How fast can a supercomputer work at the very most? Is there a theoretical limit on the speed of its operations?

Cray-1
The first true supercomputer, CRAY-1 (photo, left) made in 1976, ran at a speed of 100 megaflops. (A flop is the number of mathematical operations involving decimal fractions that a computer can make in a second. Mega = 1000.) At present the fastest supercomputer is China’s Tianhe-1 (see photo, below) which can operate at the speed of 1,000 trillion (10,00,00,00,00,00,00,000 calculations per second). Such extraordinary speed is made possible by the development of parallel processing. Dozens of microprocessors divide the task between them and work in unison to quickly arrive at the result. This obviates the need for creating free standing monoliths which in any case cannot cope with enormous data.
Tianhe-1
Although data-crunching power of a supercomputer may seem to be boundless, the main challenge in making such a machine lies in the length of its internal wiring. The speed of electrons which travel about 3,00,000 kilometers in a single second does seem exceedingly fast. But when the aim is to perform trillions of operations in that time electrons’ travel over individual wires result in a significant time lag.
To overcome this constraint, Seymour Cray, the designer of CRAY-1, kept the maximum length of any wire below 122 centimeters, below 40.5 centimeters in CRAY-2 and mere 7.6 centimeters in the CRAY-3 supercomputer. Unfortunately, all those electrons flowing through densely packed wires produced a tremendous amount of heat which could disable the entire system. Cray had to use a liquid coolant which absorbed the heat and kept temperature at ideal level. The problem of heat is easy to clear up by such methods, but the time lag in electron’ travel is likely to be a limiting factor in making faster supercomputers in future.

Additional reading:
Cray-1 (Wikipedia)
Tianhe-1 (Wikipedia)

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