In a paper published in the journal Physical Review Letters, Levitin and Toffoli present an equation for the minimum sliver of time it takes for an elementary quantum operation to occur. This establishes the speed limit for all possible computers. Using their equation, Levitin and Toffoli calculated that, for every unit of energy, a perfect quantum computer spits out ten quadrillion more operations each second than today's fastest processors.(A quadrillion is 10^15 or 1000 trillions)

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What Profs. Lev B. Levitin and Tommaso Toffoli's paper "Fundamental Limit on the Rate of Quantum Dynamics: The Unified Bound Is Tight" (Physical Review Letters, Vol. 103, Issue 16 [October 2009]; also at arXiv:0905.3417) demonstrates is that processor speed can diverge to infinity if the energy of the system diverges to infinity.

ReplyDeleteIn a previous paper by Norman Margolus and Levitin, the bound was given as t >= h/(4*E), with t being the minimum operation cycle in seconds, h being Planck's constant, and E being energy in joules. Levitin and Toffoli said paper generalizes it to all cases.

With this new bound, one obtains ~ 3.31303448*10^-34 seconds as the minimum operation cycle per joule of energy; or for the reciprocal, a maximum of ~ 3.0183809*10^33 operations per second per joule of energy.

So notice here that processor speed can increase without limit if the energy of the system is increased without limit. When the authors of the paper speak of a fundamental speed limit of computation, they are referring to per unit of energy.

In the article "Computers Faster Only for 75 More Years: Physicists determine nature's limit to making faster processors" (Lauren Schenkman, Inside Science News Service, October 13, 2009), paper co-author Levitin is quoted as saying, "If we believe in Moore's law ... then it would take about 75 to 80 years to achieve this quantum limit." What Levin is referring to here is given the current energy-density of our present ordinary matter, processors cannot be made which have greater processing-density after around said time, i.e., one won't be able to fit more processing power within the same amount of space given the current energy-density of common matter. But even with the same energy-density, one can still increase processing speed by increasing the size or number of processors, yet they would then take up more space. As well, one can increase the processing-density without limit if one increases the energy-density without limit.

In the same Inside Science article, Scott Aaronson, an assistant professor of electrical engineering and computer science at the Massachusetts Institute of Technology in Cambridge, is quoted as saying that what this bound means is that "we can't build infinitely fast computers," which is a misstatement of what the bound actually states. The bound actually states that one can build infinitely fast computers if one has an infinite amount of energy.

For the cosmological limits to computation, see physicist and mathematician Prof. Frank J. Tipler's below paper, which demonstrates that the known laws of physics (i.e., the Second Law of Thermodynamics, general relativity, quantum mechanics, and the Standard Model of particle physics) require that the universe end in the Omega Point (the final cosmological singularity and state of infinite informational capacity identified as being God), and it also demonstrates that we now have the quantum gravity Theory of Everything (TOE):

F. J. Tipler, "The structure of the world from pure numbers," Reports on Progress in Physics, Vol. 68, No. 4 (April 2005), pp. 897-964. http://math.tulane.edu/~tipler/theoryofeverything.pdf Also released as "Feynman-Weinberg Quantum Gravity and the Extended Standard Model as a Theory of Everything," arXiv:0704.3276, April 24, 2007. http://arxiv.org/abs/0704.3276

See also the below resource:

"Omega Point (Tipler)," Wikipedia, October 30, 2009. http://en.wikipedia.org/w/index.php?title=Omega_Point_%28Tipler%29&oldid=322843275