Random unitary dynamics of quantum networks

TL;DR

This paper studies the long-term behavior of quantum networks under repeated random unitary operations, revealing that their asymptotic dynamics are governed by a low-dimensional attractor space independent of operation probabilities.

Contribution

It provides a general analytical framework for understanding the asymptotic dynamics of large quantum networks with random unitary interactions, especially cyclic qubit networks.

Findings

Asymptotic dynamics are determined by a low-dimensional attractor space.

Attractor space depends only on the unitary operations, not their application probabilities.

Analytical results are derived for large cyclic qubit networks with random CNOT operations.

Abstract

We investigate the asymptotic dynamics of quantum networks under repeated applications of random unitary operations. It is shown that in the asymptotic limit of large numbers of iterations this dynamics is generally governed by a typically low dimensional attractor space. This space is determined completely by the unitary operations involved and it is independent of the probabilities with which these unitary operations are applied. Based on this general feature analytical results are presented for the asymptotic dynamics of arbitrarily large cyclic qubit networks whose nodes are coupled by randomly applied controlled-NOT operations.