On the Existence of certain Quantum Algorithms
Bjoern Grohmann

TL;DR
This paper explores whether quantum algorithms can efficiently compute maxima of conjugated elements in number fields, linking their existence to an open number theory conjecture.
Contribution
It establishes a connection between the potential of quantum algorithms for specific number-theoretic problems and an unresolved conjecture, highlighting a new research direction.
Findings
No definitive quantum algorithm proven for the problem.
The existence of such algorithms is related to an open conjecture.
Provides a theoretical framework connecting quantum computing and number theory.
Abstract
We investigate the question if quantum algorithms exist that compute the maximum of a set of conjugated elements of a given number field in quantum polynomial time. We will relate the existence of these algorithms for a certain family of number fields to an open conjecture from elementary number theory.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Quantum Mechanics and Applications
