Abstract: How fast a quantum state can evolve has attracted considerable attention in connection with quantum measurement and information processing. A lower bound on the orthogonalization time, based on the energy spread DeltaE, was found by Mandelstam and Tamm. Another bound, based on the average energy E, was established by Margolus and Levitin. The bounds coincide and can be attained by certain initial states if DeltaE=E. Yet, the problem remained open when DeltaE[not-equal]E. We consider the unified bound that involves both DeltaE and E. We prove that there exist no initial states that saturate the bound if DeltaE[not-equal]E. However, the bound remains tight: for any values of DeltaE and E, there exists a one-parameter family of initial states that can approach the bound arbitrarily close when the parameter approaches its limit. These results establish the fundamental limit of the operation rate of any information processing system.

In fact, if we go by with Moore's law, the prediction comes to roughly another 75 years before this speed limit is reached.

If components are to continue shrinking, physicists must eventually code bits of information onto ever smaller particles. Smaller means faster in the microelectronic world, but physicists Lev Levitin and Tommaso Toffoli at Boston University in Massachusetts, have slapped a speed limit on computing, no matter how small the components get.

"If we believe in Moore's laW ... then it would take about 75 to 80 years to achieve this quantum limit," Levitin said.

"No system can overcome that limit. It doesn't depend on the physical nature of the system or how it's implemented, what algorithm you use for computation … any choice of hardware and software," Levitin said. "This bound poses an absolute law of nature, just like the speed of light."

Still, 75 years is a very, very long time as far as technology is concerned. While a fundamental limit is a fundamental limit, I can certainly see new physics popping up in 75 years that will require a re-evaluation of this conclusion.

Zz.

[1] L.B. Levitin and T. Toffoli, Phys. Rev. Lett. v.103, p.160502 (2009).

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