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 10^{20}. 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