**Introducing quadratic form expansions** - Niel deBeaudrap

I will present techniques to analyze unitary operations in terms of "quadratic form expansions", a form similar to a sum over paths where the phase of each path is described by a quadratic form over the reals. I will 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 connection, we may consider 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.