One-Way Finite Automata with Quantum and Classical States

Zheng, Shenggen; Qiu, Daowen; Li, Lvzhou; Gruska, Jozef

doi:10.1007/978-3-642-31644-9_19

Cited by 28 publications

(46 citation statements)

References 21 publications

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“…If restricting the read-head in a 2QCFA to be one-way, then it is natural to get one-way finite automata with quantum and classical states (1QCFA). That is, 1QCFA are one-way versions of 2QCFA, studied by Zheng and Qiu et al [43]. It is worth mentioning that more previously a different but more practical model called as oneway quantum finite automata together with classical states (1QFAC) was proposed and studied by Qiu et al [34].…”

Section: Quantum and Semi-quantum Finite Automata Basic Models And Womentioning

confidence: 99%

Promise problems solved by quantum and classical finite automata

Zheng

Qiu

et al. 2017

Theoretical Computer Science

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The concept of promise problems was introduced and started to be systematically explored by Even, Selman, Yacobi, Goldreich, and other scholars. It has been argued that promise problems should be seen as partial decision problems and as such that they are more fundamental than decision problems and formal languages that used to be considered as the basic ones for complexity theory. The main purpose of this paper is to explore the promise problems accepted by classical, quantum and also semi-quantum finite automata. More specifically, we first introduce two acceptance modes of promise problems, recognizability and solvability, and explore their basic properties. Afterwards, we show several results concerning descriptional complexity on promise problems. In particular, we prove: (1) there is a promise problem that can be recognized exactly by measure-once one-way quantum finite automata (MO-1QFA), but no deterministic finite automata (DFA) can recognize it; (2) there is a promise problem that can be solved with error probability ǫ ≤ 1/3 by one-way finite automaton with quantum and classical states (1QCFA), but no one-way probability finite automaton (PFA) can solve it with error probability ǫ ≤ 1/3; and especially, (3) there are promise problems A(p) with prime p that can be solved with any error probability by MO-1QFA with only two quantum basis states, but they can not be solved exactly by any MO-1QFA with two quantum basis states; in contrast, the minimal PFA solving A(p) with any error probability (usually smaller than 1/2) has p states. Finally, we mention a number of problems related to promise for further study.

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Section: Quantum and Semi-quantum Finite Automata Basic Models And Womentioning

confidence: 99%

Promise problems solved by quantum and classical finite automata

Zheng

Qiu

et al. 2017

Theoretical Computer Science

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“…(ii) Note that we characterized three models of quantum finite automata in the framework of hybrid systems in [14]; all of them can be regarded as a concrete implementation of the HQA model defined in this paper. For example, CL-1QFA [5] and 1QCFA [30] are instances of C-HQA, and 1QFAC [21] are instances of Q-HQA. Thus, the HQA given by us is a generalized model.…”

Section: Definition 3 a Hybrid Quantum Automaton (Hqa) Is A Tuplementioning

confidence: 99%

“…In order to describe hybrid systems that receive inputs or actions from the outer world, we propose the notion of hybrid quantum automata (HQA) that generalize semi-quantum finite automata or other models studied by Ambainis and Watrous, and Qiu etc (see e.g. [3,5,21,30,31,29]). In fact, these automata in the mentioned references as hybrid systems have been described in a uniform way by the authors [14].…”

Section: Introductionmentioning

confidence: 99%

Quantum Markov chains: Description of hybrid systems, decidability of equivalence, and model checking linear-time properties

Feng

2015

Information and Computation

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In this paper, we study a model of quantum Markov chains that is a quantum analogue of Markov chains and is obtained by replacing probabilities in transition matrices with quantum operations. We show that this model is very suited to describe hybrid systems that consist of a quantum component and a classical one, although it has the same expressive power as another quantum Markov model proposed in the literature. Indeed, hybrid systems are often encountered in quantum information processing; for example, both quantum programs and quantum protocols can be regarded as hybrid systems. Thus, we further propose a model called hybrid quantum automata (HQA) that can be used to describe these hybrid systems that receive inputs (actions) from the outer world. We show the language equivalence problem of HQA is decidable in polynomial time. Furthermore, we apply this result to the trace equivalence problem of quantum Markov chains, and thus it is also decidable in polynomial time. Finally, we discuss model checking linear-time properties of quantum Markov chains, and show the quantitative analysis of regular safety properties can be addressed successfully.

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“…In Section 4.5, we saw a twoway QFA model that has classical as well as quantum states, and the classical states govern the computation flow and the determination of whether intermediate measurements or unitary transformations should be performed, depending on both input symbols and previous measurement results. A real-time version of such a model, realizing a unitary transformation, a projective measurement (see Figure 5), and classical evolution in each step, has been defined formally in [29], and can easily simulate any rtPFA, for instance. In this section, we focus on a restricted version of this model, and show that the full power of superoperators, generalizing unitary evolution and measurement transformations, is still retained.…”

Section: General Qfasmentioning

confidence: 99%