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Quantum Optimization
A Quantum Diophantine Equation Solution Finder
arXiv
Authors: Lara Tatli, Paul Stevenson
Year
2024
Paper ID
64028
Status
Preprint
Abstract Read
~2 min
Abstract Words
89
Citations
N/A
Abstract
Diophantine equations are multivariate equations, usually polynomial, in which only integer solutions are admitted. A brute force method for finding solutions would be to systematically substitute possible integer solutions and check for equality. Grover's algorithm is a quantum search algorithm which can find marked indices in a list very efficiently. By treating the indices as the integer variables in the diophantine equation, Grover's algorithm can be used to find solutions in brute force way more efficiently than classical methods. We present an example for the simplest possible diophantine equation.
Why This Paper Matters
- This paper contributes to the Quantum Optimization research area in the Quantum Articles archive.
- It adds a 2024 reference point for readers tracking recent quantum research.
- Diophantine equations are multivariate equations, usually polynomial, in which only integer solutions are admitted.
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