We introduce techniques to analyze unitary operations in terms of quadratic form expansions, a form similar to a sum over paths in the computational basis where the phase contributed by each path is described by a quadratic form over ℝ. We show how to relate such a form to an entangled resource akin to that of the one-way measurement model of quantum computing. Using this, we describe various conditions under which it is possible to efficiently implement a unitary operation U, either when provided a quadratic form expansion for U as input, or by finding a quadratic form expansion for U from other input data. © 2008 Springer Berlin Heidelberg.
CITATION STYLE
De Beaudrap, N., Danos, V., Kashefi, E., & Roetteler, M. (2008). Quadratic form expansions for unitaries. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5106 LNCS, pp. 29–46). Springer Verlag. https://doi.org/10.1007/978-3-540-89304-2_4
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