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
“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:
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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- Fall '13
- Logic gate, fredkin gate, Fredkin