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In this thesis, we introduce a new quantum Turing machine (QTM) model that supports general quantum operators, together with its pushdown, counter, and finite automaton variants, and examine the computational power of classical and quantum…

Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…

We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced…

Quantum Cellular Automaton (QCA) is a model for universal quantum computation and a natural candidate for digital quantum simulation of relativistic quantum fields. Here we introduce the first photonic platform for implementing…

A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability…

The way Quantum Mechanics (QM) is introduced to people used to Classical Mechanics (CM) is by a complete change of the general methodology) despite QM historically stemming from CM as a means to explain experimental results. Therefore, it…

The main goal of this paper is to give a rigorous mathematical description of systems for processing quantum information. To do it authors consider abstract state machines as models of classical computational systems. This class of machines…

We present and discuss a formal approach for describing the quantum to classical crossover based on the group-theoretic construction of generalized coherent states. The method was originally introduced by L. Yaffe in 1982 for tackling…

We show that quantum theory (QT) is a substructure of classical probabilistic physics. The central quantity of the classical theory is Hamilton's function, which determines canonical equations, a corresponding flow, and a Liouville equation…

A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…

Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is…

Quantum computers are considered as a part of the family of the reversible, lineary-extended, dynamical systems (Quanputers). For classical problems an operational reformulation is given. A universal algorithm for the solving of classical…

This study introduces a method for simulating quantum systems using electrical networks. Our approach leverages a generalized similarity transformation, which connects different Hamiltonians, enabling well-defined paths for quantum system…

We show that the separability of states in quantum mechanics has a close counterpart in classical physics, and that conditional mutual information (a.k.a. conditional information transmission) is a very useful quantity in the study of both…

We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from…

In automata theory, the quantum computation has been widely examined for finite state machines, known as quantum finite automata (QFAs), and less attention has been given to the QFAs augmented with counters or stacks. Moreover, to our…

In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.

In physics, one is often misled in thinking that the mathematical model of a system is part of or is that system itself. Think of expressions commonly used in physics like "point" particle, motion "on the line", "smooth" observables, wave…

Classical and quantum correlation functions are derived for a system of non-interacting particles moving on a circle. It is shown that the decaying behaviour of the classical expression for the correlation function can be recovered from the…

In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in…