3 ms·

They literally mean "not spending any energy doing the computation". We spend energy on computation for two fundamental reasons: 1) zeroing data and 2) error c

They literally mean "not spending any energy doing the computation". We spend energy on computation for two fundamental reasons: 1) zeroing data and 2) error correction. You avoid zeroing data by doing reversible computation. You avoid error correction by finding really really well behaved / stable systems. Time crystals are reversible basically by definition, and Wilczek is saying that maybe there might be some time crystals that are also well behaved and do something interesting enough to encode computations.

dangirsh 10y ago
IIRC reversible computations only take zero energy if you perform them infinitely slowly.
- lgas 10y ago
  Just curious, is there a difference between infinitely slowly and not at all?
  - drdeca 10y ago
    I think the idea is that as the speed approaches 0, the energy cost also approaches 0.
  - cyphar 10y ago
    "Infinitely slowly" is a theme in physics. What is actually meant by the term is "slow enough that you can approximate it as being infinitely slow". Now, obviously the idea of approximating an infinite value with a finite one seems dodgy, but the idea is that if some process converges to the "purely theoretical and infinitely slow" solution quickly then you can make that kind of approximation (physics is generally not obsessed with precision). As a concrete example, most of thermodynamics becomes insanely complicated for very rapid changes in pressure and temperature. And in many cases, you cannot actually compute the state of the system (without making a bunch of approximations). But, if you make some assumptions and approximations, thermodynamics becomes much more simple even though you've added some error factors due to your approximations (but it's definitely "good enough"). In general, the first thing you learn as part of a physics degree is that approximations and assumptions are just part of how you do science. Without them, we'd all be stuck dealing with insanely complicated equations that probably are not solvable. And at the end of the day, the unsolvable part of whatever equation you're dealing with wouldn't actually have a significant effect on the result (so you can generally ignore it).
- mickronome 10y ago
  I'm thinking that if the computation is actually the time evolution of a suitably structured time crystal, one which by definition is traversing/existing in its own ground state. Then either no computation can be done, or it must not require any energy. Reading out the answer must AFAIU (which is very superficial) however take energy, not unlikely to be exactly proportional to any part of the answer not read / erased, and thus closing the apparent loophole, and making you still being right :)
SomeStupidPoint 10y ago
Just for reference, for people unfamiliar with the name: Wilczek also worked on the theory of anyons, the non-Abelian form of which are at the heart of Microsoft's work on topological quantum computers. (He was the one who coined the term 'anyon'.) His work on anyons coupled with his work on time crystals makes him highly qualified to speak on what would be useful computational structures.

dangirsh 10y ago

IIRC reversible computations only take zero energy if you perform them infinitely slowly.

lgas 10y ago
Just curious, is there a difference between infinitely slowly and not at all?
- drdeca 10y ago
  I think the idea is that as the speed approaches 0, the energy cost also approaches 0.
- cyphar 10y ago
  "Infinitely slowly" is a theme in physics. What is actually meant by the term is "slow enough that you can approximate it as being infinitely slow". Now, obviously the idea of approximating an infinite value with a finite one seems dodgy, but the idea is that if some process converges to the "purely theoretical and infinitely slow" solution quickly then you can make that kind of approximation (physics is generally not obsessed with precision). As a concrete example, most of thermodynamics becomes insanely complicated for very rapid changes in pressure and temperature. And in many cases, you cannot actually compute the state of the system (without making a bunch of approximations). But, if you make some assumptions and approximations, thermodynamics becomes much more simple even though you've added some error factors due to your approximations (but it's definitely "good enough"). In general, the first thing you learn as part of a physics degree is that approximations and assumptions are just part of how you do science. Without them, we'd all be stuck dealing with insanely complicated equations that probably are not solvable. And at the end of the day, the unsolvable part of whatever equation you're dealing with wouldn't actually have a significant effect on the result (so you can generally ignore it).
mickronome 10y ago
I'm thinking that if the computation is actually the time evolution of a suitably structured time crystal, one which by definition is traversing/existing in its own ground state. Then either no computation can be done, or it must not require any energy. Reading out the answer must AFAIU (which is very superficial) however take energy, not unlikely to be exactly proportional to any part of the answer not read / erased, and thus closing the apparent loophole, and making you still being right :)

SomeStupidPoint 10y ago

Just for reference, for people unfamiliar with the name: Wilczek also worked on the theory of anyons, the non-Abelian form of which are at the heart of Microsoft's work on topological quantum computers. (He was the one who coined the term 'anyon'.) His work on anyons coupled with his work on time crystals makes him highly qualified to speak on what would be useful computational structures.