Year: 2020
Type: conference-paper
Abstract: The Hidden Subgroup Problem (HSP) is a computational problem which includes as special cases integer factorization, the discrete logarithm problem, graph isomorphism, and the shortest vector problem. The celebrated polynomial-time quantum algorithms for factorization and the discrete logarithm are restricted versions of a generic polynomial-time quantum solution to the HSP for abelian groups, but despite focused research no polynomial-time solution for general groups has yet been found. We propose a generalization of the HSP to include arbitrary algebraic structures and analyze this new problem on powers of 2-element algebras. We prove a complete classification of every such power as quantum tractable (i.e. polynomial-time), classically tractable, quantum intractable, or classically intractable. In particular, we identify a class of algebras for which the generalized HSP exhibits super-polynomial speedup on a quantum computer compared to a classical one.
Authors: Matthew Moore, Taylor Walenczyk
Institution: University of Kansas
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3003989734