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I am not familiar with analog computers and have found no reference that systematically discuss how errors may be modeled in an analog computer. An answer or citations are welcome. I am talking about random errors.

Along this line, what are the major types of noise in analog computers?

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  • \$\begingroup\$ Somewhat related found on the Quantum Computing stack : What exactly is meant by "noise" in the following context? \$\endgroup\$ Commented Nov 23 at 8:09
  • \$\begingroup\$ This is good. Thank you. The only advantage that a quantum computer has over an optical computer is that it is noiseless or free of errors. The struggle with making quantum computers is exactly the inability to get anywhere close to error free. \$\endgroup\$ Commented Nov 23 at 14:25
  • \$\begingroup\$ The only error in analog computers is random thermal and electronic noise in the analog signals. So the error model is just that noise. Analog computers do not generate discrete (digital) signals, so there are no discrete errors. \$\endgroup\$ Commented Nov 23 at 17:51
  • \$\begingroup\$ Thanks. I guess analog circuits differ from each other too much to have one universal error model. I guess I should reference how noise and errors are modeled in communication channels. \$\endgroup\$ Commented Nov 24 at 5:24
  • \$\begingroup\$ @YuanJohnJiang that would be a good start – and even there, there's many models, depending on what the communication channel actually models (a telephone channel is not a microwave link, is not the same as a long-distance fiberoptic link, and that's all different from the flash memory store/readout channel; all four are communication channels). But the more basic models are subjects of common textbooks, such as the excellent and freely available "A Foundation in Digital Communication" by Lapidoth. \$\endgroup\$ Commented Nov 24 at 23:26

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I believe quantum computers are a form of analog computers if an analog computer is defined as computing continuous variables.

There is Continuous-Value quantum computation, indeed, but usually the point about quantum computers is that the quanta have quantized states, i.e., not continuous states. So, let's start with "this (in its generality is wrong), but it doesn't invalidate the question".

However, their errors are modeled as bit errors.

No, not usually. That's definitely wrong. (The result of a quantum computer's computation might be something you can interpret in bits; but it's not the way errors are modelled, unless you look at the quantum computer as a black box with bits coming out, in which case all sensible things you can do is assign error probabilities.)

I am not familiar with analog computers and have found no reference that systematically discuss how errors may be modeled in an analog computer.

wikipedia would be your friend, the analog computer article is well-sourced.

Anyways, you don't care about classical analog computers, but about quantum computers.

So, read an intro book to quantum computers. Errors and error correction in quantum computers are so central to them that any textbook covers them, early on. The go-to book is "Mike & Ike", correctly called

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2010.

The introduction chapter can be downloaded from one of the authors, and would have resolved quite a few misconceptions.

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  • \$\begingroup\$ Thanks for citing the wiki. But I find no discussion on error modeling. Your understanding of quantization is wrong. Quantum physics really says that the energy of a light (and all EM) wave or the mass of an electron wave is discrete. Any other features are all standard wave characteristics. The discussion on this question should help. physics.stackexchange.com/questions/858452/… \$\endgroup\$ Commented Nov 23 at 14:16
  • \$\begingroup\$ as said, you really want to read a textbook on quantum computers; the usual ways to model errors in these is not continuous, exactly because things that don't affect the quantum state don't matter as errors. Hence, really, you need your basics to not come from isolated answers from stackexchange sites, but from a better systemic understanding. Textbooks. Read one! (that's why I explicitly recommended one that has a clear focus on errors and how noise relates) \$\endgroup\$ Commented Nov 23 at 14:18
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    \$\begingroup\$ I'm a trained (applied) physicist and know well that the mathematics of quantum physics is all good. But the physicists' understanding or explanation in WORDs is all wrong. This is just a different wording of what Feynman said. Let' get down to math instead of words. What a quantum computer can do is no more than (unitary) transforming vectors of complex numbers $(x_1, x_2, ..., x_N)$. \$\endgroup\$ Commented Nov 23 at 14:41
  • \$\begingroup\$ sure, but again, for the third time, you're asking about how errors are modelled, and I'm telling you about errors, not about the physics that make up quantum computers. Have you checked the chapter I've linked to? \$\endgroup\$ Commented Nov 23 at 15:20
  • \$\begingroup\$ I assume you mean the Nielsen and Chuang book. I ask about analog computers exactly because I'm not satisfied with what the physicists have done. Their attention is on the errors due to spontaneous emissions. All frequency modulated qubits -- superconductor, trapped ion and neutral atom type -- suffer from them. But they are not intrinsic. Photonic qubits (mode modulated) don't have the same type of errors. \$\endgroup\$ Commented Nov 23 at 16:49

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