Related papers: Magic coins are useful for small-space quantum mac…
Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not being fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example…
Unambiguous non-deterministic finite automata have intermediate expressive power and succinctness between deterministic and non-deterministic automata. It has been conjectured that every unambiguous non-deterministic one-way finite…
A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations to a universal set by the addition of `magic' quantum states. In this context, we develop a general…
A recently introduced classical simulation method for universal quantum computation with magic states operates by repeated sampling from probability functions [M. Zurel et al. PRL 260404 (2020)]. This method is closely related to sampling…
The fundamental principles of quantum mechanics, such as its probabilistic nature, allow for the theoretical ability of quantum computers to generate statistically random numbers, as opposed to classical computers which are only able to…
We explore bounds of {\em time-space tradeoffs} in language recognition on {\em two-way finite automata} for some special languages. We prove: (1) a time-space tradeoff upper bound for recognition of the languages $L_{EQ}(n)$ on {\em…
Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are…
We show that every quantum computation can be described by Bayesian update of a probability distribution on a finite state space. When applied to the model of quantum computation with magic states, the size of this state space only depends…
We show on the example of the Arnold cat map that classical chaotic systems can be simulated with exponential efficiency on a quantum computer. Although classical computer errors grow exponentially with time, the quantum algorithm with…
This paper presents efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with $\epsilon$-transitions. It gives an algorithm for testing the exponential ambiguity of an automaton $A$ in time…
Deutsch, Feynman, and Manin viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a…
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…
As Machine Translation (MT) becomes increasingly commonplace, understanding how the general public perceives and relies on imperfect MT is crucial for contextualizing MT research in real-world applications. We present a human study…
We examine the characteristic features of reversible and quantum computations in the presence of supplementary external information, known as advice. In particular, we present a simple, algebraic characterization of languages recognized by…
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,…
In this paper, we modify some previous definitions of fuzzy Turing machines to define the notions of accepting and rejecting degrees of inputs, computationally. We use a BFS-based search method and obtain an upper level bound to guarantee…
While Large Language Models (LLMs) excel at temporal reasoning tasks like event ordering and duration estimation, their ability to perceive the actual passage of time remains unexplored. We investigate whether LLMs perceive the passage of…
We discuss counterintuitive aspects of probabilities for systems of identical particles obeying quantum statistics. Quantum coins and children (two level systems) and quantum dice (many level systems) are used as examples. It is emphasized…
In this paper, we consider Turing machines based on unsharp quantum logic. For a lattice-ordered quantum multiple-valued (MV) algebra E, we introduce E-valued non-deterministic Turing machines (ENTMs) and E-valued deterministic Turing…
Quantum computers take advantage of interfering quantum alternatives in order to handle problems that might be too time consuming with algorithms based on classical logic. Developing quantum computers requires new ways of thinking beyond…