  The quantum circuit layout (QCL) problem is to map a quantum circuit such
that the constraints of the device are satisfied. We introduce a quantum
circuit mapping heuristic, QXX, and its machine learning version, QXX-MLP. The
latter infers automatically the optimal QXX parameter values such that the
layed out circuit has a reduced depth. In order to speed up circuit
compilation, before laying the circuits out, we are using a Gaussian function
to estimate the depth of the compiled circuits. This Gaussian also informs the
compiler about the circuit region that influences most the resulting circuit's
depth. We present empiric evidence for the feasibility of learning the layout
method using approximation. QXX and QXX-MLP open the path to feasible large
scale QCL methods.
