Related papers: On the state complexity of semi-quantum finite aut…
Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of…
We continue the systematic investigation of probabilistic and quantum finite automata (PFAs and QFAs) on promise problems by focusing on unary languages. We show that bounded-error QFAs are more powerful than PFAs. But, in contrary to the…
Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks.…
Quantum finite automata (QFA) are basic computational devices that make binary decisions using quantum operations. They are known to be exponentially memory efficient compared to their classical counterparts. Here, we demonstrate an…
While quantum architectures are still under development, when available, they will only be able to process quantum data when machine learning algorithms can only process numerical data. Therefore, in the issues of classification or…
We design machines that learn how to rotate a quantum bit about an initially unknown direction, encoded in the state of a spin-j particle. We show that a machine equipped with a quantum memory of O(log j) qubits can outperform all machines…
Recent years have seen significant activity on the problem of using data for the purpose of learning properties of quantum systems or of processing classical or quantum data via quantum computing. As in classical learning, quantum learning…
The core of quantum machine learning is to devise quantum models with good trainability and low generalization error bound than their classical counterparts to ensure better reliability and interpretability. Recent studies confirmed that…
A two-way deterministic finite state automaton with one counter (2D1CA) is a fundamental computational model that has been examined in many different aspects since sixties, but we know little about its power in the case of unary languages.…
Standard formulations of quantum theory are based on complex numbers: Quantum states can be in superpositions, with weights given by complex probability amplitudes. Motivated by quantum theory promising a range of practical advantages over…
For the last few decades, classical machine learning has allowed us to improve the lives of many through automation, natural language processing, predictive analytics and much more. However, a major concern is the fact that we're fast…
We first show that given a $k_1$-letter quantum finite automata $\mathcal{A}_1$ and a $k_2$-letter quantum finite automata $\mathcal{A}_2$ over the same input alphabet $\Sigma$, they are equivalent if and only if they are…
The future development of quantum technologies relies on creating and manipulating quantum systems of increasing complexity, with key applications in computation, simulation and sensing. This poses severe challenges in the efficient…
Recently, the use of mathematical methods and computer science applications have got significant response among biochemists and biologists to modeling the biological systems. The computational and mathematical methods have enormous…
It is becoming increasingly clear that, if a useful device for quantum computation will ever be built, it will be embodied by a classical computing machine with control over a truly quantum subsystem, this apparatus performing a mixture of…
Multi-letter {\it quantum finite automata} (QFAs) were a quantum variant of classical {\it one-way multi-head finite automata} (J. Hromkovi\v{c}, Acta Informatica 19 (1983) 377-384), and it has been shown that this new one-way QFAs…
Whether winning blackjack or navigating busy streets, achieving desired outcomes requires agents to execute adaptive strategies, strategies where actions depend contextually on past events. In complexity science, this motivates memory as an…
The simulation of quantum effects requires certain classical resources, and quantifying them is an important step in order to characterize the difference between quantum and classical physics. For a simulation of the phenomenon of…
Quantum resources may provide advantage over their classical counterparts. We say this as quantum advantage. Here we consider a single communication task to study different approaches of observing quantum advantage. We say this setting as a…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…