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STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
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Given a verifier circuit for a problem in QMA, we show how to exponentially amplifythe gap between its acceptance probabilities in the 'yes' and 'no' cases, with a methodthat is quadratically faster than the procedure given by Marriott and Watrous [1]. Ourconstruction is natively quantum, based on the analogy of a product of two reflections anda quantum walk. Second, in some special cases we show how to amplify the acceptanceprobability for good witnesses to 1, making a step towards the proof that QMA withone-sided error (QMA1) is equal to QMA. Finally, we simplify the filter-state method tosearch for QMA witnesses by Poulin and Wocjan [2].