Related papers: Improved constructions of quantum automata
Two quantum finite automata are equivalent if for all input string $\omega$ over the input alphabet the two automata accept $\omega$ with equal probability. In [Theoret. Comput. Sci. 410 (2009) 3006-3017], it was shown that a $k_1$-letter…
Quantum fingerprinting is a technique that maps classical input word to a quantum state. The obtained quantum state is much shorter than the original word, and its processing uses less resources, making it useful in quantum algorithms,…
The classical powerset construction is a standard method converting a non-deterministic automaton into a deterministic one recognising the same language. Recently, the powerset construction has been lifted to a more general framework that…
Stochastic languages are the languages recognized by probabilistic finite automata (PFAs) with cutpoint over the field of real numbers. More general computational models over the same field such as generalized finite automata (GFAs) and…
We show that a special case of the Feferman-Vaught composition theorem gives rise to a natural notion of automata for finite words over an infinite alphabet, with good closure and decidability properties, as well as several logical…
We present five examples where quantum finite automata (QFAs) outperform their classical counterparts. This may be useful as a relatively simple technique to introduce quantum computation concepts to computer scientists. We also describe a…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
We show that there are quantum devices that accept all regular languages and that are exponentially more concise than deterministic finite automata (DFA). For this purpose, we introduce a new computing model of {\it one-way quantum finite…
Herein we survey the main results concerning quantum automata and machines with classical control. These machines were originally proposed by Sernadas et al in [37], during the FCT QuantLog project. First, we focus on the expressivity of…
This paper introduces a formal metalanguage called the lambda-q calculus for the specification of quantum programming languages. This metalanguage is an extension of the lambda calculus, which provides a formal setting for the specification…
In this work we use a framework of finite-state automata constructions based on equivalences over words to provide new insights on the relation between well-known methods for computing the minimal deterministic automaton of a language.
We implement a quantum hashing algorithm which is based on a fingerprinting technique presented by Ambainis and Frievalds, 1988, on gate-based quantum computers. This algorithm is based on a quantum finite automaton for a unary language…
Quantum technology has the potential to revolutionize how we acquire and process experimental data to learn about the physical world. An experimental setup that transduces data from a physical system to a stable quantum memory, and…
The space P of pure states of any physical system, classical or quantum, is identified as a Poisson space with a transition probability. The latter is a function p: PxP -> [0,1]; in addition, a Poisson bracket is defined for functions on P.…
Every language recognized by a non-deterministic finite automaton can be recognized by a deterministic automaton, at the cost of a potential increase of the number of states, which in the worst case can go from $n$ states to $2^n$ states.…
We show that one-way quantum one-counter automaton with zero-error is more powerful than its probabilistic counterpart on promise problems. Then, we obtain a similar separation result between Las Vegas one-way probabilistic one-counter…
Let $f$ denote length preserving function on words. A classical algorithm can be considered as $T$ iterated applications of black box representing $f$, beginning with input word $x$ of length $n$. It is proved that if $T=O(2^{n/(7+e)}), e…
It is an open problem to characterize the class of languages recognized by quantum finite automata (QFA). We examine some necessary and some sufficient conditions for a (regular) language to be recognizable by a QFA. For a subclass of…
In a recent paper we have described an optical implementation of a measure-once one-way quantum finite automaton recognizing a well-known family of unary periodic languages, accepting words not in the language with a given error…
Probabilistic omega-automata are variants of nondeterministic automata for infinite words where all choices are resolved by probabilistic distributions. Acceptance of an infinite input word can be defined in different ways: by requiring…