Are random pure states useful for quantum computation?

Details Are random pure states useful for quantum computation? Are random pure states useful for quantum computation?

2008-12-16

arxiv.org/abs/0812.3001v1

Phys. Rev. Lett. 102, 190502 (2009)

Physics

Quantum Physics

No. But we need 5 pages to say why

Scientific paper

10.1103/PhysRevLett.102.190502

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.

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