Symmetry constraints on temporal order in measurement-based quantum computation

R. Raussendorf
(University of British Columbia, Department of Physics and Astronomy, Vancouver, BC, Canada)
P. Sarvepalli
(School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, GA, USA)
T.-C. Wei
(C.N. Yang Institute for Theoretical Physics, State University of New York, Stony Brook, New York, USA)
P. Haghnegahdar
(University of British Columbia, Department of Physics and Astronomy, Vancouver, BC, Canada)

We discuss the interdependence of resource state, measurement setting and temporal order in measurement-based quantum computation. The possible temporal orders of measurement events are constrained by the principle that the randomness inherent in quantum measurement should not affect the outcome of the computation. We provide a classification for all temporal relations among measurement events compatible with a given initial stabilizer state and measurement setting, in terms of a matroid. Conversely, we show that classical processing relations necessary for turning the local measurement outcomes into computational output determine the resource state and measurement setting up to local equivalence. Further, we find a symmetry transformation related to local complementation that leaves the temporal relations invariant.

In Bart Jacobs, Peter Selinger and Bas Spitters: Proceedings 8th International Workshop on Quantum Physics and Logic (QPL 2011), Nijmegen, Netherlands, October 27-29, 2011, Electronic Proceedings in Theoretical Computer Science 95, pp. 219–250.
Published: 1st October 2012.

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