Quantum Chaos and Quantum Computing Structures

TL;DR

This paper introduces a quantum computing framework capable of emulating classical nonlinear maps and exploring quantum chaos, revealing three distinct phases of quantum ensemble dynamics including regular, chaotic, and complex stochastic behavior.

Contribution

It presents a novel quantum computing structure that reproduces classical nonlinear dynamics and chaos, and reinterprets the quantum analog of the Poincaré map within this framework.

Findings

Quantum structures can emulate classical nonlinear maps.

Identification of three phases of quantum ensemble dynamics.

Reinterpretation of the quantum Poincaré map in this context.

Abstract

A system of quantum computing structures is introduced and proven capable of making emerge, on average, the orbits of classical bounded nonlinear maps on \mathbb{C} through the iterative action of path-dependent quantum gates. The effects of emerging nonlinear dynamics and chaos upon the quantum averages of relevant observables and quantum probabilities are exemplified for a version of Chirikov's standard map on \mathbb{C} . Both the individual orbits and ensemble properties are addressed so that the Poincar\'e map for Chirikov's standard map, in the current quantum setting, is reinterpreted in terms of a quantum ensemble which is then formally introduced within the formalized system of quantum computing structures, in terms of quantum register machines, revealing three phases of quantum ensemble dynamics: the regular, the chaotic and an intermediate phase called complex quantum stochastic phase which shares similarities to the edge of chaos notion from classical cellular automata and classical random boolean networks' evolutionary computation.