ar X iv : 0 81 0 . 51 09 v 2 [ qu an t - ph ] 2 O ct 2 00 9 NP vs QMA log ( 2 )

نویسنده

  • Salman Beigi
چکیده

Although it is believed unlikely that NP-hard problems admit efficient quantum algorithms, it has been shown that a quantum verifier can solve NP-complete problems given a “short” quantum proof; more precisely, NP ⊆ QMAlog(2) where QMAlog(2) denotes the class of quantum Merlin-Arthur games in which there are two unentangled provers who send two logarithmic size quantum witnesses to the verifier. The inclusion NP ⊆ QMAlog(2) has been proved by Blier and Tapp by stating a quantum MerlinArthur protocol for 3-coloring with perfect completeness and gap 1 24n6 . Moreover, Aaronson et al. have shown the above inclusion with a constant gap by considering e O( √ n) witnesses of logarithmic size. However, we still do not know if QMAlog(2) with a constant gap contains NP. In this paper, we show that 3-SAT admits a QMAlog(2) protocol with the gap 1 n 3+ǫ for every constant ǫ > 0.

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تاریخ انتشار 2009