Fast amplification of QMA
Daniel Nagaj, Paweł Wocjan, Y. Zhang · Quantum Information and Computation · 2009
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 QMA_1 is equal to QMA. Finally, we simplify the filter-state method to search for QMA witnesses by Poulin and Wocjan.