Related papers: Are Quantum-Classical Hybrids compatible with Onto…
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
This paper proposed a quantum analogue of classical queue automata by using the definition of the quantum Turing machine and quantum finite-state automata. However, quantum automata equipped with storage medium of a stack has been…
In the Copenhagen viewpoint, part of the world is quantized and the complementary part remains classical. From a formal dynamic aspect, standard theory is incomplete since it does never account for the so-called 'back-reaction' of quantized…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
Simulations that couple different classical molecular models in an adaptive way by changing the number of degrees of freedom on the fly, are available within reasonably consistent theoretical frameworks. The same does not occur when 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 consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…
Although quantum computers are predicted to have many commercial applications, less attention has been given to their potential for resolving foundational issues in quantum mechanics. Here we focus on quantum computers' utility for the…
We employ quantum circuit learning to simulate quantum field theories (QFTs). Typically, when simulating QFTs with quantum computers, we encounter significant challenges due to the technical limitations of quantum devices when implementing…
Here we show that the concepts behind such terms as entanglement, qubits, quantum gates, quantum error corrections, unitary time evolution etc., which are usually ascribed to quantum systems, can be adequately realized on a set of coupled…
We introduce a quantum analogue of a classical synchronizing automaton. In classical case the state of a system evolves according to a set of rules forming an alphabet, and sequences of these rules, called words, govern its evolution.…
Quantum and classical systems can consistently be coupled via non-unitary time-irreversible mechanisms. In this paper we characterize which kind of corresponding dynamics converge in the stationary regime to a thermal hybrid state, that is,…
Possibility of state cloning is analyzed in two types of generalizations of quantum mechanics with nonlinear evolution. It is first shown that nonlinear Hamiltonian quantum mechanics does not admit cloning without the cloning machine. It is…
We consider discrete and integer-valued cellular automata (CA). A particular class of which comprises "Hamiltonian CA" with equations of motion that bear similarities to Hamilton's equations, while they present discrete updating rules. The…
We present a consistent framework of coupled classical and quantum dynamics. Our result allows us to overcome severe limitations of previous phenomenological approaches, like evolutions that do not preserve the positivity of quantum states…
Although the foundations of quantum and classical physics are much different, it is often difficult to pinpoint which features of a particular system are intrinsically "quantum". Perhapse, the most clear-cut distinction between "classical"…
A formulation of quantum-classical hybrid dynamics is presented, which concerns the direct coupling of classical and quantum mechanical degrees of freedom. It is of interest for applications in quantum mechanical approximation schemes and…
Representation of classical dynamics by unitary transformations has been used to develop unified description of hybrid classical-quantum systems with particular type of interaction, and to formulate abstract systems interpolating between…
Entanglement between quantum and classical objects is of special interest in the context of fundamental studies of quantum mechanics and potential applications to quantum information processing. In quantum optics, single photons are treated…