Embedding classical dynamics in a quantum computer

Understand

We develop a framework for simulating measure-preserving, ergodic dynamical systems on a quantum computer.

• Our approach provides a new operator-theoretic representation of classical dynamics by combining ergodic theory with quantum information science.
• The resulting quantum embedding of classical dynamics (QECD) enables efficient simulation of spaces of classical observables with exponentially large dimension using a quadratic number of quantum gates.
• The QECD framework is based on a quantum feature map for representing classical states by density operators on a reproducing kernel Hilbert space, $\mathcal H $, and an embedding of classical observables into self-adjoint operators on $\mathcal H$.