Qudits: The Real Future of Quantum Computing?
spectrum.ieee.org
spectrum.ieee.org
I've been recently exploring computational metamaterials for photonic computation.
http://users.ece.utexas.edu/~aalu/research%20-%20page%203.ht... (there's quite a few papers on this but unfortunately they are all paywalled. Spoiler alert, they seem to be based entirely on Fourier transform).
These computational metamaterials don't need electricity to be powered (you need something that will shoot the photons on them and read back the values off tho).
Machine learning would be much, much faster on these as you have O(1) differential calculus.
They don't heat up. You can possibly build a house sized CPU out of these. I can see it, a city block sized CPU and a nuclear reactor next to it.
Did you know that on an analog machine, you can do sort in O(n)?
https://en.wikipedia.org/wiki/Spaghetti_sort
Hit me up if you wanna chat about this. I've seen the "light" (xdddd) now and can't go back to stupid bits.
I'm not like super married to the metamaterials but analog photonic trumps quantum for just about every task I can think of.
that's quite a bold claim. im pretty intrigued, but it seems like there isn't a lot of easily accessible information on this topic. the wikipedia article on analog computers mostly focuses on mechanical ones from the past. do you have any recommended starter readings for analog computation? is it a model that has the computational time complexity of a non-deterministic turing machine? thanks.
As for classification, there's some work on this e.g. this http://www.cs.princeton.edu/~ken/MCS86.pdf
I believe it's not non-deterministic, as in some sense, if you can pose the problem in a differentiable way, it's better than non-determinism.
It's like being in a maze. An analog computer like robot can perceive the slight tilt of the floor that goes from the entrance to the exit and just follows that tilt. It takes the robot an optimal number of steps too.
A non-deterministic Turing would kind of split itself into N different robots and start exploring all the turns. It might find the answer eventually but e.g. it will consume that much more energy.
This analogy might be silly but I hope it conveys how very different analog machines are.
unless you are saying that in an analog case we can ignore the rules of the maze and can go through walls. but then are we still solving the same problem? seems like the time complexity comparison no longer makes sense if you redefine the constraints of the problem.
Not ignore, but you have a lot more information about the problem and you have a general direction of the solution.
ND turing can split and like explore multiple corridors at once. But in the end all those robots that don't end up finding exit just wasted energy. I guess you don't care about this in complexity theory but this is a huge gain in practice.
Is this a reasonable mental model of what your describing?
Also when I say quantum I really mean digital quantum computer, I still have to decide what to think of quantum analog computers.
Unlikely.
That's the thing, it can solve a lot of computations at the same time however an analog computer can recognize the direction of the solution therefore the number of simultaneous solutions doesn't really matter.
You haven't really explained your second point, but assuming it's true, you'll only be able to "recognize the direction" within your margin of error. Your noise floor will be way above the required precision to explore a high-dimensional space.
Analog computers never achieved common use because of noise and lack of practical error correction. Even the human brain evolved to be mostly digital and we almost never focus on being exact.
You are talking about electric analog, I'm talking about photonic analog.
How is the brain mostly digital?
For a trivially simple concrete example, consider the task of computing the results of the SHA-256 hashing algorithm, which is primarily bottlenecked by bit shifts and rotates on integers. How would your analog machine compare to conventional digital computers? Is there any literature on this?
I might be talking out of my butt but fundamentally I think that eventually we'll realize that a lot of the currently supposedly solved problems might need to be rethought. I'm inclined to believe that hashing falls under these but don't quote me on that.
As for literature, I can't recommend anything in particular. But there's something on amazon, arxiv etc. I'm not sure what part of this are you most interested in, I guess what you are talking about could be complexity?
It's ok, it took me some time to realize that the bit-copper orthodoxy need to be toppled as well.
> Analog on such small scales is overwhelmed by noise and very low precision.
But here we are making more and more photonic and optic things. Fiber optic is taking over. There quite a bit of work in silicon-photonic design (you can check this book https://smile.amazon.com/Silicon-Photonics-Design-Devices-Sy...
I mean there's noise yes, but it's actually somewhat manageable in a photonic setup.
> You are fighting the laws of thermodynamics.
Nowhere near as much as with copper. A fiber optic cable doesn't heat up.
> I certainly don't see how it beats quantum computers at the things they are good at over classical computers.
O(1) differential calculus is magic for a lot of purposes.
Can it sort names or addresses?
Otherwise for integers you don't have buy spaghetti and just use a computer to do a radix sort which is O(nw).
Another thing with analog computers is to think how they scale. I can sort 1M items on my laptop. What is the practical application of buying 1M strands of spaghetti.
Why couldn't it? Ideally they can represent real numbers with infinite precision which are identical to strings.
https://en.wikipedia.org/wiki/Real_computation
But even in non-real computation this shouldn't be a problem, the same way you can sort strings even though you have only 32/64 bits of memory at a time if that's what you are hinting at.
> Another thing with analog computers is to think how they scale.
I don't think that scale has ever been a problem for analog computers.
I'd think an array of 1B spaghetti strands might pose a few difficulties above what sorting those numbers on computers would.
There's this class https://www.utdallas.edu/atec/docs/virtual-analog-computing.... but the resources aren't online.
How will such a machine to add two numbers look like?
If a binary device has a hardware fault, bits that are in error still have a 50% chance of being correct. It seems like a single component failing here would make this worse (five times worse if it wasn't quantum).
I don't know whether or not the pros outweigh the cons here, or at what radix they do (there's probably some statistical analysis that can answer that), but ten just _seems_ like too much.
The issue that quantum computers have is not so much that individual qubits get errors, but rather that quibits become entangled with the rest of the universe, erasing our ability to take advantage of any quantom effect. To prevent this, you need to very carefully contain the quibits to prevent them from interacting with anything apart from highly controlled manipulations. The more quibits you have, the harder this becomes. If you can replace this with quidits that have more states, you can do the same computation, while needing fewer particles, making containment easier.