Comment by HarHarVeryFunny | Hacker News Reader

Comment by HarHarVeryFunny | Hacker News Reader

HarHarVeryFunny

It's interesting that analog computers embody both meanings of "analog" - that of continuous quantities vs discrete/digital ones, and also of one thing being comparable to ("an analog of", cf analogy) something else.

The article seems to put a bit of a silly spin on an interesting subject by wanting to present analog computers as a potential alternative to digital ones, when in fact that is only rarely going to be possible.

Digital computers support programming - solving of problems by describing the process by which they are to be solved, whereas analog computers instead support solving of (limited types) of problem by building an analog of the problem (which you could think of as "describing" the problem, rather than how to solve it), either using analog electronics (a patch panel analog computer), or by building a physical analog of it such as the Antikythera mechanism which models the motions of the planets.

The article oddly omits any mention of quantum computers which (unless I'm totally misguided!) are essentially a type of analog computer - one that is no replacement for digital computers and general problem solving since it can't be programmed, but rather only works when one can configure it to be an analog of the problem to be solved. As with any other type of analog computer, the problem is then solved by letting the system run and the dynamics play out.

Quantum/classical is orthogonal to the analog/digital distinction. There are analog quantum computers and digital quantum computers.

Analog quantum computers (like annealers) are simpler to make, and they have a lot more play w.r.t. their building blocks when trying to make interesting effects... but ultimately they are limited by noise. Digital quantum computers restrict themselves to finite gate sets, often requiring expensive decompositions to do basic operations (e.g. [1]), but those gates are compatible with error correction so noise can be suppressed arbitrarily (e.g. [2]). It's very similar to how an analog classical computer can do addition with two resistors and a junction, but the accuracy is limited by the precision of the resistance. Whereas a digital classical computer will decompose the addition problem into bits and gain more precision by adding bits so that increasing precision becomes about increasing quantity instead of quality.

[1]: https://www.mathstat.dal.ca/~selinger/newsynth/

[2]: https://arxiv.org/abs/1208.0928

Right, but even with the "digital quantum computer" (i.e. error-corrected quantum computer) aren't they still used in same fashion as an analog computer - one has to configure (cf patch panel) the computer into being an analog of the problem to be solved, then let the natural dynamics do it's thing, rather than being able to program it to perform some step-wise algorithm of the user's choosing?

No, that's not true at all.

For example, a chemistry simulation can be done in first quantization; where the state is a list of superposed 2s-complement integers indicating the positions of the electrons (as opposed to a more direct one-qubit=one-position mapping). And the list is initialized in a way that satisfies the Pauli exclusion principle by using a sorting network [1]. This is presumably not at all how Nature does it.

Another example is factoring. Shor's factoring algorithm is not at all like behaving analogous to a physical system. It's about modular exponentiation and Fourier transforms; math things not physics things.

Yet another example is Hamming weight phasing. If you need to rotate many qubits by a common angle around the Z axis, you can achieve that effect more cheaply by temporarily computing their Hamming weight (under superposition) and then rotating the first qubit of the Hamming weight register by the angle, the second by twice the angle, the third by four times the angle, etc. And actually that various-rotation-angles operation can then also be replaced by an addition into a special reusable phase gradient state; this achieves the desired effect by phase kickback [2]. Adding the Hamming weight of their spins into a helper state is probably not how Nature goes about precessing electrons in a uniform magnetic field.

[1]: https://arxiv.org/abs/1711.10460

[2]: https://arxiv.org/abs/1709.06648

Isn't that where the term analog for continuous values comes from though? That they are voltages that vary in proportion to physical quantities? And therefore analogous to those quantities.

Makes sense - I was wondering about the connection, but lazily looking up the etymology of the word didn't provide any obvious answer.

Yep: https://english.stackexchange.com/questions/241379/what-is-t...

Quantum computers deserve to be mentioned in discussions about analog computers. Under the assumption that nature is quantum at its core it follows that every analog computer could instead by replaced by a quantum computer running a suitable algorithm.

This connection opens doors for research in both directions, how to design quantum algorithms and how to built physical computing systems that make use of quantum mechanics.

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