Related papers: Quantum Dynamics Simulation with Classical Oscilla…
The classical and quantum dynamics of the noncanonically coupled oscillators is considered. It is shown that though the classical dynamics is well--defined for both harmonic and anharmonic oscillators, the quantum one is well--defined in…
Glauber coherent states of quantum systems are reviewed. We construct the tomographic probability distributions of the oscillator states. The possibility to describe quantum states by tomographic probability distributions (tomograms) is…
A quantum unitary evolution alternated with measurements is simulated by a bubble filled with fictitious particles called amplitude quanta that move chaotically and can be transformed by the simple rules that look like chemical reactions. A…
We use spin coherent states to compare classical and quantum evolution of a simple paradigmatic, discrete-time quantum dynamical system exhibiting chaotic behavior in the classical limit. The spin coherent states are employed to define a…
The relation that exists in quantum mechanics among action variables, angle variables and the phases of quantum states is clarified, by referring to the system of a generalized oscillator. As a by-product, quantum-mechanical meaning of the…
The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the…
In previous work, we introduced a formalism that maps classical networks of nonlinear oscillators onto a quantum-like Hilbert space. We demonstrated that specific network transformations correspond to quantum gates, underscoring the…
Motivated by quantum gravity, semi-classical theory, and quantum theory on curved spacetimes, we study the system of an oscillator coupled to two spin-1/2 particles. This model provides a prototype for comparing three types of dynamics: the…
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.…
Macroscopic ensembles of radiating dipoles are ubiquitous in the physical and natural sciences. In the classical limit the dipoles can be described as damped-driven oscillators, which are able to spontaneously synchronize and collectively…
We develop a framework for simulating measure-preserving, ergodic dynamical systems on a quantum computer. Our approach provides a new operator-theoretic representation of classical dynamics by combining ergodic theory with quantum…
Simulating key static and dynamic properties of matter -- from creation in the Big Bang to evolution into sub-atomic and astrophysical environments -- arising from the underlying fundamental quantum fields of the Standard Model and their…
In this paper, we develop a new classical simulation of quantum bit (qubit) by use of analog components in order to be able to simulate the quantum properties such as the superposition of states. As part of this new approach, we have also…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum…
We investigate new features, especially of entanglement dynamics, which arise in a quantum-classical hybrid. As a model, we study the coupling between two quantum mechanical two-level systems, i.e. two q-bits, and a classical harmonic…
While quantum simulation is one of the most promising applications of modern quantum devices, accessible simulation times are fundamentally limited by finite coherence times due to omnipresent noise. Based on the ideas of relational…
It is often argued that two linearly coupled quantum harmonic oscillators, even when cooled to their ground state, display no inherently quantum features beyond quantized energy levels. Here, we challenge this view by showing that their…
We describe quantum behaviors of a simple harmonic oscillator, starting from the classical mechanics. By imposing two conditions on the phase points generated from a symplectic algorithm, we obtain discrete energy levels, satisfying $E_n…