Efficient Distributed Quantum Computing

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I will explain how to simulate arbitrary quantum circuits on a distributed quantum computer (DQC), in which the pairs of qubits that are allowed to interact are restricted to the edges of some (connected) graph G.  Even for graphs with only a modest number of long-range qubit interactions, such as the hypercube, this simulation is, in fact, efficient.  Furthermore, for all graphs, the emulation scheme is very close to being optimal. 
Secondly I will present an efficient quantum algorithm for parallel unrestricted memory look-up.  As an application, I will show that the space-time trade off for Element Distinctness and Collision Finding can be improved. 
Both results arise from applying the ideas of reversible sorting networks to quantum computing.