Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance

Area of Science:

• Quantum Computing
• Quantum Information Science
• Computational Complexity

Background:

• Classical computers face exponential time complexity for integer factorization, underpinning modern cryptography.
• Shor's quantum factoring algorithm offers a polynomial-time solution, but experimental realization remains challenging.

Purpose of the Study:

• To experimentally demonstrate the simplest instance of Shor's quantum factoring algorithm.
• To showcase precise control and modeling techniques for complex quantum systems.

Main Methods:

• Implementation of Shor's algorithm for factoring N=15 using seven spin-1/2 nuclei as qubits.
• Utilizing liquid-state nuclear magnetic resonance (NMR) techniques for quantum bit manipulation.
• Development of a parameter-free model for decoherence effects in the quantum system.

Main Results:

• Successful factorization of the integer 15 into its prime factors, 3 and 5.
• Demonstration of precise quantum bit control and system modeling.
• Validation of a predictive model for decoherence in NMR-based quantum computing.

Conclusions:

• The study provides the first experimental demonstration of Shor's quantum factoring algorithm.
• The employed NMR techniques show potential for scalable quantum information processing.
• Precise control and decoherence modeling are crucial for advancing quantum computing.