Realization of a scalable Shor algorithm.

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.