Characterizations of one-way general quantum finite automata

TL;DR

This paper introduces and analyzes a generalized model of one-way quantum finite automata where input symbols induce trace-preserving quantum operations, showing they recognize only regular languages with bounded error.

Contribution

It characterizes the language recognition power of measure-once and measure-many 1gQFA, demonstrating they recognize only regular languages and establishing conditions for their equivalence.

Findings

Both MO-1gQFA and MM-1gQFA recognize only regular languages.

The measurement frequency does not affect the recognition power in 1gQFA.

A necessary and sufficient condition for MM-1gQFA equivalence is provided.

Abstract

In this paper we study a generalized model named one-way general quantum finite automata} (1gQFA), in which each symbol in the input alphabet induces a trace-preserving quantum operation, instead of a unitary transformation. Two different kinds of 1gQFA will be studied: measure-once one-way general quantum finite automata} (MO-1gQFA), and measure-many one-way general quantum finite automata (MM-1gQFA). We prove that MO-1gQFA recognize, with bounded error, precisely the set of all regular languages. We prove that MM-1gQFA also recognize only regular languages with bounded error. Thus, MM-1gQFA and MO-1gQFA have the same language recognition power, which is greatly different from the conventional case in which the number of times the measurement is performed in the computation generally affects the language recognition power of one-way QFA. Finally, we present a sufficient and necessary condition for two MM-1gQFA to be equivalent.