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Just need some clarification: Results derived as the output of "running" a "quantum circuit" constructed from "quantum gates" are distributed in a certain way, based on the design, and the multiple possible outputs have a distribution with the desired one having the highest probability of occurrence. By using more qubits the "signal to noise" ratio may be improved (by using the appropriate implementation of the "quantum circuit").

Is my interpretation right or I am missing some key components?

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  • $\begingroup$ Increasing the number of qubits won't magically increase the likelihood of getting the correct results. The probability of getting correct results is highly dependent on the noise levels and the specific algorithm employed. Terms like "signal to noise" ratio simply do not make sense in quantum computing (unless you manage to put forward a precise definition for "signal" in the quantum computing paradigm). Please do not use analogies to try to learn the subject; it'll only confuse you (and is one of the shortest routes to full-blown crackpottery). $\endgroup$ – Sanchayan Dutta Nov 28 '19 at 4:16
  • $\begingroup$ @Sanchayan First point: When you have a group of values derived from a measurement where each can have a different probability of occurrence and you have one which need to stand out - this one is the "signal" and all the other are noise. Second point: depending on what you attempt to compute you "design" your circuit - this is what is called ASSP (Application Specific Signal Processor) where the input is Signal which are processed by the Circuit (processor) to create the processed output - the measure gate. Third point: nothing happens magically - it needs to be designed properly. $\endgroup$ – Moti Nov 28 '19 at 6:54
  • $\begingroup$ Okay, your definition of SNR and ASSP make more sense now, but I do not see the need of invoking them here. If you want to ask whether increasing number of qubits can increase the likelihood of getting correct results you can ask that concisely by removing the unnecessary terminologies. Or at least, include the definitions in the question body. $\endgroup$ – Sanchayan Dutta Nov 28 '19 at 7:01
  • $\begingroup$ If you think the interpretation is wrong - I will be happy to learn. Even pointing to the right article will suffice. And with regard to the use of more qubits - it can not make the result correct. It will make it more distinct with better probability to be correct. $\endgroup$ – Moti Nov 28 '19 at 7:06
  • $\begingroup$ Yes, after you've clarified the terms in the comments above I do think the question is answerable. I'll try writing up an answer in the evening, if someone doesn't beat me to it. $\endgroup$ – Sanchayan Dutta Nov 28 '19 at 7:12
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Yes, when you run an algorithm, often specified as a sequence of gates, you get different results according to some probability distribution.

Assuming we are talking about an error-free computation (this is where, in this field, we use the terminology "noise" which is distinct from the "noise" of "signal to noise ratio"), then most algorithms that you will currently find are designed in such a way that as the size of the input increases (and you therefore use more qubits), the success probability tends to 1 (increasing signal to noise ratio, to use your terminology). However, for a fixed input, you cannot always just throw more qubits at the problem and somehow magically expect to improve the probability of the correct outcome. (That said, some algorithms such as phase estimation do work like that.)

Instead, what you can do is exactly what you'd do with probabilistic classical computation: repeat the computation many times and perform a majority vote for the answer. You could do this in parallel, using more qubits, but you can also do it sequentially, and not use any extra qubits at all.

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  • $\begingroup$ Thanks for the clear response and confirming my BASIC understanding. I would add that the Shannon limitation may be (with the proper variation) applied to QC. $\endgroup$ – Moti Nov 28 '19 at 18:49

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