Related papers: A Unified Combination of Classical and Quantum Sys…
Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…
A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…
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…
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical…
Conventional canonical quantization procedures directly link various c-number and q-number quantities. Here, we advocate a different association of classical and quantum quantities that renders classical theory a natural subset of quantum…
Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
We present an alternative quantization procedure for the one-dimensional non-relativistic quantum mechanics. We show that, for the case of a free particle and a particle in a box, the complete classical and quantum correspondence can be…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
In this Letter we propose two path integral approaches to describe the classical mechanics of spinning particles. We show how these formulations can be derived from the associated quantum ones via a sort of geometrical dequantization…
Quantifying the resources available to a quantum computer appears to be necessary to separate quantum from classical computation. Among them, entanglement, nonstabilizerness and coherence are arguably of great significance. We introduce…
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
Systems with constraints pose problems when they are quantized. Moreover, the Dirac procedure of quantization prior to reduction is preferred. The projection operator method of quantization, which can be most conveniently described by…
Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations,…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
The act of describing how a physical process changes a system is the basis for understanding observed phenomena. For quantum-mechanical processes in particular, the affect of processes on quantum states profoundly advances our knowledge of…
We introduce Qunity, a new quantum programming language designed to treat quantum computing as a natural generalization of classical computing. Qunity presents a unified syntax where familiar programming constructs can have both quantum and…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…