A Quantum Diophantine Equation Solution Finder
Keywords:
Quantum computing, Grover’s algorithm, Diophantine equationsAbstract
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 values for the unknown variables 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 a brute force way more efficiently than classical methods. We present a hand-coded example for the simplest possible Diophantine equation, and results for a more complicated, but still simulable, equation encoded with a high-level quantum language.
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Copyright (c) 2025 Lara Tatli and Paul Stevenson
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