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...

In this work we use the wave equation to obtain a classical analogue of the quantum search algorithm and we verify that the essence of search algorithms resides in the establishment of resonances between the initial and the searched states. In particular we show that, within a set of N vibration...

We analyze the responses of a quantum search algorithm to an external monochromatic field and to the decoherences introduced through measurement processes. The external field in general affects the functioning of the search algorithm. However, depending on the values of the field parameters,...

A double SQUID manipulated by fast magnetic flux pulses can be used as a tunable flux qubit. In this paper we study the requirements for the qubit operation and evaluate the dissipation and decoherence due to the manipulation, with particular attention to the contribution related to the applied...