Measurement-based quantum computation on graph states and undecidable logic theories
M. Van den Nest, H. J. Briegel · arXiv (Cornell University) · 2006
We establish a connection between measurement-based computation on graph states and the field of mathematical logic. We show that the computational power of graph states as resources for measurement-based quantum computation is reflected in the expressive power of (classical) formal logic languages defined on the underlying graphs. In particular, it is shown that for all graph states which disallow efficient classical simulation of measurement-based quantum computations, the underlying graphs are associated with undecidable logic theories. Here undecidability is to be interpreted in the sense of Goedel, meaning that there exist propositions, expressible in the above classical formal logic, which cannot be proven or disproven.