
  • To present a scalable and robust quantum solution for number analysis.

Main Methods:

  • Developed a superconducting quantum circuit with a native multiplier Hamiltonian.
  • Utilized quantum annealing to find M and N such that P = M × N.
  • Performed circuit simulations and experimental demonstrations at 10 mK.

Main Results:

  • Successfully demonstrated 2-bit prime factorization via circuit simulation.
  • Experimentally verified the 2-bit factorization at cryogenic temperatures.
  • Identified conditions for high success probability and retrieval of all factor pairs.

Conclusions:

  • The proposed quantum annealing method is a practical approach to prime factorization.
  • The superconducting circuit is robust, scalable, and offers an alternative to Shor's algorithm.
  • This work paves the way for quantum-enhanced number theoretic computations.