Lecture Notes 2.C

# Rather than discarding information it keeps it around

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Unformatted text preview: an equivalent reversible computation. Rather than discarding information, it keeps it around so it can later “decompute” it. This was logical reversibility; he did not deal with the problem of physical reversibility. ¶2. Brownian Computers: Or “Brownian motion machines.” This was an attempt to suggest a possible physical implementation of reversible computation. “the mean free path of the system’s trajectory was much shorter than the distance between neighboring computational states” (see also [B82]). ¶3. Therefore: “In absence of any energy input, the system progressed essentially via a random walk, taking an expected time of ⇥(n2 ) to advance n steps.” ¶4. A small energy input biases the process in the forward direction, so that it precedes linearly, but still very slowly. ¶5. Compare “DNA polymerization, which (under normal conditions, such as during cell division) proceeds at a rate on the order of only 1,000 nucleotides per second, with a dissipation of ⇠ 40kB T per step.” This is about 1 eV (see ¶7 below). Note that DNA replication includes error-correcting operations. ¶6. Energy coe cient: Since “asymptotically reversible processes (including the DNA example) proceed forward at an adjustable speed, C. REVERSIBLE COMPUTING 51 proportional to the energy dissipated per step,” deﬁne an energy coefﬁcient: def cE = Ediss /fop , “where Ediss is the energy dissipated per operation, and fop is the frequency of operations.” ¶7. “In Bennett’s original DNA process, the energy coe cient comes out to about cE = 1eV/kHz.” That is, for DNA, cE ⇡ 40kT /kHz = 40 ⇥ 26 meV/kHz ⇡ 1 eV/kHz. ¶8. But it would be desirable to operate at GHz frequencies and energy dissipation below kB T . Recall that at room temp. kB T ⇡ 26 meV (Sec. A ¶6, p. 31). So we need energy coe cients much lower than DNA. This is an issue, of course, for molecular computation. ¶9. Information Mechanics group: In 1970s, Ed Fredkin, Tommaso To↵oli, et al. at MIT. ¶10. Ballistic computing: F &...
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