How does reversible/quantum computing help with protein transcription or DNA replication? Neither of those exotic computing techniques reduce the fundamental thermodynamic cost of physical bit erasures/copies from what I understand.
Because we get to use the Margolus-Levitin limit, which states:
A quantum system of energy E needs at least a time of h/4e to go from one state to an orthogonal state, where h is the Planck constant (6.626×10−34 J⋅Hz−1[1]) and E is average energy.
This means we get 15 orders of magnitude decrease from your estimates of 1E-19 joules for one bit, which is much better news for nanotech.
I have even better news for total computation limits: 5.4x10^50 operations per second for a kilogram of matter.
The limit for speed is this:
The Margolus–Levitin theorem, named for Norman Margolus and Lev B. Levitin, gives a fundamental limit on quantum computation (strictly speaking on all forms on computation). The processing rate cannot be higher than 6 × 10^33 operations per second per joule of energy.
And since you claimed that computational limits matter for biology, the reason is obvious.
The nice thing about quantum computers is that they’re mostly reversible, ie swaps can always be done with zero energy, until you make a measurement. Once you do, you have to pay the energy cost, which I showed in the last comment. We don’t need anything else here.
The nice thing about quantum computers is that they’re mostly reversible, ie bit erasures can always be done with zero energy,
You seem confused here—reversible computations do not, can not erase/copy bits, all they can do is swap/transfer bits, moving them around within the computational system. Bit erasure is actual transference of the bit entropy into the external environment, outside the bounds of the computational system (which also breaks internal quantum coherence from what I recall, but that’s a side point).
Replication/assembly requires copying bits into (and thus erasing bits from) the external environment. This is fundamentally an irreversible computation.
How does reversible/quantum computing help with protein transcription or DNA replication? Neither of those exotic computing techniques reduce the fundamental thermodynamic cost of physical bit erasures/copies from what I understand.
Because we get to use the Margolus-Levitin limit, which states:
This means we get 15 orders of magnitude decrease from your estimates of 1E-19 joules for one bit, which is much better news for nanotech.
I have even better news for total computation limits: 5.4x10^50 operations per second for a kilogram of matter.
The limit for speed is this:
And since you claimed that computational limits matter for biology, the reason is obvious.
A link to the Margolus-Levitin theorem:
https://en.m.wikipedia.org/wiki/Margolus–Levitin_theorem
In the fully reversible case, the answer is zero energy is expended.
That doesn’t help with bit erasures and is thus irrelevant to what I’m discussing—the physical computations cells must perform.
The nice thing about quantum computers is that they’re mostly reversible, ie swaps can always be done with zero energy, until you make a measurement. Once you do, you have to pay the energy cost, which I showed in the last comment. We don’t need anything else here.
Thanks to porby for mentioning this.
You seem confused here—reversible computations do not, can not erase/copy bits, all they can do is swap/transfer bits, moving them around within the computational system. Bit erasure is actual transference of the bit entropy into the external environment, outside the bounds of the computational system (which also breaks internal quantum coherence from what I recall, but that’s a side point).
Replication/assembly requires copying bits into (and thus erasing bits from) the external environment. This is fundamentally an irreversible computation.