Measurement-based quantum computation and undecidable logic

Details Measurement-based quantum computation and undecidable logic Measurement-based quantum computation and undecidable logic

2006-10-06

arxiv.org/abs/quant-ph/0610040v2

Physics

Quantum Physics

10 pages. Presentation improved. Paper to appear in Found. Phys.; currently published online

Scientific paper

10.1007/s10701-008-9212-6

We establish a connection between measurement-based quantum computation and the field of mathematical logic. We show that the computational power of an important class of quantum states called graph states, representing resources for measurement-based quantum computation, is reflected in the expressive power of (classical) formal logic languages defined on the underlying mathematical graphs. In particular, we show that for all graph state resources which can yield a computational speed-up with respect to classical computation, the underlying graphs--describing the quantum correlations of the states--are associated with undecidable logic theories. Here undecidability is to be interpreted in a sense similar to Goedel's incompleteness results, meaning that there exist propositions, expressible in the above classical formal logic, which cannot be proven or disproven.

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