Blueprint for experiments exploring the quantum recurrence theorem on a coupled multiqubit system

The quantum form of the Poincaré recurrence theorem stipulates that a system with a time-independent Hamiltonian and discrete energy levels returns arbitrarily close to its initial state in a finite time. Qubit systems, being highly isolated from their dissipative surroundings, provide a possible experimental test bed for studying this theoretical construct. Here, we investigate an <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>N</a:mi> </a:math> -qubit system, weakly coupled to its environment. We present quantitative analytical and numerical results on both the revival probability and time, and demonstrate that the system indeed returns arbitrarily close to its initial state, but in a time exponential in the number of qubits <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>N</b:mi> </b:math> , with revival times that are astronomically large for systems with just a few tens of qubits. Given the lifetimes achievable in present-day superconducting multiqubit systems, we propose a realistic experimental test of this theory and its size scaling. This provides insights into how thermalization emerges in isolated quantum systems.