Supercomputers, by 2010, could be carrying out more than 1,000 trillion calculations per second.
The ambitious goal has been set by the US government to help its scientists tackle problems that would otherwise take too long to simulate.
Venerable supercomputer maker Cray has declared its aim of being the first to reach the goal and has embarked on a long-term research programme to make the machines that will finish the job.
Cray has already unveiled the first machine, the X1, that it hopes will be a stepping stone to the petaflop calculation goal.
The processors inside the X1 can carry out more than 12.8 billion calculations per second. One billion calculations per second is known as a gigaflop.
Clusters of X1 machines bring together up to 1,048 processors and a peak performance of more than 12,000 gigaflops - still far short of the ultimate goal.
Steve Scott, spokesman for Cray, said there was still a pressing need to create dedicated supercomputers, despite the success many people have had using the idle processor time of thousands of desktop PCs.
He said although such clusters of PCs could tackle some problems, there were many others that could only be satisfactorily tackled with stand-alone supercomputers.
Scott said designing a supercomputer to handle trillions of calculations per second involved more than just fast computer chips. The whole system had to be optimised to ensure that all the processors in the system were being used all the time and could continuously crunch through lots of numbers, he said.
Following the X1, Cray is working on a machine called the Black Widow which it hopes to unveil around 2005. Following that will be the machine it hopes will break the petaflop barrier.
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