  In this research, we present a quantum circuit design and implementation for
a parallel universal linear bounded automata. This circuit is able to
accelerate the inference of algorithmic structures in data for discovering
causal generative models. The computation model is practically restricted in
time and space resources. A classical exhaustive enumeration of all possible
programs on the automata is shown for a couple of example cases. The precise
quantum circuit design that allows executing a superposition of programs, along
with a superposition of inputs as in the standard quantum Turing machine
formulation, is presented. This is the first time, a superposition of classical
automata is implemented on the circuit model of quantum computation, having the
corresponding mechanistic parts of a classical Turing machine. The
superposition of programs allows our model to be used for experimenting with
the space of program-output behaviors in algorithmic information theory. Our
implementations on OpenQL and Qiskit quantum programming language is copy-left
and is publicly available on GitHub.
