We exhibit a quantum circuit that performs the Quantum Fourier Transform on $n$ qubits in $ (n)$ depth. Thus, a parallel quantum computer can carry out the QFT in linear time. We conjecture that this can, in fact, be reduced to $ ({\rm log} n)$ depth, which would place the QFT in the class {\bf...

Given an initial distribution of sand in an Abelian sandpile, what final state does it relax to after all possible avalanches have taken place? In d = 3*, we show that this problem is P-complete, so that explicit simulation of the system is almost certainly necessary. We also show that the...