In systems composed of coupled oscillating elements the saddle points form a network. The above networks belong to a system of five elements. The saddle points are depicted as points. Every saddle point is connected to four others: two of these connections lead to the particular saddle point, two others away from it. The figure shows two possible paths (orange and blue) the system may take. Each path corresponds to the result of a calculation. MPI for Dynamics and Self-Organization |
A
computer is much more than simply hardware. Foremost, it is a principle
for the processing of data and information. The essence of the
conventional computer for example, which has long had a decisive effect
on our daily life, is not to be sought in transistors, chips and
semiconductors. Rather, it is characterized by the ways and means of
performing calculations with the help of two easily distinguishable
states (conventionally known as 0 and 1). Scientists at the Max Planck
Institute for Dynamics and Self-Organization in Göttingen have now
developed a completely new principle for information processing. Their
so-called complex network computer is equally capable of performing arbitrary calculations, but does this under completely different conditions.
“In
contrast to classical data processing on a PC, our new approach is not
based on a binary system of zeros and ones”, explains Marc Timme, head
of the Network Dynamics research group at Institute. What is more, a complex network computer
could in principle be built from any oscillating system. “The simplest
example is a pendulum”, says Timme. However, particular electrical
circuits whose components rhythmically exchange charge with each other,
or lasers can also be said to oscillate. If several such units are
linked—as with a number of pendulums connected to each other by a
spring—they exhibit a special dynamic behaviour which lends itself to
the processing of data.
A choreography of oscillations correspond to a state of the whole system
The
key to this behaviour are so-called saddle points: states of the whole
system which are stable in some respects and unstable in others.
“Imagine
a ball sitting in the hollow of a real saddle,” explains Timme. If this
ball is moved exactly parallel to the horse’s back and then released,
it will always roll back into the hollow. The initial state is stable
with respect to this kind of disturbance. But if the ball is set in
motion perpendicularly to the horse’s back, it is a completely different
matter: the ball will fall off; the state is unstable. In the case of
connected pendulums, a special relation between the oscillations, in
which particular pendulums move synchronously, corresponds to such a
saddle point state.
In
systems of connected oscillating elements, such saddle points form a
kind of network: in response to an external disturbance that
destabilizes a particular saddle point , the whole system shifts to
another one. “In our example system each saddle point leads to two
others, which in turn are connected with two further saddle points,”
explains Fabio Schittler Neves from the Institute. Which path the system
actually takes in this net of possible states depends on the kind of
disturbance.
“In
our design, we regard each disturbance as an input signal that can be
composed of several components,” says Schittler Neves. Each component is
coupled to one of the oscillating elements of the whole system. In the
case of a group of coupled pendulums, for instance, a component signal
corresponds to a slight impact on one of the pendulums. The relative
strength of these component signals determines to which new saddle point
state the system will tend.
All logical operations can be performed in one network
The
input signal thus determines the path taken through the network of
saddle points. The path taken corresponds to the result of the
calculation. “The state then taken by the system allows inferences about
the relative strengths of the individual signal components,” explains
Timme. “It’s a kind of sorting by size.”
In
their latest publication, the researchers were now able to show that a
complete system of logic can be built on this: all the logical
operations—such as addition, multiplication or negation—can be
represented. However, whereas a classical computer uses one component—a
subsystem of the whole computer—to perform a particular logical
operation like, for example, addition, the operation in a complex network computer takes place in the whole network simultaneously.
“All logical operations can therefore be performed similarly in this network,” explains Timme.
This
means that even relatively small systems can perform an unbelievably
large number of possible operations: whereas five oscillating elements
provide only ten different system states and can therefore perform only
ten different calculations, 100 elements provide 5 x 1020. This number
represents 10,000 times the number of letters in all the books in all
the libraries in the world. In addition, the complex network computer performs some tasks, such as the coarse sorting of figures, much faster than its conventional equivalent.
The new principle of calculation enables a robot to navigate its way through an obstacle course
The
new principle of calculation has also proved itself in its first
practical application. It allowed the scientists to build a simple robot
which finds its own way through an obstacle course. The input signals
from its sensors correspond to the disturbances of the system. “In this
case, electrical oscillators could serve as the hardware,” explains
Schittler Neves. “This very first application shows how the robot’s
brain functions when the basic principle of the complex network computer
is imitated,” he adds.
The scientists are currently working on a physical implementation in electronic hardware.
“We
are still far away from a powerful computer in the true sense of the
word,” says Timme. “But we were able to demonstrate that the idea
basically works.”
The
current status is therefore comparable with that of the quantum
computer. The theory of performing computations with the help of quantum
algorithms is continually advancing. However, whether the hardware
might be based on semiconductor structures, superconductors,
arrangements of single atoms or completely different physical systems is
still a subject for further research.
“In the case of complex network computers,
it is probably not going to be coupled pendulums,” say Timme with a
smile. Effective computation would require several thousand of such
coupled pendulums. The system is more suitable for illustrative
purposes. Systems of coupled lasers seem more promising to the
researchers. Not only do they offer precisely controlled frequencies,
which are a further requirement for complex network computers,
they also operate in a particularly high range of up to several billion
oscillations per second, enabling a computer to calculate particularly
fast.
Source: Max Planck Institute
