Fast amplification of QMA (pp1053-1068)
          Daniel Nagaj, Pawel Wocjan, and Yong Zhang
          doi: https://doi.org/10.26421/QIC9.11-12-8
Abstracts: 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 [1]. 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 (QMA1) is equal to QMA. Finally, we simplify the filter-state method to search for QMA witnesses by Poulin and Wocjan [2].
Key words: QMA, amplification, witness-reusing, phase estimation, Jordan�s lemma