Related papers: Implementing the Koopman-von Neumann approach on c…
Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman-von Neumann theory, this paper addresses the long-standing problem of formulating a dynamical theory of classical-quantum coupling. The proposed model not only…
The growing computational demands of classical neural networks have intensified the search for energy-efficient and powerful computational alternatives. Quantum neural networks (QNNs) implemented on integrated photonic platforms offer a…
We present a super-polynomial improvement in the precision scaling of quantum simulations for coupled classical-quantum systems in this paper. Such systems are found, for example, in molecular dynamics simulations within the…
Most modern classical processors support so-called von Neumann architecture with program and data registers. In present work is revisited similar approach to models of quantum processors. Deterministic programmable quantum gate arrays are…
In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…
Nelson's stochastic mechanics links quantum mechanics to an underlying Brownian motion with the identification $\hbar = m\sigma$. Ghose's interpolating equation introduces a continuous parameter $\lambda$ that suppresses the quantum…
We deal with the reversible dynamics of coupled quantum and classical systems. Based on a recent proposal by the authors, we exploit the theory of hybrid quantum-classical wavefunctions to devise a closure model for the coupled dynamics in…
Classical mechanics (CM), like quantum mechanics (QM), can have an operatorial formulation. This was pioneered by Koopman and von Neumann (KvN) in the 30's. They basically formalized, via the introduction of a classical Hilbert space,…
The original intent of the Koopman-von Neumann formalism was to put classical and quantum mechanics on the same footing by introducing an operator formalism into classical mechanics. Here we pursue their path the opposite way and examine…
Quantum computing has brought a paradigm change in computer science, where non-classical technologies have promised to outperform their classical counterpart. Such an advantage was only demonstrated for tasks without practical applications,…
Motivated by recent discussions on the possible role of quantum computation in plasma simulations, here we present different approaches to Koopman's Hilbert-space formulation of classical mechanics in the context of Vlasov-Maxwell kinetic…
It has long been known that there exists a coordinate transformation which exactly maps the quantum free particle to the quantum harmonic oscillator. Here we extend this result by reformulating it as a unitary operation followed by a time…
Continuous-variables (CV) quantum optics is a natural formalism for neural networks (NNs) due to its ability to reproduce the information processing of such trainable interconnected systems. In quantum optics, Gaussian operators induce…
Koopman and von Neumann (KvN) extended the Liouville equation by introducing a phase space function $S^{(K)}(q,p,t)$ whose physical meaning is unknown. We show that a different $S(q,p,t)$, with well-defined physical meaning, may be…
The Koopman-von Neumann (KvN) mechanics is an approach that was formulated long ago to answer the question regarding the existence of a Hilbert space representation of classical mechanics. KvN mechanics is a non-relativistic theory, and it…
The Eisenhart lift establishes a fascinating connection between non-relativistic and relativistic physics, providing a space-time geometric understanding of non-relativistic Newtonian mechanics. What is still little known, however, is the…
We define an observable-space framework of Quantum Koopman Algorithms (QKAs) for simulating the dynamics of both linear quantum and nonlinear classical systems, based on approximately closed sets of observables and efficient coherent…
Variational quantum algorithms (VQAs) provide a promising approach to achieving quantum advantage for practical problems on near-term noisy intermediate-scale quantum (NISQ) devices. Thus far, most studies on VQAs have focused on…
Descriptions of classical mechanics in Hilbert space go back to the work of Koopman and von Neumann in the 1930s. Decades later, van Hove derived a unitary representation of the group of contact transformations which recently has been used…