Quantum chaos in small quantum networks

Abstract

We study a 2-spin quantum Turing architecture, in which discrete local rotations {α m } of the Turing-head spin alternate with quantum controlled NOT operations. We show that a single chaotic parameter input {α m } leads to a chaotic dynamics in the entire Hilbert space. The instability of periodic orbits on the Turing head and ‘chaos swapping’ onto the Turing tape are demonstrated explicitly as well as exponential parameter sensitivity of the Bures metric.