Quantum Computing of Poincare Recurrences and Periodic Orbits

Abstract

Quantum algorithms are built enabling to find Poincar\'e recurrence times and periodic orbits of classical dynamical systems. It is shown that exponential gain compared to classical algorithms can be reached for a restricted class of systems. Quadratic gain can be achieved for a larger set of dynamical systems. The simplest cases can be implemented with small number of qubits.