Montek Singh COMP Aug 25, 2011

 Cellular automata  Quantum dot cellular automata (QCA)  Wires and gates using QCA  Implementation

 Discrete model studied in computability ◦ grid made up of “cells” ◦ each cell can be in one of finite number of states ◦ each cell has a defined “neighborhood” ◦ at each new time step, the state of a cell is determined by the state of its neighborhood in prior time step Conway’s Game of Life

 e.g., “Rule 30”  e.g., “Rule 110”

 Seashell patterns ◦ each cell’s pigment controlled by activating and inhibiting activity of neighbors Conus textile

 QCA ◦ proposed models of quantum computation ◦ analogous to conventional CAs  but based on quantum mechanical phenomenon of “tunneling”  Quantum dots ◦ 4-dot cell  basic unit of storage and computation  two states: -1 and +1  electrostatic repulsion

 Wires formed by juxtaposition of cells ◦ if leftmost is controlled externally, all others align same direction ◦ like “dominoes” falling

 Key idea is to place cells at 45 degrees w.r.t. each other  Two branches used here, one can work too

 Majority gate ◦ 2 out of 3 inputs determine output  Can you make? ◦ AND gate ◦ OR gate

 Single-plane crossover without “touching”! ◦ values along two wires propagate independently

 QCA clocking ◦ “freeze” cell when clock low  equivalent to latching ◦ free it up when clock high  equivalent to computing  Often use 4 or more clock phases

 Metal-island ◦ aluminum dots ◦ 1 micron, so very low temperatures  Semiconductor ◦ 20 nm, so ordinary temperatures ◦ most common  Molecular ◦ single molecules, so very fast ◦ future, not yet  Magnetic ◦ magnetic exchange interactions instead of electron tunneling ◦ room temperature