Koopman–von Neumann approach to quantum simulation of nonlinear classical dynamics
I. Joseph
Abstract
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.
Topics & Concepts
Hamiltonian (control theory)Von Neumann architectureNonlinear systemPhase spaceUnitary stateNonlinear Schrödinger equationMathematical physicsQuantumHermitian matrixSchrödinger's catQuantum dynamicsOperator (biology)Unitary operatorMathematicsClassical mechanicsPhysicsHilbert spaceMathematical analysisQuantum mechanicsPure mathematicsBiochemistryLawRepressorPolitical scienceGeneTranscription factorMathematical optimizationChemistryModel Reduction and Neural NetworksQuantum many-body systemsQuantum Computing Algorithms and Architecture