Swarm intelligence and evolutionary algorithms (SI&EAs) have been widely applied to various fields. In this paper, we make the first attempt, to our best knowledge, to apply an SI&EA, Quantum Particle Swarm Optimization (QPSO), for addressing the task scheduling problem in Device-Edge-Cloud Cooperative Computing (DE3C) which is one of the most widespread and new computing paradigms. We first formulate the problem and propose a QPSO based method to solve the problem with a reasonable time. Then we summarize the existing variants of QPSO, which exploit various improvement schemes for QPSO. At last, we conduct simulated experiments to evaluate the performance of QPSO and its variants on solving the task scheduling problem of DE3C, and have the following findings. (1) QPSO outperforms several up-to-date heuristics and SI&EAs in both the user satisfaction and the resource efficiency. (2) Existing improvement methods have no appreciable effect on QPSO for solving large-scale problems. (3) The performance of an improvement for QPSO depends mostly on randomness of the offset added to particle movements.