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### Paper:

TR14-181 | 19th December 2014 21:20

#### The space "just above" BQP

TR14-181
Authors: Scott Aaronson, Adam Bouland, Joseph Fitzsimons, Mitchell Lee
Publication: 22nd December 2014 13:06
We explore the space "just above" BQP by defining a complexity class PDQP (Product Dynamical Quantum Polynomial time) which is larger than BQP but does not contain NP relative to an oracle. The class is defined by imagining that quantum computers can perform measurements that do not collapse the wavefunction. This (non-physical) model of computation can efficiently solve problems such as Graph Isomorphism and Approximate Shortest Vector which are believed to be intractable for quantum computers. Furthermore, it can search an unstructured N-element list in $\tilde O(N^{1/3})$ time, but no faster than $\Omega(N^{1/4})$, and hence cannot solve NP-hard problems in a black box manner. In short, this model of computation is more powerful than standard quantum computation, but only slightly so.