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Classical artificial neural networks, built from perceptrons as theirelementary units, possess enormous expressive power. Here we investigate aquantum neural network architecture, which follows a similar paradigm. It isstructurally equivalent to so-called (1+1)D quantum cellular automata, whichare two-dimensional quantum lattice systems on which dynamics takes place indiscrete time. Information transfer between consecutive time slices -- oradjacent network layers -- is governed by local quantum gates, which can beregarded as the quantum counterpart of the classical perceptrons. Along thetime-direction an effective dissipative evolution emerges on the level of thereduced state, and the nature of this dynamics is dictated by the structure ofthe elementary gates. We show how to construct the local unitary gates to yielda desired many-body dynamics, which in certain parameter regimes is governed bya Lindblad master equation. We study this for small system sizes throughnumerical simulations and demonstrate how collective effects within the quantumcellular automaton can be controlled parametrically. Our study constitutes astep towards the utilisation of large-scale emergent phenomena in large quantumneural networks for machine learning purposes.

Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks