Dominant couplings in qubit networks with controlled interactions

TL;DR

This paper investigates how competing two- and three-qubit interactions influence the long-term behavior of qubit networks, revealing that the dominance of two-qubit interactions emerges when three-qubit interactions coexist.

Contribution

The study introduces a solvable qubit network model to analyze the impact of controlled three-qubit interactions on asymptotic states, highlighting the dominance of two-qubit interactions in combined scenarios.

Findings

Networks with purely three-qubit interactions show different asymptotics based on control qubits.

Two-qubit interactions dominate when combined with three-qubit interactions.

Presence of two types of three-qubit interactions results in asymptotics similar to two-qubit cu-interactions.

Abstract

Systems evolving under the influence of competing two-body and three-body interactions, are of particular interest in exploring the stability of equilibrium states of strongly interacting many-body system. We present a solvable model based on qubit networks, which allows us to investigate the intricate influence of these couplings on the possible asymptotic equilibrium states. We study the asymptotic evolution of finite qubit networks under two and three-qubit interactions. As representatives of three-qubit interactions we choose controlled unitary interactions (cu-interactions) with one and two control qubits. It is shown that networks with purely three-qubit interactions exhibit different asymptotic dynamics depending on whether we deal with interactions controlled by one or two qubits. However, when we allow three-qubit interactions next to two-qubit interactions, the asymptotics is dictated by two-qubit interactions only. Finally, we prove that the simultaneous presence of two types of three-qubit interactions results in the asymptotic dynamics characteristic for two-qubit cu-interactions.