Classically Time-Controlled Quantum Automata: Definition and Properties

Fuente: arXiv
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Main Authors: Díaz-Caro, Alejandro, Villagra, Marcos
Format: Preprint
Published: 2018
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author Díaz-Caro, Alejandro
Villagra, Marcos
author_facet Díaz-Caro, Alejandro
Villagra, Marcos
contents In this paper, we introduce classically time-controlled quantum automata or CTQA, which is a reasonable modification of Moore-Crutchfield quantum finite automata that uses time-dependent evolution and a "scheduler" defining how long each Hamiltonian will run. Surprisingly enough, time-dependent evolution provides a significant change in the computational power of quantum automata with respect to a discrete quantum model. Indeed, we show that if a scheduler is not computationally restricted, then a CTQA could even decide the Halting problem. In order to unearth the computational capabilities of CTQAs we study the case of a computationally restricted scheduler. In particular, we showed that depending on the type of restriction imposed on the scheduler, a CTQA can (i) recognize non-regular languages with cut-point, even in the presence of Karp-Lipton advice, and (ii) recognize non-regular promise languages with bounded-error. Furthermore, we study the cutpoint-union of cutpoint languages by introducing a new model of Moore-Crutchfield quantum finite automata with a rotating tape head. CTQA presents itself as a new model of computation that provides a different approach to a formal study of "classical control, quantum data" schemes in quantum computing.
format Preprint
id arxiv_https___arxiv_org_abs_1807_05385
institution arXiv
publishDate 2018
record_format arxiv
spellingShingle Classically Time-Controlled Quantum Automata: Definition and Properties
Díaz-Caro, Alejandro
Villagra, Marcos
Formal Languages and Automata Theory
Computational Complexity
Quantum Physics
68Q05, 68Q45, 81P68
F.1.1
In this paper, we introduce classically time-controlled quantum automata or CTQA, which is a reasonable modification of Moore-Crutchfield quantum finite automata that uses time-dependent evolution and a "scheduler" defining how long each Hamiltonian will run. Surprisingly enough, time-dependent evolution provides a significant change in the computational power of quantum automata with respect to a discrete quantum model. Indeed, we show that if a scheduler is not computationally restricted, then a CTQA could even decide the Halting problem. In order to unearth the computational capabilities of CTQAs we study the case of a computationally restricted scheduler. In particular, we showed that depending on the type of restriction imposed on the scheduler, a CTQA can (i) recognize non-regular languages with cut-point, even in the presence of Karp-Lipton advice, and (ii) recognize non-regular promise languages with bounded-error. Furthermore, we study the cutpoint-union of cutpoint languages by introducing a new model of Moore-Crutchfield quantum finite automata with a rotating tape head. CTQA presents itself as a new model of computation that provides a different approach to a formal study of "classical control, quantum data" schemes in quantum computing.
title Classically Time-Controlled Quantum Automata: Definition and Properties
topic Formal Languages and Automata Theory
Computational Complexity
Quantum Physics
68Q05, 68Q45, 81P68
F.1.1
url https://arxiv.org/abs/1807.05385