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Comment by mrfusion | Hacker News Reader

But isn’t everything we compute ultimately tied to a physical system?

A computer is broken up into small discrete steps where error correction can happen. The essential idea is that the logical space of the computer is a suitably "discrete" set of points in the actual phase space of the system on which it is embdedded. By discrete, I mean that there is some radius around each valid point of the phase space, such that the collection of all of the balls of that radius around the valid points are still disjoint. I have a special operator that I then use to map each ball down to its corresponding point called a projection (Invoking this operator requires me to generate waste heat, see Landauer's principle. Also, in reality, I do not have points. I have small regions contained in larger regions).

I then generate a system of computational primitives which reliably map the small regions inside of these larger regions, with the result that I can perform projection, computation, projection, and be reasonably certain that my process deterministic acts on the small regions, without knowing anything about the particular computation that I have performed except that it was made out of the primitives.

This projection gets performed after every computational step, and is the thing that separates a digital computer from an analog computer. It is also a thing that separates digital computers from quantum computers, except that the physicists (in my mind incorrectly) believe that they have a scheme which can perform the error correction without damaging the logical state, and can use this scheme to produce a high enough fidelity state at the start that the whole program can be run without loss of coherence.

This is a very interesting way of thinking about computation - do you have any sources you recommend?

His explanation is kind of the high-fidelity version of the first day of digital electronics class. Digital computation relies on voltage levels that are high or low. The voltage level of the output of a step is not directly related to the voltage of the input, just whether that voltage falls in the low range or the high range. This fact prevents inexact voltage from compounding over time. Maybe you're using 3.3v logic; one step's input could be 3.2v and that would still be a high, and the output, if high, might be 3.5v. Non-digital systems don't inherently have that constant resetting of levels back to discrete values like digital systems do.

I had a lot of finals, and the answer to this comment that I did not write was essentially accurate. The people who think about computers this way are the people who have to implement them on analog devices, aka the electrical engineers. There is a discrete analog (lol) in the form of coding theory, since it often more practical to make a slightly noisy discrete space and then perform discrete error correction.

I was looking at your other comments to see how I should answer you, and I gathered that I can just link you papers. I imagine Von neumann and Hamming and shannon all have something to say about this topic, but since we're talking about quantum computing, I believe the relevant work can be found in these, and their references.

https://arxiv.org/abs/quant-ph/9705052

https://arxiv.org/abs/quant-ph/0403025

I'll check back on this thread if you have questions. If I had all of the answers to my own questions though, I would be famous.

Yes but most of the time the compute abstractions are reasonably accurate that a slight loss of fidelity is still magnitudes better than physical experimentation. For example if you want to build a Boston dynamics style robotic dog, a kinematics simulator coupled with a CAD tool can get you a long way cheaply versus having to build hundreds of prototypes.

Isn't it an abstraction that can be concretized in more than one way? Either voltages in silicon or buckets of water should give you the same answer.

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