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Prime factorization using quantum annealing and computational algebraic geometry
Raouf Dridi1, Hedayat Alghassi1
11QB Information Technologies (1QBit), Vancouver, British Columbia, V6C 2B5, Canada.
Scientific Reports
|February 22, 2017
Summary
This study introduces a new algorithm combining quantum annealing and Gröbner bases for prime factorization. It successfully factored large bi-primes using a quantum processor, advancing computational capabilities.
Area of Science:
- Quantum Computing
- Computational Algebraic Geometry
Background:
- Prime factorization is a fundamental problem in number theory and cryptography.
- Existing factorization methods face scalability challenges with increasing number sizes.
Purpose of the Study:
- To develop a novel algorithm for prime factorization by integrating quantum annealing and computational algebraic geometry.
- To demonstrate the algorithm's efficacy on large bi-prime numbers.
Main Methods:
- Utilized quantum annealing for computational tasks.
- Employed Gröbner bases from computational algebraic geometry.
- Developed an autonomous algorithm combining these two approaches.
Main Results:
- Successfully factored all bi-primes up to 200,000.
- Achieved the largest factorization to date using a quantum processor.
- Demonstrated that Gröbner bases can reduce Hamiltonian degrees.
Conclusions:
- The novel algorithm offers a promising hybrid approach for prime factorization.
- Quantum computing, augmented with algebraic geometry techniques, shows potential for tackling complex computational problems.
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