<p>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.</p>
<p>You say:</p>
<blockquote>
<p>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.</p>
</blockquote>
<p>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.</p>
<p>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.</p>

CC BY-SA 4.0
2022-09-18T02:04:04.327Z
"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.
XL _At_Here_There
CC BY-SA 4.0
2022-09-18T02:09:52.700Z
I suspect it is not because of engineering, so we have to try in opposite direction, perhaps, we may find the reason.
XL _At_Here_There
CC BY-SA 4.0
2023-06-16T03:59:17.153Z
Jin-yi Cai gives a negative answer to your opinion and supports me： https://rjlipton.wpcomstaging.com/2023/06/14/a-little-noise-makes-quantum-factoring-fail/
XL _At_Here_There
CC BY-SA 4.0
2023-06-16T12:22:17.120Z
Read the comments on Lipton's blog — Jin-Yi Cai's computation is not as novel as Lipton makes it sound.
Peter Shor 
CC BY-SA 4.0
2023-06-20T04:18:06.807Z
https://www.nature.com/articles/s41586-023-06096-3  I think the article is a propaganda.
XL _At_Here_There
CC BY-SA 4.0
2024-09-09T03:46:43.227Z
https://wp.optics.arizona.edu/opti646/wp-content/uploads/sites/55/2016/08/Haroche-Raimond.pdf
XL _At_Here_There
CC BY-SA 4.0
2023-01-13T15:18:47.490Z
https://www.quantamagazine.org/new-algorithm-closes-quantum-supremacy-window-20230109/
XL _At_Here_There
CC BY-SA 4.0
2022-09-17T17:43:29.510Z
2022-09-17T23:10:28.803Z
2022-09-17T23:10:28.803Z
Peter Shor 
<p>While the &quot;No Cloning Theorem&quot; holds that we cannot copy an arbitrary state, simply by using more gates we can reduce the likelihood of receiving a significant error.</p>
<p>A clear introduction is both
<a href="https://depts.washington.edu/emsp/finalreportexamples/JimSayreCapstone-quantumerrorcorrection-final.pdf" rel="nofollow noreferrer">https://depts.washington.edu/emsp/finalreportexamples/JimSayreCapstone-quantumerrorcorrection-final.pdf</a></p>
<p>And Wikipedia!</p>
<p><a href="https://en.wikipedia.org/wiki/Magic_state_distillation" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Magic_state_distillation</a></p>
<p>I hope that helps.</p>

CC BY-SA 4.0
2022-12-02T12:31:15.843Z
2022-12-02T13:30:33.190Z
2022-12-02T13:30:33.190Z
user67998
<p>Anyone has proved the error rate of quantum computation is bounded by (less than) a <strong>constant</strong>  rather  than a function dependent on time and environment by quantum theory? For error rate and error correction of quantum computer, see <a href="https://arxiv.org/abs/2208.09964" rel="nofollow noreferrer">Peter Shor</a>.</p>
<p>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.</p>
<p>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</p>
<p><strong>UPDATE:</strong> 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.</p>

CC BY-SA 4.0
2022-09-30T07:07:09.883Z
Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/139537/discussion-on-question-by-xl-at-here-there-is-it-proved-that-error-rate-of-quan).
Bjørn Kjos-Hanssen
CC BY-SA 4.0
2023-06-16T03:57:25.123Z
receent research support my opinion https://rjlipton.wpcomstaging.com/2023/06/14/a-little-noise-makes-quantum-factoring-fail/
XL _At_Here_There
CC BY-SA 4.0
2024-03-21T13:30:25.040Z
It has now been experimentally demonstrated that [quantum error correction](https://www.nature.com/articles/s41586-023-06927-3) can improve the error rate for logical qubits beyond the underlying error rate for the physical qubits.
Peter Shor 
CC BY-SA 4.0
2023-01-13T15:19:11.203Z
https://www.quantamagazine.org/new-algorithm-closes-quantum-supremacy-window-20230109/
XL _At_Here_There
<quantum-computing><quantum-information><physics>
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
XL _At_Here_There
# 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

(Asked by: username_0 on 2022-09-07)

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](https://arxiv.org/abs/2208.09964).

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.

**Tags:** quantum-computing, quantum-information, physics

> **Comments:**
> **username_1**: Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/139537/discussion-on-question-by-xl-at-here-there-is-it-proved-that-error-rate-of-quan).  
> **username_0**: https://www.quantamagazine.org/new-algorithm-closes-quantum-supremacy-window-20230109/  
> **username_0**: receent research support my opinion https://rjlipton.wpcomstaging.com/2023/06/14/a-little-noise-makes-quantum-factoring-fail/  
> **username_2**: It has now been experimentally demonstrated that [quantum error correction](https://www.nature.com/articles/s41586-023-06927-3) can improve the error rate for logical qubits beyond the underlying error rate for the physical qubits.  

---

## 2 answers

### Answer by username_2 on 2022-09-17. Score: 5

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.

> **Comments:**
> **username_0**: "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.  
> **username_0**: I suspect it is not because of engineering, so we have to try in opposite direction, perhaps, we may find the reason.  
> **username_0**: https://www.quantamagazine.org/new-algorithm-closes-quantum-supremacy-window-20230109/  
> **username_0**: Jin-yi Cai gives a negative answer to your opinion and supports me： https://rjlipton.wpcomstaging.com/2023/06/14/a-little-noise-makes-quantum-factoring-fail/  
> **username_2**: Read the comments on Lipton's blog — Jin-Yi Cai's computation is not as novel as Lipton makes it sound.  
> **username_0**: https://www.nature.com/articles/s41586-023-06096-3  I think the article is a propaganda.  
> **username_0**: https://wp.optics.arizona.edu/opti646/wp-content/uploads/sites/55/2016/08/Haroche-Raimond.pdf  

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### Answer by username_3 on 2022-12-02. Score: -1

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.


---

