Relaxation to Equilibrium in a Quantum Network

TL;DR

This paper investigates how fully connected quantum networks of qubits, modeled with CNOT interactions, relax to equilibrium, providing analytical estimates and numerical validation up to 16 qubits, highlighting the role of network size.

Contribution

It offers new analytical and numerical insights into the relaxation dynamics of quantum networks with CNOT interactions, emphasizing the impact of network size on equilibration.

Findings

Analytical estimates of relaxation times

Numerical validation up to 16 qubits

Network size influences convergence rate

Abstract

The approach to equilibrium of quantum mechanical systems is a topic as old as quantum mechanics itself, but has recently seen a surge of interest due to applications in quantum technologies, including, but not limited to, quantum computation and sensing. The mechanisms by which a quantum system approaches its long-time, limiting stationary state are fascinating and, sometimes, quite different from their classical counterparts. In this respect, quantum networks represent a mesoscopic quantum systems of interest. In such a case, the graph encodes the elementary quantum systems (say qubits) at its vertices, while the links define the interactions between them. We study here the relaxation to equilibrium for a fully connected quantum network with CNOT gates representing the interaction between the constituting qubits. We give a number of results for the equilibration in these systems, including analytic estimates. The results are checked using numerical methods for systems with up to 15-16 qubits. It is emphasized in which way the size of the network controls the convergency.