Fast Amplification of QMA

Details Fast Amplification of QMA Fast Amplification of QMA

2009-04-09

arxiv.org/abs/0904.1549v1

QIC Vol.9 No.11&12 (2009), 1053-1068

Physics

Quantum Physics

15 pages

Scientific paper

Given a verifier circuit for a problem in QMA, we show how to exponentially amplify the gap between its acceptance probabilities in the `yes' and `no' cases, with a method that is quadratically faster than the procedure given by Marriott and Watrous. Our construction is natively quantum, based on the analogy of a product of two reflections and a quantum walk. Second, in some special cases we show how to amplify the acceptance probability for good witnesses to 1, making a step towards the proof that QMA with one-sided error is equal to QMA. Finally, we simplify the filter-state method to search for QMA witnesses by Poulin and Wocjan.

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