Many Known Quantum Algorithms Are Optimal: Symmetry-Based Proofs

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Oscar Galindo, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow

Publication Date

6-1-2021

Comments

Technical Report: UTEP-CS-21-59a

Abstract

Many quantum algorithms have been proposed which are drastically more efficient that the best of the non-quantum algorithms for solving the same problems. A natural question is: are these quantum algorithms already optimal -- in some reasonable sense -- or they can be further improved? In this paper, we review recent results showing that many known quantum algorithms are actually optimal. Several of these results are based on appropriate invariances (symmetries).