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Realization of a scalable Shor algorithm.

Thomas Monz1, Daniel Nigg2, Esteban A Martinez2

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Researchers demonstrate a scalable quantum algorithm for factoring large numbers. This quantum computing advancement successfully factored 15 using seven qubits and modular multipliers, achieving over 99% accuracy.

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Area of Science:

  • Quantum Computing
  • Number Theory
  • Algorithm Development

Background:

  • Quantum algorithms, like Shor's algorithm, offer superior performance over classical methods for specific computational tasks.
  • Scalability in quantum computing hardware, error correction, and algorithm implementation is crucial for practical applications.

Purpose of the Study:

  • To present a scalable realization of Shor's algorithm for integer factorization.
  • To demonstrate the feasibility of implementing advanced quantum algorithms on current quantum hardware.

Main Methods:

  • Implementation of a scalable Shor algorithm based on Kitaev's proposal.
  • Utilizing an ion-trap quantum computer with seven qubits and four auxiliary qubits.
  • Employing generalized arithmetic operations, specifically modular multipliers.

Main Results:

  • Successfully factored the number 15 using the implemented scalable Shor algorithm.
  • Achieved a confidence level exceeding 99% for the correct factorization.
  • Demonstrated the scalability of the algorithm within the ion-trap architecture.

Conclusions:

  • The presented work validates a scalable approach to Shor's algorithm, a key milestone in quantum computation.
  • This realization highlights the potential of ion-trap quantum computers for complex number-theoretic problems.
  • The successful factorization of 15 with high confidence paves the way for tackling larger numbers.