Related papers: Implementing the Koopman-von Neumann approach on c…
Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman-von Neumann formulation of classical mechanics. The Koopman-von Neumann formulation implies that the…
This work is to consolidate current literature on Koopman-von Neumann (KvN) Mechanics into a simple and easy to understand text. KvN Mechanics is a branch of Classical Mechanics that has been recast into the mathematical language of Quantum…
The Koopman-von Neumann (KvN) formulation brings classical mechanics to Hilbert space, but many techniques familiar from quantum mechanics remain missing. One would hope to solve eigenvalue problems, obtain orthonormal eigenstates of…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
The Koopman--von Neumann (KvN) formulation of spectrally truncated fluid and plasma dynamics is considered as a potential approach for quantum computation. The KvN framework embeds the Liouville equation into a Hilbert space with…
In this thesis we study several features of the operatorial approach to classical mechanics pionereed by Koopman and von Neumann (KvN) in the Thirties. In particular in the first part we study the role of the phases of the KvN states. We…
Although quantum computing holds promise to accelerate a wide range of computational tasks, the quantum simulation of quantum dynamics as originally envisaged by Feynman remains the most promising candidate for achieving quantum advantage.…
To simulate plasma phenomena, large-scale computational resources have been employed in developing high-precision and high-resolution plasma simulations. One of the main obstacles in plasma simulations is the requirement of computational…
This is a review of recent research exploring and extending present-day quantum computing capabilities for fusion energy science applications. We begin with a brief tutorial on both ideal and open quantum dynamics, universal quantum…
The Koopman-von Neumann equation describes the evolution of wavefunctions associated with autonomous ordinary differential equations and can be regarded as a quantum physics-inspired formulation of classical mechanics. The main advantage…
In this paper we find a simple rule to reproduce the algebra of quantum observables using only the commutators and operators which appear in the Koopman-von Neumann (KvN) formulation of classical mechanics. The usual Hilbert space of…
This paper revisits the textbook 'particle in a box', but from the point of view of Koopman-von Neumann (KvN) mechanics. KvN mechanics is a way to describe \emph{classical} dynamics in a Hilbert space. That simple fact changes the usual…
The Koopman-von Neumann (KvN) theory is one where the dynamical momentum is not canonically conjugate to position, i.e., position and momentum are deconjugated. From this point of view, we show that the KvN theory arises from quantum…
Based on Koopman's theory of classical wavefunctions in phase space, we present the Koopman-van Hove (KvH) formulation of classical mechanics as well as some of its properties. In particular, we show how the associated classical Liouville…
In this paper we continue the study, started in [1], of the operatorial formulation of classical mechanics given by Koopman and von Neumann (KvN) in the Thirties. In particular we show that the introduction of the KvN Hilbert space of…
Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…
Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman…
The study of mathematical connections between operator-theoretic formulations of classical dynamics and quantum mechanics began at least as early as the 1930s in work of Koopman and von Neumann and was developed in later decades by many…
While it is well-known that quantum mechanics can be reformulated in terms of a path integral representation, it will be shown that such a formulation is also possible in the case of classical mechanics. From Koopman-von Neumann theory,…
We propose an explicit algorithm based on the Linear Combination of Hamiltonian Simulations technique to simulate both the advection-diffusion equation and a nonunitary discretized version of the Koopman-von Neumann formulation of nonlinear…