Well, seeing as I work in the Bristol QI thoeory group I guess it was only a matter of time before I was an author on a paper which uses tricks involving random quantum states.
Below is the abstract for this new paper that I’ve written together with Caterina Mora and Andreas Winter.
Are random pure states useful for quantum computation?
We show the following: a randomly chosen pure state as a resource for measurement-based quantum computation, is – with overwhelming probability – of no greater help to a polynomially bounded classical control computer, than a string of random bits. Thus, unlike the familiar “cluster states”, the computing power of a classical control device is not increased from P to BQP, but only to BPP. The same holds if the task is to sample from a distribution rather than to perform a bounded-error computation. Furthermore, we show that our results can be extended to states with significantly less entanglement than random states.