Implementing the Koopman-von Neumann approach on continuous-variable photonic quantum computers

• URL: http://arxiv.org/abs/2512.13887v1
• Date: Mon, 15 Dec 2025 20:45:33 GMT
• Title: Implementing the Koopman-von Neumann approach on continuous-variable photonic quantum computers
• Authors: Xinfeng Gao, Olivier Pfister, Stefan Bekiranov,
• Abstract summary: Koopman-von Neumann (KvN) formalism recasts classical mechanics in a Hilbert space framework using complex wavefunctions and linear operators.<n>Mapped to quantum computing, KvN offers a promising route to simulate classical dynamical systems.<n>We specifically explore the implementation of the KvN approach on continuous-variable photonic quantum computing architectures.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Koopman-von Neumann (KvN) formalism recasts classical mechanics in a Hilbert space framework using complex wavefunctions and linear operators, akin to quantum mechanics. Instead of evolving probability densities in phase space (as in Liouville's equation), KvN uses a Schrödinger-like equation for a classical wavefunction, with commuting position and momentum operators. Mapped to quantum computing, KvN offers a promising route to simulate classical dynamical systems using quantum algorithms by leveraging unitary evolution and quantum linear algebra tools, potentially enabling efficient classical-to-quantum mappings without invoking full quantum uncertainty. In this work, we specifically explore the implementation of the KvN approach on continuous-variable photonic quantum computing architectures, with the goals of leveraging quantum simulation for both sampling and computing intractable nonlinear dynamics. We will demonstrate its implementation and feasibility with two problems: the harmonic oscillator and a 1D partial differential equation governing nonlinear dynamics.

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