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

TL;DR

This paper explores using continuous-variable quantum computing to simulate classical nonlinear dynamics, addressing limitations of qubit-based methods by proposing a CVQC approach with explicit gate synthesis for anharmonic vibrational systems.

Contribution

It introduces a CVQC algorithm for classical dynamics simulation, overcoming projection issues in qubit-based methods, with explicit gate synthesis for anharmonic vibrational Hamiltonians.

Findings

CVQC naturally avoids projection artifacts

Proposed explicit gate synthesis for anharmonic systems

Enhanced simulation of classical nonlinear dynamics

Abstract

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 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.