Applied/ACMS/abs23

Title: Quantum information for simulation of classical dynamics

Abstract: We present a framework for simulating classical dynamical systems by finite-dimensional quantum system amenable to implementation on a quantum computer. Using ideas from kernel-based machine learning, the framework employs a quantum feature map for representing classical states by density operators on a reproducing kernel Hilbert space (RKHS). Simultaneously, a mapping is employed to represent classical observables by quantum observables on the RKHS such that quantum mechanical expectation values are consistent with pointwise function evaluation. With this approach, quantum states and observables evolve under the Koopman operator of the dynamical system in a consistent manner with classical evolution. Moreover, the state of the quantum system can be projected onto a finite-rank density operator on a tensor product Hilbert space, enabling efficient implementation in a quantum circuit. We illustrate our approach with quantum circuit simulations of low-dimensional dynamical systems, as well as actual experiments on the IBM Quantum System One.