The quantum circuit layout problem is to map a quantum circuit to a quantum computing device, such that the constraints of the device are satisfied. The optimality of a layout method is expressed, in our case, by the depth of the resulting circuits. We introduce QXX, a novel search-based layout method, which includes a configurable Gaussian function used to: emph{i)} estimate the depth of the generated circuits; emph{ii)} determine the circuit region that influences most the depth. We optimize the parameters of the QXX model using an improved version of random search (weighted random search). To speed up the parameter optimization, we train and deploy QXX-MLP, an MLP neural network which can predict the depth of the circuit layouts generated by QXX. We experimentally compare the two approaches (QXX and QXX-MLP) with the baseline: exponential time exhaustive search optimization. According to our results: 1) QXX is on par with state-of-the-art layout methods, 2) the Gaussian function is a fast and accurate optimality estimator. We present empiric evidence for the feasibility of learning the layout method using approximation.
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