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arXiv · 0904.1549

Fast Amplification of QMA

Daniel Nagaj·Pawel Wocjan·Yong Zhang
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Abstract

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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Daniel Nagaj, Pawel Wocjan, Yong Zhang. 2009-04-09. Fast Amplification of QMA. https://arxiv.org/abs/0904.1549

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