Testing integrability with a single bit of quantum information

Abstract

We show that deterministic quantum computing with a single bit (DQC1) can determine whether the classical limit of a quantum system is chaotic or integrable using O(N) physical resources, where $N$ is the dimension of the Hilbert space of the system under study. This is a square root improvement over all known classical procedures. Our study relies strictly on the random matrix conjecture. We also present numerical results for the nonlinear kicked top.

Minor changes taking into account Howard Wiseman's comment: quant-ph/0305153. Accepted for publication in Phys. Rev. A