Does something like Mohs' scale exist for quantum computing? (eg. classical = 0, hybrid = 5, pure quantum = 10)

Mohs' scale: a scale of hardness used in classifying minerals. It runs from 1 to 10 using a series of reference minerals, and a position on the scale depends on the ability to scratch minerals rated lower.

The idea came from seeing this answer which mentions "Mohs' scale of Sci-fi hardness."

  • 7
    $\begingroup$ I don't think it is necessarily that constructive to just fling every concept that is useful in one field into the field of quantum computing and see what sticks. I would suggest that if you are going to try and do this you at least suggest a relevant use-case for it or some motivation as to why it is needed. E.g. in this case some way of distinguishing computers based on their resources. This problem is already addressed by the study of quantum computational complexity. Therefore a better question could be to ask for a user-friendly computational complexity hierarchy based on resource? $\endgroup$ Jul 19 '18 at 8:58
  • $\begingroup$ @SLessyTall That is a great idea that I had not previously considered. Thank you for the suggestion! $\endgroup$
    – user820789
    Jul 19 '18 at 13:10

This is not exactly like Mohs' hardness scale, but it's a series of 5 different definitions of quantum comptuers by Michele Mosca:

Definition 1: Since the world is quantum, any computer is a quantum computer. Conventional computers are just weak quantum computers, since they don’t exploit intrinsically quantum effects, such as superposition and entanglement.

Definition 2: A quantum computer is a computer that uses intrinsically quantum effects that cannot naturally be modeled by classical physics. Classical computers may be able to mathematically simulate instances of such computers, but they are not implementing the same kinds of quantum operations.

Definition 2’: Definition 2, where there are strong tests or proofs of the quantum effects at play (e.g. by doing Bell tests).

Definition 3: A quantum computer is a computer that uses intrinsically quantum effects to gain some advantage over the best known classical algorithms for some problem.

Definition 4: A quantum computer is a computer that uses intrinsically quantum effects to gain an asymptotic speed-up over the best known classical algorithms for some problem. (The difference with definition 3 is that the advantage is a fundamental algorithmic one that grows for larger instances of the problem; versus advantages more closely tied to hardware or restricted to instances of some bounded size.)

Definition 5: A quantum computer is a computer that is able to capture the full computational power of quantum mechanics, just as conventional computers are believed to capture the full computational power of classical physics. This means, e.g. that it could implement any quantum algorithm specified in any of the standard quantum computation models. It also means that the device is in principle scalable to large sizes so that larger instances of computational problems may be tackled.

Source: https://qz.com/194738/why-nobody-can-tell-whether-the-worlds-biggest-quantum-computer-is-a-quantum-computer/#footnote

  • 1
    $\begingroup$ I think this answer is good enough that it demonstrates that the question should not have been closed. This is definitely useful and interesting, especially as we descend the hierarchy. $\endgroup$
    – Charles
    Jul 21 '21 at 0:16

We used Mohs' scale in Earth Science class to measure the hardness of rocks. If we could scratch it with our finger nail it meant the rock had a hardness of 2 or less. If not it had a hardness of 3 or more. Then if that rock could be scratched by another rock we would assign something greater and if it could scratch softer rocks we'd give it something less. Eventually we were able to come up with a self-consistent order of hardness for all rocks in the data set.

I do not see why you are comparing this to quantum computers. Why Mohs' scale and not the Richter scale or the Kinsey scale or the pH scale?

To answer your question: There is no such scale I know of for quantum, classical, hybrid computers. The reason why is probably the fact that those three (quantum, classical, hybrid) are the only things on the scale worth mentioning, so it is a ternary scale (1,2, or 3) not something more sophisticated like a 1-10. We therefore don't have to use numbers and can just use the names, which are more descriptive, self-explanatory, and therefore clear.

  • $\begingroup$ Indeed the name is arbitrary. The idea came to me after seeing this answer which mentions "Mohs' scale of Sci-fi hardness." I think at least a scale of 5 for quantum so if it is a hybrid you can tell if it is more classical or quantum. $\endgroup$
    – user820789
    Jul 2 '18 at 21:41
  • $\begingroup$ Maybe you could mention that in the question then. $\endgroup$ Jul 2 '18 at 22:02
  • $\begingroup$ However, when it comes to quantum computing, sometimes we have to be careful not to take our pants off too early. It is a fun and interesting subject to study, and we have made a lot of excellent contributions to science, mathematics, and computer science in our pursuit to building quantum computers, but there is not much point in going overboard with scales of how quantum a quantum computer is, when there is no evidence that valuable quantum computers will ever exist at all. Mosca has a scale of quantumness of quantum computers, but it is not a numerical scale like Mohs'. I'll post another. $\endgroup$ Jul 2 '18 at 22:06
  • $\begingroup$ Please note as well that my question is if something like Mohs' scale existed (which is to say I did not ask if Mohs' scale applies to quantum). $\endgroup$
    – user820789
    Jul 2 '18 at 22:08

Not the answer you're looking for? Browse other questions tagged or ask your own question.