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If you drop a glass cup on the ground, it will break and shatter into pieces. This happens all the time and is consistent with quantum mechanics. But it never happens that a shattered glass cup rearranges itself from the ground into someone's hand as a whole glass cup, even though this is also consistent with quantum mechanics. We see from this example that not everything that is consistent with quantum mechanics is possible.

As far as I know, scalable quantum computing has never been demonstrated either backwards in time or forwards in time. So a fortiori, I would think that this would be good enough evidence to suggest that scalable quantum computing is impossible. Yet, some physicists believe that scalable quantum computing is still possible. Why?

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You mean aside from the bit where small scale quantum calculating elements can be built and run today? – dmckee♦ Aug 30 '12 at 14:02
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May not be the most well formulated question, but certainly does not deserve a -1. Added a +1. @Craig Feinstein: Wiki is a bit outdated, but still useful. en.wikipedia.org/wiki/Quantum_computer – Antillar Maximus Aug 30 '12 at 14:25
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@Craig so based on your comment, it sounds like you're interested in whether quantum computing is scalable, not just whether it's possible. (Because it clearly is possible; primitive implementations of Shor's algorithm do exist.) Is that accurate? – David Zaslavsky♦ Aug 30 '12 at 18:08
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Related: physics.stackexchange.com/q/7412/2451 – Qmechanic♦ Aug 30 '12 at 20:05
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Well, I down voted you because your 'question' is trite and argumentative. If everything but the title was removed it would be an improvement. – user2963 Aug 31 '12 at 12:29
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The reason is Shor error correction. Shor demonstrated that by using 9 bits for every bit, you can reverse any decoherence event on any of the 9 bits by doing some measurements on auxiliary quantities. Before the existence of error correction, it was plausible to say (and Unruh did say) the quantum computers are unphysical, because they require no error in a macroscopic system. This is an impossible position to hold past 1996.

The error correction method has been made more efficient since, by Shor and collaborators, and the upshot is that if you make a small quantum computer which is coherent for long enough time, and you can encode some dozens of qubits robustly so that you can reverse the errors faster than they occur, you can scale up the computation indefinitely without problems.

This makes quantum computation feasable for sure, and there is no way to argue that it is impossible without arguing that quantum mechanics fails.

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That's only on paper and 16 years ago. – Craig Feinstein Aug 31 '12 at 3:20
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@CraigFeinstein: It's a series of papers for one, with many citations and extensions (including a demonstration that at some finite small decoherence rate quantum computation becomes feasable), and it completely solves the problem. Why would you need another? – Ron Maimon Aug 31 '12 at 8:36
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16 years ago and also an active field since then. See for instance the QEC 2011 conference. – Emilio Pisanty Aug 31 '12 at 14:01
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@CraigFeinstein: The error correction is based on the assumption of uncorrelated errors. The evidence for this is that this is the same assumption as for classical error correction, and classical error correction works. If quantum error correction fails, it is not likely because the correlations in the environment are correlated by magic, but rather it is because quantum mechanics is not exact. – Ron Maimon Aug 31 '12 at 16:53
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@CraigFeinstein: You are not alone in this belief--- this is at the heart of what makes QM mysterious, and it has finally been distilled to an experimental question. I am not sure if quantum mechanics is exact. If you look at the question 't Hooft asks "Why do some people dismiss simple quantum models?", you will see that like you, he believes quantum mechanics is not exact. I gave a proposal for a hidden variable scheme which in my opinion works, but I genuinely don't know if nature is quantum mechanical or not, at these system sizes. Nobody knows. We'll find out with a quantum computer. – Ron Maimon Aug 31 '12 at 17:28
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Your information is slightly outdated. Quantum computing is possible. They even sucessfully implemented Shor's Algorithm to factorize a product of primes. In 2009.

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You might find this lecture by Scott Aaronson insightful.

http://www.scottaaronson.com/democritus/lec14.html

He basically makes an very convincing defence of quantum computing against arguments made by quantum computing skeptics. I certainly found it very interesting when I read it!

Also, your "entropic" argument is not entirely correct. A physical system will not change its state to one with much lower entropy spontaneously (except with overwhelmingly low probability). However, it can be brought to a state of lower entropy by performing work on it. This for example is what a refrigerator does!

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My argument is not really about entropy. It's about things that don't happen in real life, but can happen in theory. Scalable QM can happen in theory, but there is no evidence that it can happen in real life. Yet, it seems that some physicists believe that it must happen in real life or else QM theory is wrong. – Craig Feinstein Aug 31 '12 at 3:26
What do you mean precisely by something that can happen in theory but cannot happen in real life? This is a very troublesome statement. As Aaronson points out, Immanuel Kant even wrote a complete treatise to demolish it. In any case, it is true that there might be some fundamental reason why a quantum computer cannot be built, but all we have is evidence that IT CAN be built. – Juan Miguel Arrazola Aug 31 '12 at 19:14
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This whole thing is very confusing to me. I'll have to concede now that I think quantum mechanics must break down once you get things to be on the level of scalable quantum computing. There's just no way I can conceive of it working. Thank you for your answer. – Craig Feinstein Aug 31 '12 at 20:58
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Demonstration in "Real Life". Others have given you many other sources, what more do you want?

Survey of NMR Quantum Computing

D-Wave, a commercial vendor

Quantum Information Processing with Trapped ions

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very good, thank you – Craig Feinstein Aug 31 '12 at 13:46
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Several prominent physicists are on record as being pessimistic about the prospects for unlimited scalability of Quantum Computing - See for example http://arxiv.org/abs/quant-ph/0311039

(I found that link when web-searching on "Gerard 't Hooft" and "sudden death", as I recall him speculating in an on-line lecture that at some calculation/complexity threshold, quantum computing devices would undergo an unaccountable but unavoidable "sudden death", the quantum equivalent of a core dump!)

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That's what I believe and have always believed. But I haven't been able to prove it. – Craig Feinstein Sep 2 '12 at 18:07

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