Montek Singh
COMP790-084
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

Semiconductor

Molecular

Magnetic
◦ aluminum dots
◦ 1 micron, so very low temperatures
◦ 20 nm, so ordinary temperatures
◦ most common
◦ single molecules, so very fast
◦ future, not yet
◦ magnetic exchange interactions instead of electron
tunneling
◦ room temperature