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2008

Are random pure states useful for quantum computation?

Bremner, Michael J., Mora, Caterina, Winter, Andreas

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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.

Are random pure states useful for quantum computation? · Around

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Then

S. D. Barrett, S. D. Bartlett, A. C. Doherty, D. Jennings, T. Rudolph, “Transitions in the computational power of thermal states for measurement-based quantum computation”, arXiv:0807.4797 (2008)
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D. Gross, S. Flammia, J. Eisert, “Most quantum states are too entangled to be useful as computational resources”, arXiv:0810.4331 (2008)

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