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 (bounded-error, quantum polynomial time), but only to BPP (bounded-error, probabilistic polynomial time). 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.
Bremner
Michael J
MJ
Department of Computer Science, University of Bristol, Bristol BS8 1UB, United Kingdom. michael.bremner@bris.ac.uk
Mora
Caterina
C
Winter
Andreas
A