Exponentially more concise quantum recognition of non-RMM regular languages

Qiu, Daowen; Li, Lvzhou; Mateus, Paulo; Sernadas, Amı́lcar

doi:10.48550/arxiv.0909.1428

Cited by 7 publications

(10 citation statements)

References 39 publications

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“…In the study of QFA, an important problem is to characterize the language classes recognized by various models (e.g., [1,5,7]). This problem was considered for CL-1QFA in [6,17] and for 1QFAC in [25]. Using our results presented in the previous sections, we can show that the three hybrid models indeed have the same language recognition power in the following sense.…”

Section: Language Recognition Power and Equivalence Problem Of Hybrid...mentioning

confidence: 60%

“…Very recently, Qiu et al [25] proposed a new hybrid model called 1QFA together with classical states (1QFAC, for short) which consists of a quantum component and a classical one. On scanning an input symbol, the two components interact in the following way: first the quantum component undergoes a unitary operator that is determined by the current classical state and the scanned symbol, and then the classical component evolves like a DFA.…”

Section: Hybrid Models Of Qfamentioning

confidence: 99%

“…After scanning the whole input string, a projective measurement determined by the final classical state is performed on the final quantum state, giving the accepting and rejecting probabilities. In [25], it was proved that 1QFAC recognize all regular languages and are exponentially more concise than DFA for certain languages.…”

Section: Hybrid Models Of Qfamentioning

confidence: 99%

“…Last but not least, quantum engineering systems developed in the further will most probably have a classical human-interactive interface and a quantum processor, and thus they are hybrid models. In fact, hybrid models have already been encountered several times in quantum computing, varying from quantum Turing machines [27] and quantum finite automata [4,6,25] to multiple-prover quantum interactive proof systems (the model of complexity class MIP * [8]) and quantum programming [28]. 2 This paper aims to characterize the structure of these hybrid models in a uniform framework and to clarify the relationship between these models and others.…”

Section: Motivation and Contribution Of The Papermentioning

confidence: 99%

“…Recently, Qiu et al [25] proposed a new model named 1QFA together with classical states (1QFAC), defined as follows. 4 Definition 2.…”

Section: Qfac: a Hybrid Model With Classical-quantum Communicationmentioning

confidence: 99%

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On hybrid models of quantum finite automata

Feng

2015

Journal of Computer and System Sciences

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In the literature, there exist several quantum finite automata (QFA) models with both quantum and classical states. These models are of particular interest,as they show praiseworthy advantages over the fully quantum models in some nontrivial aspects. This paper characterizes these models in a uniform framework by proposing a general hybrid model consisting of a quantum component and a classical one which can interact with each other. The existing hybrid QFA can be naturally regarded as the general model with specific communication patterns (classical-quantum, quantum-classical, and two-way, respectively). We further clarify the relationship between these hybrid QFA and some other quantum models. In particular, it is shown that hybrid QFA can be simulated exactly by QFA with quantum operations, which in turn has a close relationship with two early proposed models: {\it ancialla QFA} and {\it quantum sequential machines}.Comment: The paper has been revised such that it is more concise and has a better structure. All comments are welcom

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Section: Language Recognition Power and Equivalence Problem Of Hybrid...mentioning

confidence: 60%

Section: Hybrid Models Of Qfamentioning

confidence: 99%

Section: Hybrid Models Of Qfamentioning

confidence: 99%

Section: Motivation and Contribution Of The Papermentioning

confidence: 99%

“…Recently, Qiu et al [25] proposed a new model named 1QFA together with classical states (1QFAC), defined as follows. 4 Definition 2.…”

Section: Qfac: a Hybrid Model With Classical-quantum Communicationmentioning

confidence: 99%

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On hybrid models of quantum finite automata

Feng

2015

Journal of Computer and System Sciences

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Generalizations of the distributed Deutsch–Jozsa promise problem

Gruska

Qiu

Zheng

2015

Math. Struct. Comp. Sci.

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In the distributed Deutsch-Jozsa promise problem, two parties are to determine whether their respective strings x, y ∈ {0, 1} n are at the Hamming distance H(x, y) = 0 or H(x, y) = n 2 . Buhrman et al. (STOC' 98) proved that the exact quantum communication complexity of this problem is O(log n) while the deterministic communication complexity is Ω(n). This was the first impressive (exponential) gap between quantum and classical communication complexity. In this paper, we generalize the above distributed Deutsch-Jozsa promise problem to determine, for any fixed n 2 ≤ k ≤ n, whether H(x, y) = 0 or H(x, y) = k, and show that an exponential gap between exact quantum and deterministic communication complexity still holds if k is an even such that 1 2 n ≤ k < (1 − λ)n, where 0 < λ < 1 2 is given. We also deal with a promise version of the well-known disjointness problem and show also that for this promise problem there exists an exponential gap between quantum (and also probabilistic) communication complexity and deterministic communication complexity of the promise version of such a disjointness problem. Finally, some applications to quantum, probabilistic and deterministic finite automata of the results obtained are demonstrated. (D. Qiu). 2We prove that quantum communication complexity of DISJ λ is not more than log 3 3λ (3 + 2 log n) while the deterministic communication complexity is Ω(n). For example, if λ = 1 4 , then the quantum communication complexity of DISJ λ is not more than 3 + 2log n while the deterministic communication complexity is more than 0.007n. We prove also that probabilistic communication complexity of DISJ λ is not more than log 3 λ log n. Therefore, there is an exponential gap between quantum (and also probabilistic) communication complexity and deterministic communication complexity of the above promise problem.Number of states is a natural complexity measure for all models of finite automata and state complexity of finite automata is one of the research fields with many applications [36]. There is a variety of methods how to prove lower bounds on the state complexity and methods as well as the results of communication complexity are among the main ones [23,25,26]. In this paper we also show how to make use of our new communication complexity results to get new state complexity bounds.The paper is structured as follows. In Section 2 basic needed concepts and notations are introduced and models involved are described in details. Communication complexities and query complexities of the promise problems EQ k and DJ k are investigated in Section 3. Communication complexity of the promise problem DISJ λ is dealt with in Section 4. Applications to finite automata are explored in Section 5. Some open problems are discussed in Section 6. PreliminariesIn this section, we recall some basic definitions about communication complexity, query complexity and quantum finite automata. Concerning basic concepts and notations of quantum information processing, we refer the reader to [18,29]. Communication comp...

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Characterizations of one-way general quantum finite automata

Qiu

Zou

et al. 2009

Preprint

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Exponentially more concise quantum recognition of non-RMM regular languages

Cited by 7 publications

References 39 publications

On hybrid models of quantum finite automata

On hybrid models of quantum finite automata

Generalizations of the distributed Deutsch–Jozsa promise problem

Characterizations of one-way general quantum finite automata

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