Quadratic Form Expansions for Unitaries

Details Quadratic Form Expansions for Unitaries Quadratic Form Expansions for Unitaries

2008-01-16

arxiv.org/abs/0801.2461v1

Physics

Quantum Physics

20 pages, 3 figures; (extended version of) accepted submission to TQC 2008

Scientific paper

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 when the phase contributed by each path is described by a quadratic form over $\mathbb R$. 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.

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