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Two Approaches to Quantum Simulation of Classical Dynamics

Ilon Joseph, Alessandro R. Castelli, Vasily Geyko +6 more

Bulletin of the American Physical SocietyMar 19, 20210 citations

Koopman–von Neumann approach to quantum simulation of nonlinear classical dynamics

Ilon Joseph

This paper shows how to use quantum computers to simulate nonlinear and non-Hamiltonian classical dynamics by using the Koopman-von Neumann approach, which reformulates the classical system as an equivalent Schrodinger equation with a Hermitian Hamiltonian and a unitary evolution operator on phase space.

arXiv:2003.09980Physical Review ResearchOct 19, 2020109 citations

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

Sam Cochran, JAMES M. STOKES, Paramsothy Jayakumar +1 more

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.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.

arXiv:2407.08006AVS Quantum ScienceApr 8, 20252 citations

Quantum Simulations of Classical Systems

Rolando D. Somma, Gerardo Ortíz, Cristian D. Batista +1 more

Bulletin of the American Physical SocietyMar 8, 20070 citations

Toward quantum simulations of sphaleron dynamics at colliders

Min Huang, Yingying Li, Yandong Liu +1 more

Sphaleron dynamics in the Standard Model at high-energy particle collisions remains experimentally unobserved, with theoretical predictions hindered by its nonperturbative real-time nature. In this work, we investigate a quantum simulation approach to this challenge. Taking the 1 + 1 D O ( 3 ) nonlinear σ -model as a protocol towards studying dynamics of the sphaleron in electroweak theory, we identify the sphaleron configuration and establish lattice parameters that reproduce continuum sphaleron energies with controlled precision. We then develop quantum algorithms to simulate sphaleron evolutions where quantum effects can be included. This work lays the ground to establish quantum simulations for studying the interaction between classical topological objects and particles in the quantum field theory that are usually inaccessible to classical methods and computations.Sphaleron dynamics in the Standard Model at high-energy particle collisions remains experimentally unobserved, with theoretical predictions hindered by its nonperturbative real-time nature. In this work, we investigate a quantum simulation approach to this challenge. Taking the 1 + 1 D O ( 3 ) nonlinear σ -model as a protocol towards studying dynamics of the sphaleron in electroweak theory, we identify the sphaleron configuration and establish lattice parameters that reproduce continuum sphaleron energies with controlled precision. We then develop quantum algorithms to simulate sphaleron evolutions where quantum effects can be included. This work lays the ground to establish quantum simulations for studying the interaction between classical topological objects and particles in the quantum field theory that are usually inaccessible to classical methods and computations.

arXiv:2510.08910Physical review. D/Physical review. D.Feb 17, 20260 citations

Nonlinear quantum dynamics

Salman Habib

arXiv:quant-ph/0505046Springer eBooksJun 25, 20062 citations

Quantum Simulation of Nonlinear Classical Dynamics

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