  Measurement-based quantum computation (MBQC) is a paradigm for quantum
computation where computation is driven by local measurements on a suitably
entangled resource state. In this work we show that MBQC is related to a model
of quantum computation based on Clifford quantum cellular automata (CQCA).
Specifically, we show that certain MBQCs can be directly constructed from CQCAs
which yields a simple and intuitive circuit model representation of MBQC in
terms of quantum computation based on CQCA. We apply this description to
construct various MBQC-based Ans\"atze for parameterized quantum circuits,
demonstrating that the different Ans\"atze may lead to significantly different
performances on different learning tasks. In this way, MBQC yields a family of
Hardware-efficient Ans\"atze that may be adapted to specific problem settings
and is particularly well suited for architectures with translationally
invariant gates such as neutral atoms.
