# Is it proved that error rate of quantum computation is bounded by constant rather than a function dependent on time and environment by quantum theory

Anyone has proved the error rate of quantum computation is bounded by (less than) a constant rather than a function dependent on time and environment by quantum theory? For error rate and error correction of quantum computer, see Peter Shor.

I think assumptions to estimate error of quantum computation may be too simple to be practical or true, the quantum computation then has to be just a theoretical computational model.

Excuse me for posting such a question closely related to quantum theory, since physicists on physics.exchange have prohibited me from posting any suspicion about quantum computer, :D

UPDATE: Threshold theorem has to be proved with assumptions that is consistent to physics law, especially consistent to QFT, since there are fundamental obstacles to implementing scalable quantum computer; if we are unable to do so, I think we have to try to solve problem in another direction， the opposite direction, that is, trying to refute them (The assumptions infering scalable quantum computer) by physics theory.

• Comments are not for extended discussion; this conversation has been moved to chat. Sep 30, 2022 at 7:07
• quantamagazine.org/… Jan 13 at 15:19

As far as I know, nobody has come up with a convincing physics reason that fault-tolerant quantum computing is fundamentally impossible. However, it is a formidable engineering task, which is why we haven't succeeded in accomplishing it, and probably won't for at least another decade or two.

You say:

I think we have to try to solve problem in another direction, the opposite direction, that is, trying to refute (the assumptions inferring scalable quantum computer) by physics theory.

You seem to think that nobody has tried to refute the assumptions that go into the threshold theorem, which asserts that fault-tolerant quantum computing is possible. Further, you seem to think that if people tried to refute these assumptions, it would be fairly easy to do.

This isn't at all true. People have tried. Some people (Gil Kalai and Mikhail Dyakonov, for example) have even published papers explaining why they think fault-tolerant quantum computing is impossible. But most physicists do not believe that they have made a convincing argument to this effect.

• "Further, you seem to think that if people tried to refute these assumptions, it would be fairly easy to do.", no, I don't think so. And I have known that Gil Kalai and Milhail Dyakonov paper And now I vote up your answer. Sep 18, 2022 at 2:04
• I suspect it is not because of engineering, so we have to try in opposite direction, perhaps, we may find the reason. Sep 18, 2022 at 2:09
• quantamagazine.org/… Jan 13 at 15:18

While the "No Cloning Theorem" holds that we cannot copy an arbitrary state, simply by using more gates we can reduce the likelihood of receiving a significant error.

A clear introduction is both https://depts.washington.edu/emsp/finalreportexamples/JimSayreCapstone-quantumerrorcorrection-final.pdf

And Wikipedia!

https://en.wikipedia.org/wiki/Magic_state_distillation

I hope that helps.