Related papers: Probabilistic and quantum finite automata with pos…
The challenge of pattern recognition is to invoke a strategy that can accurately extract features of a dataset and classify its samples. In realistic scenarios this dataset may be a physical system from which we want to retrieve…
History-deterministic automata are those in which nondeterministic choices can be correctly resolved stepwise: there is a strategy to select a continuation of a run given the next input letter so that if the overall input word admits some…
In recent years, the modeling interest has increased significantly from the molecular level to the atomic and quantum scale. The field of computational chemistry plays a significant role in designing computational models for the operation…
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…
In this paper the notion of quantum finite one-counter automata (QF1CA) is introduced. Introduction of the notion is similar to that of the 2-way quantum finite state automata by A.Kondacs and J.Watrous. The well-formedness conditions for…
We present a simple construction of quantum automata which achieve an exponential advantage over classical finite automata. Our automata use \frac{4}{\epsilon} \log 2p + O(1) states to recognize a language that requires p states…
Quantum Phase Estimation is a crucial component of several front-running quantum algorithms. Improving the efficiency and accuracy of QPE is currently a very active field of research. In this work, we present a hybrid quantum-classical…
We find an application in quantum finite automata for the ideas and results of [JL21] and [JL22]. We reformulate quantum finite automata with multiple-time measurements using the algebraic notion of near-ring. This gives a unified…
In the literature, there exist several interesting hybrid models of finite automata which have both quantum and classical states. We call them semi-quantum automata. In this paper, we compare the descriptional power of these models with…
The emptiness and containment problems for probabilistic automata are natural quantitative generalisations of the classical language emptiness and inclusion problems for Boolean automata. It is well known that both problems are undecidable.…
The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied…
Recent developments in Quantum Machine Learning have seen the introduction of several models to generalize the classical perceptron to the quantum regime. The capabilities of these quantum models need to be determined precisely in order to…
Recent breakthroughs in generative machine learning, powered by massive computational resources, have demonstrated unprecedented human-like capabilities. While beyond-classical quantum experiments can generate samples from classically…
We present characterisations of "exact" gap-definable classes, in terms of indeterministic models of computation which slightly modify the standard model of quantum computation. This follows on work of Aaronson [arXiv:quant-ph/0412187], who…
In this paper, we introduce and explore a new model of {\it quantum finite automata} (QFA). Namely, {\it one-way finite automata with quantum and classical states} (1QCFA), a one way version of {\it two-way finite automata with quantum and…
We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering…
Quantum simulation advantage over classical memory limitations would allow compact quantum circuits to yield insight into intractable quantum many-body problems, but the interrelated obstacles of large circuit depth in quantum time…
Probabilistic B\"uchi Automata (PBA) are randomized, finite state automata that process input strings of infinite length. Based on the threshold chosen for the acceptance probability, different classes of languages can be defined. In this…
Through superposition, a quantum computer is capable of representing an exponentially large set of states, according to the number of qubits available. Quantum machine learning is a subfield of quantum computing that explores the potential…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…