Measurement-based quantum computation from Clifford quantum cellular automata

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 (CQCAs). 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 parametrized 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 are particularly well suited for architectures with translationally invariant gates such as neutral atoms.