Abstract: Recently, a number of hardware platforms became available where large scale complex quantum spin system dynamics (such as a quantum spin glass) could potentially be addressed experimentally, including trapped ions systems and superconducting circuits. From the theoretical point of view, analysis of the dynamics of such complex systems is challenging and therefore we take the so called "bottom up" approach. We analyze simple models that are analytically tractable and at the same time retain key features of the complex spin models, with the idea of developing some intuition that can be applied in more realistic cases. In this spirit, I will discuss a specific model, a fully connected cluster of spins with uniform interactions (uniform p-spin model), and describe its dynamics including the effects of multiqubit quantum co-tunneling at finite temperature. One question we are particularly interested in in this work is the role the extensive quantum tunneling could play in quantum computation. Quantum annealing algorithm proposed by Nishimori and coauthors PRE (1992) relies on quantum tunneling and has been conjectured to improve upon the performance of classical simulated annealing, an algorithm designed to solve complex optimization NP-hard problems (such as finding a ground state of a spin glass). Using the example of the uniform p-spin model we will show that quantum annealing algorithm relying on extensive incoherent co-tunneling and thermalization dynamics could outperform the standard simulated annealing in a range of parameters.