The complexity class PDQP SPUR Final Paper: Summer 2013
Mitchell Lee, Adam Bouland, Scott T. Aaronson · 2013
Quantum computers are believed to be strictly more computationally powerful than classical computers, but not so much more powerful that they can solve NP-complete problems eciently. This is because of the result that a quantum computer takes ( N 1=2 ) time to search an unstructured N-element list for a particular marked item, as opposed to poly(logN) time for a nondeterministic computer. On the other hand, many seemingly innocuous modications of quantum mechanics increase the power of quantum computers drastically enough that they can solve NP-complete problems eciently [3]. This paper denes a model of computation slightly more powerful than quantum computation, but only slightly so. In particular, we show that by allowing on-collapsing measurements, we can solve eciently problems such as Graph Isomorphism and Approximate Shortest Vector which are believed to be intractable for quantum computers. We can also search an unstructured N-element list for a particular marked item in ~ O(N 1=3 ) time, but no faster than ( N 1=4 ).