An application of continuous-variable gate synthesis to quantum simulation of classical dynamics

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. A less explored possibility with comparably far-reaching technological applicability is the quantum simulation of classical nonlinear dynamics. Attempts to develop digital quantum algorithms based on the Koopman–von Neumann (KvN) formalism have met with challenges because of the necessary projection step from an infinite-dimensional Hilbert space to the finite-dimensional subspace described by a collection of qubits. This finitization produces numerical artifacts that limit solutions to very short time horizons. In this paper, we review continuous-variable quantum computing (CVQC), which naturally avoids such obstacles, and a CVQC algorithm for KvN simulation of classical nonlinear dynamics is advocated. In particular, we present explicit gate synthesis for product-formula Hamiltonian simulation of anharmonic vibrational dynamics.