On the (im)possibility of quantum computing by Gheorghe Sorin Paraoanu

A truly excellent paper. Digital physics appears to be an uncomfortable subject for many in the theoretical physics community (especially string theorists), but you have thoughtfully and rigorously explored some of the puzzles it poses. Also, good writing. Bravo.

While perhaps pleasant to read, I find the arguments narrow and not "up to date" with recent scientific progress.

For example, why does the author see quantum computation almost exclusively as a means to factorize numbers? For me, the discussion about number theory comes "out of the blue", unmotivated. This probably comes from the authors narrow premise that number theory is all about finding an efficient algorithm for factorization.

Also, recent (and quite spectacular) experimental evidence that molecular biological systems are using some kind of quantum computation (at least, they have a way to maintain macroscopic quantum coherence in noisy environments) is ignored. See, for example, Paul Davies recent review in Physics World (http://physicsworld.com/cws/article/print/39669).

Such claims about the "impossibility of quantum computation" might in fact be a good sign for its prosperous future.

Hello Owen and Daryl - thanks a lot for the kind words.

Andreas - I am happy that you enjoyed the essay. I think I owe you some clarifications:

I am using factorization just as an example.

I am not saying that number theory is all about factoring numbers, but it is certainly a lot about primes and their properties. The same with quantum computing: while there are several quantum algorithms, not all of them are truly useful - the "killer application" for quantum computing is in the end factoring numbers.

I don't have access to the paper by Paul Davies, but I suppose it comments on these two important results that appeared 2 years ago:

*G. S. Engel et al., Evidence for wavelike energy transfer through quantum

coherence in photosynthetic systems, Nature 446, 782-784 (2007).

* H. Lee, Y.-C. Cheng, and G. R. Fleming, Coherence dynamics in photosynthesis:

protein protection of excitonic coherence. Science 316, 1462(2007)

These results have electrified the "quantum" community. It would be indeed fascinating if quantum effects were to play a role in making life tick. I mean quantum effects in the strong sense, that of producing and using entanglement and superpositions to make certain processes more efficient, like in a quantum computer. We are far from having any solid evidence that this is the case in biological systems. This whole discussion is too involved to be just mentioned or squeezed in a short essay. There is a very good review-style paper on arXiv addressing all the relevant issues in detail:

arXiv:0806.4552, Entanglement and intra-molecular cooling in biological systems? - A quantum thermodynamic perspective

Authors: Hans J. Briegel, Sandu Popescu

Hello,

Just a brief follow-up on the discussion above about factorization, which, in terms of mathematical beauty at least, looks like an ugly duck.

On the other hand, factorization is the mathematical equivalent of splitting matter: prime numbers are the "atoms" out of which any integer number is made of. Not being able to factorize efficiently numbers seems to be a symptom

of the more general idea that it is not always possible to break down complex, large-scale entities into distinct, "elementary" units. That is, it hints to a failure of reductionism already at the

mathematical level. P.W. Anderson wrote a famous essay in 1972 titled "More is different" - and indeed so: although things are made of parts,

given the large numbers involved, it could be

principially impossible to express the higher-order, emergent laws, in terms of elementary components - and, while many of us accept that this is indeed the case for example with biology versus

physics, it is quite surprising that such a limitation could be embedded already at the mathematical level.

... Then also the fact that

gravity is notoriously difficult to reconcile with quantum mechanics becomes by this a bit more understandable:

the general theory of relativity is an "intensely classical" theory, requiring concepts such as

clocks, measuring rods, and so on, which have intrinsic properties (unlike quantum-mechanical entities).

Many years ago, Wigner wrote an

excellent review on the conceptual tension between quantum theory and relativity

(Rev. Mod. Phys. 29,255 (1957)).

In this sense,

if, in general, reducing higher-level laws to lower-level laws would require exponentially-increasing

(in the number of components) resources, then it could be that there exists a true epistemological gap

between "elementary" and "emergent" laws - and not only that we will never find a theory of everything

but the concept itself is inconsistent. In other words, our ability of completely classifying

reality into elementary entities is impaired when

complex objects - which have no underlying symmetry - are considered.

Quantum computing

can be then regarded as a particular attempt to jump-pass this gap, by assuming full control over

the emergent properties of a complex system through local manipulations of the individual components.

P.S. Apologies for the terrible editing of the comment above.

Gheorghe

A very interesting - and very well argued - essay, with a great surprise ending. Some comments:

1. You conclude with the words: "But surprising connections between number theory and physics have been discovered [15]. Something tells us that we are just scratching the top of the iceberg here, and the reason for saying so is that these connections seem to occur precisely in topics such as renormalizable field theories, low-dimensional field theories, etc., where (despite the success in comparison with experiments), we have the least intellectual confidence that the concepts we are using are the optimal ones".

I have just read another essay on Nuclear Physics by Norman Cook which - surprise surprise - features numerology as a fundamental issue. Numerology (unexplained numerical relationships e.g. the distribution of primes) is the raw material of Number Theory. No surprise, it is the concluding issue dealt with in my essay.

2. Your last sentence is "Maybe, after all [16], in the beginning was the number. ". I think you misunderstand the quotation in a scientific sense. Kronecker was only half right. Except for computers, words are not numbers.

Gheorghe

I think your last paragraph is a good way to start looking at fundamentals (although its Biblical Garden of Eden overtones may frighten some around here and lose you a few friends).

Thanks for your kind words. People either like what I wrote very much, or not at all. Going by the ratings there are more of the latter. This does not surprise me. It was written to be enjoyed, especially by me. It's really only a form of therapy to keep my blood pressure down.

PS No one has yet refuted any of my 10 points - despite the low marks. Interesting insight on the psychology of the group.

Dear Georghe,

When I got aware of basic mistakes in mathematics and its application to physics, I arrived at two serious suspicions:

- Apparent time symmetry of the wavefunction can be explained as an artifact due to improper interpretation for the result of complex calculus of equivalent mathematics. Maybe, even SUSY is affected. Let's wait for results from LHC.

- Complex representation of unilateral functions does not provide an additional degree of freedom but just additional redundancy. The EPR issue reiterates Buridan's ass. I suggest abandoning questionable, unnecessary, and belief-based rigor in mathematics and return to humble pragmatism instead. Because quantum entanglement was introduced by Schroedinger in reaction to EPR, I do not entirely exclude that all of the many (?) pieces of progress towards quantum computing as promised are possibly elusive.

May I ask you to check this?

Regards,

Eckard

I apologize for misspelling you Gheorghe.

Let me add some reasons why I tend to distrust:

We both have perhaps in common that we grew up within a communist country. Mutually contradicting ideologies cannot be true. Berlin was heavily punished for mistakes.

I wonder a bit how Nimtz does still manage to find experts who seem to accept his evidence for having measured propagation of signals with a speed in excess of c. While I did not deal thoroughly with his mistake, I realized that it relates to questionable but generally accepted mathematical basics.

Zeh commented in a blog at FQXi on one more allegedly sensational experimental evidence.

I feel embarrassed by how stubborn not just PRL ignores justified objections against a paper by Gompf et al. For a valid link and details see [link:www.fqxi.org/community/forum/topic/527] recent discussion on my essay. [/unlink]

In JASA "confirming evidence" was published although Ren provided compelling direct measurements that exclude the correctness of a Nobel price awarded tenet. .

Eckard

Dear Gheorghe,

Let me guess: The letters h in your name make sure in Romanesc language that George is pronounced like a German, not French or English. Right? It happens that my guesses are correct.

I refer to your essay. As an expert you certainly right: Quantum computers do not yet exist. I recall that already several years ago an enterprise announced first available quantum computers. My guess was: This sounds like fraud.

You wrote:

Counting is perhaps the first mathematical trick we learn as children ...

--- I would like to object. I see the first step the recognition of a unity that then can be recognized repeatedly and thereafter be counted. Ancient Greeks understood that two is the first number.

You continued: ... Construction of the universe... . Maybe, after all [bible], in the beginning was the number.

--- Do not mystify a failure.

Do you absolutely exclude a third scenario?

Regards,

Eckard

The most meaningful limit imposed by Nature would still be present even if quantum computation turns out to be a howling success: the fact that in the end, when the qubit is measured and its output read, to quote Hans C. von Baeyer: "all we've got is one lousy classical bit."

Maybe, for all we know, an uncollapsed, superposed qubit contains all the information in the cosmos, it might be a microcosm of the Mind of God, but a fat lot of good that'll do us. The human mind can't read the quantum code and never will. So since a quantum computer would simply be a very, very, very fast classical computer please at least let us have that much. Pretty please.

Hello Eckard and Nick,

After reading your comments I started to wonder: what is in the end the most elementary process of knowledge - if you want, the "epistemological atom"? One guess is that it is the act of separation: the understanding of the difference. This is what newborns must do first: to figure out that the world is made of distinct objects. This makes possible counting and organizing the objects in sets.

It is very interesting that the possibility of differentiating is clearly allowed in the classical world but so much trickier in quantum physics, where, as we all know, we have indistinguishability and so on. Still, this doesn't seem to preclude our ability to count these indistinguishable particles. So it is possible to count without differentiating, which is one nice thing to wonder about ....

Best wishes,

G.S.P.

As Zeilinger puts it, "A photon is a click in a photon counter." Which led another physicist (forget exactly who) to wonder if AZ is a click in an Anton counter.

Must ponder that.

It was David Mermin, who's often fun. The full quote:

"Photons are clicks in photon counters." A special case of Aage Bohr and Ole UIfbeck's rule that there are no particles, only clicks. Would Anton agree that electrons are clicks in electron counters? Are fullerenes clicks in fullerene counters? Is Anton a click in an Anton counter?

Dear Gheorghe,

"This is what newborns must do first: to figure out that the world is made of distinct objects. This makes possible counting and organizing the objects in sets."

-- Yes.

".... in quantum physics, where, as we all know, we have indistinguishability and so on. Still, this doesn't seem to preclude our ability to count these indistinguishable particles. So it is possible to count without differentiating, which is one nice thing to wonder about ...."

-- I do not attribute uncertainty just to quantum physics but to any pair of conjugate variables including time and frequency.

In order to hope for counting without having distinct objects, one must be at least as naive and insane as was Georg Cantor.

Will it be a nice thing to wonder about why neither aleph_2 nor quantum computers nor the search for SUSY with LHC were successful? Wouldn't it be better to check whether the arguments of a nobody like me might be not entirely unfounded?

Meanwhile I consider 3,000,000,000.00 € for the LHC experiment peanuts as compared to some bubbles on the finance market. Nonetheless, doesn't physics deserve honest realism?

Regards,

Eckard