© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

10.2.4.3 Bekenstein-Bounded Computation

A fundamental upper limit on the number of possible quantum states in a bounded region (e.g., the maximum number of bits that can be coded in a bounded region) -- is given by the Bekenstein Bound¹⁹⁹⁰ as:

{Eqn. 10.10}

within a spherical region of radius R containing energy E = mc² where m is the enclosed mass, c = 3 x 10⁸ m/sec (speed of light), and h = h / 2 p where h = 6.63 x 10^-34 joule-sec (Planck's constant). Maximum processing speed 'I is then bounded by the minimum time for a state transition, which cannot be less than the time required for light to cross the region of radius R, or:

{Eqn. 10.11}

Thus in theory, a single carbon atom of mass m = 2 x 10^-26 kg and radius R ~ 0.15 nm could be impressed with up to I_Bek ~ 10⁸ bits and could process information up to 'I_Bek ~ 10²⁶ bits/sec in an optimally-designed quantum computer. For a 1 micron³ computer of mass ~10^-15 kg, I_Bek ~ 10²² bits maximum storage capacity and 'I_Bek ~ 10³⁷ bits/sec maximum processing capacity. These values are not the least upper limits; Schiffer and Bekenstein¹⁹⁹¹ estimate that the Bekenstein Bound probably overestimates I and 'I by at least a factor of 100, but Likharev¹⁹⁹² and Margolus and Levitin²³¹⁹ have derived similar limits. In 1998, proposed reversible quantum computer systems would perform significantly below the Bekenstein Bound.^1993,1994

Last updated on 24 February 2003