Superiority of exact quantum automata for promise problems

TL;DR

This paper demonstrates that a specific family of promise problems can be solved exactly by simple two-state quantum automata, outperforming classical automata whose size grows unbounded, highlighting quantum automata's efficiency.

Contribution

It introduces an infinite family of promise problems solvable exactly by minimal quantum automata, showcasing their superiority over classical automata in certain cases.

Findings

Quantum automata solve the promise problems exactly.

Classical automata size grows without bound for these problems.

Quantum automata require only two states.

Abstract

In this note, we present an infinite family of promise problems which can be solved exactly by just tuning transition amplitudes of a two-state quantum finite automata operating in realtime mode, whereas the size of the corresponding classical automata grow without bound.