Prime factorization algorithm based on parameter optimization of Ising model.

Area of Science:

• Quantum Computing
• Cryptography
• Computational Mathematics

Background:

• RSA cryptosystem relies on the difficulty of integer factorization.
• Shor's algorithm is a known quantum algorithm for factorization but requires significant qubit resources.
• D-Wave quantum computers offer a different approach to quantum computation.

Purpose of the Study:

• To present a novel quantum computing method for RSA deciphering.
• To demonstrate the potential of D-Wave quantum computers for integer factorization.
• To compare the proposed method with Shor's algorithm in terms of efficiency and resource requirements.

Main Methods:

• Developed a new quantum algorithm distinct from Shor's algorithm.
• Utilized D-Wave's quantum computing software environment.
• Optimized Ising model parameters, reducing local field and coupling coefficients by over 33% and 26% respectively.

Main Results:

• Successfully factored a 20-bit integer (1028171), achieving a new benchmark in quantum computing for RSA deciphering.
• The method demonstrated improved stability of qubit chains.
• The factorization required fewer resources compared to Shor's algorithm for the same integer.

Conclusions:

• The D-Wave quantum computer shows significant potential for breaking RSA encryption.
• The novel method is more resource-efficient than Shor's algorithm for factoring certain integers.
• Post-quantum cryptography strategies should consider the capabilities of D-Wave quantum computers.