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In this work we apply deep neural networks to find the non-equilibrium steadystate solution to correlated open quantum many-body systems. Motivated by theongoing search to find more powerful representations of (mixed) quantum states,we design a simple prototypical convolutional neural network and show thatparametrizing the density matrix directly with more powerful models can yieldbetter variational ansatz functions and improve upon results reached by neuraldensity operator based on the restricted Boltzmann machine. Hereby we give upthe explicit restriction to positive semi-definite density matrices. However,this is fulfilled again to good approximation by optimizing the parameters. Thegreat advantage of this approach is that it opens up the possibility ofexploring more complex network architectures that can be tailored to specificphysical properties. We show how translation invariance can be enforcedeffortlessly and reach better results with fewer parameters. We present resultsfor the dissipative one-dimensional transverse-field Ising model and atwo-dimensional dissipative Heisenberg model compared to exact values.

Deep Neural Networks as Variational Solutions for Correlated Open Quantum Systems