Boaz Barak wrote a nice essay which I reblog to you below about skepticism of quantum computers. His essay is centered around a description of four scenarios (or possible “worlds” in the style of Russel Impagliazzo) about the matter. Boaz’ world are called

Superiorita(quantum computers are realistic and computational superior),Popscitopia(Quantum computers are realistic and can solve NP-complete problems), Skepticland(quantum computers are not realistic),and Classicatopia(quantum algorithms can efficiently be simulated on a classical computers).Apropos Russel’s universes, Boaz told me about a new cryptography “world” called Obfustopia that can be found (along with some modification of the original worlds) in Boaz’ survey paper. I heard about it and about the related important LWE (learning with errors) problem also from Alon Rosen.

Boaz’ essay also includes Boaz’ own optimistic personal view and also some very brief critique of my skeptical stance. Boaz conclude his personal opinion with:

The bottom line is that, as far as I can tell, Superiorita is the most beautiful and evidence-supported world that is currently on offer.Boaz’ main argument for his point of view is:

…as far as I can tell, these engineering difficulties are not fundamental barriers and with sufficient hard work and resources the noise can be driven down to as close to zero as needed.This is indeed the crux of matters and my analysis gives good reasons to think that Boaz is not correct. The different opinions are described in the pictures below and the crux of matters is “can we cross the

green line?”

Common expectationsIt is a common belief that by putting more effort for creating

qubitsthe noise level can be pushed down to as close to zero as we want. Once the noise level is small enough and cross thegreen line,quantum error correction allowslogical qubitsreducing the noise even further with small amount of additional effort . Very high qualitytopological qubitsare also expected.

The picture suggested by my analysisMy analysis (see here and here and here) gives good reasons to expect that we will not be able to reach the

green lineand that all attempts forlogicalandtopologicalqubits will yield bad quality qubits.## Finer Worlds

One can make a finer division of the superiorita world, and, in my view, the three most relevant worlds are the following:

Quantopia– The model of quantum circuits is the correct description of local quantum systems in nature and therefore universal quantum computation is possible. Quantum supremacy and robust quantum information are present and perhaps even ubiquitous in the physical world. Quantum systems, quantum information and computation are analogous to classical systems, classical information and computation. Quantum error correction is analogous to classical error correction: an important engineering tool but not the thing that makes the qualitative difference whether scalabale communication or computation is possible. (This represents Boaz’ beliefs expressed in his post and his later comments.)

Superiorita(Quantum noise below the threshold.) Quantum systems are inherently noisy. Time-dependent quantum evolutions necessarily interacts with the environment and are therefore noisy. The model of noisy quantum circuits is the correct description of local quantum systems in nature. Quantum error-correction shows that small islands representing noiseless quantum circuits can be created and may also exist in nature. Hence quantum computation is possible. (This is perhaps the most common view among researchers in quantum information.)

Skeptica– (Quantum noise above the threshold.) Quantum systems are inherently noisy. Time-dependent quantum evolutions necessarily interacts with the environment. The model of noisy quantum circuits is the correct description of local quantum systems in nature. The noise level cannot be pushed below the level allowing quantum error-correction and quantum fault-tolerance. Hence quantum computation is not possible. Quantum supremacy is not demonstrated in nature and cannot be demonstrated in the laboratory. (This is were I stand).There are, of course people who are skeptical about quantum computers from other reasons like the young Boaz who simply did not like physics. There are people who for various reasons are skeptical of quantum mechanics.

Quantopia suggests that “quantum supremacy” and “robust quantum information” will be present and in fact ubiquitous in the physical world, while under ” superiorita” quantum supremacy represents rare a islands inside a large “decoherence desert” (as Daniel Gottesman referred to it in his beautiful picture portrayed in this post.) The difference between quantopia and superiorita is relevant to Scott Aaronson’s hope that quantum computers promise

trillion dollarsindustry via simulations. While additional computing power is always welcome this idea is less promising in the superiorita scenario where the usefulness of quantum computers to simulation is less clear.Anyway, here is Boaz’ piece.

(see also pdf version)

*Quantum computing* is one of the most exciting developments of computer science in the last decades. But this concept is not without its critics, often known as “quantum computing skeptics” or “skeptics” for short. The debate on quantum computing can sometimes confuse the *physical* and *mathematical* aspects of this question, and so in this essay I try to clarify those. Following Impagliazzo’s classic essay, I will give names to scenarios or “potential worlds” in which certain physical or mathematical conditions apply.

## Potential worlds

**Superiorita** is the world where it is feasible to build scalable quantum computers, and these computers have exponential advantage over classical computers. That is, in superiorita there is no fundamental physical roadblock to building large quantum computers, and hence the class BQP is a good model of computation that is physically realizable. More precisely, in superioriata the amount of resources (think…

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I’m with you Gil, but what to make of the like of this well credentialed startup? http://www.afr.com/leadership/entrepreneur/csiros-main-sequence-ventures-backs-qctrl-a-quantum-computing-firmware-startup-20171031-gzc0to

Dear Philip, thanks! I follow the amazing commercial activity towards quantum computers with great interest. See this post https://gilkalai.wordpress.com/2017/04/03/the-race-to-quantum-technologies-and-quantum-computers-useful-links/ which have frequent (bi-monthly) updates.

I think that the picture I draw is the correct one, which is a bit scary given the very different picture representing the common expectations. In any case, there is a good argument for my stance, it has very interesting consequences, and there is quite a bit more to do. Experiments in the near future (next few years) will be very telling!

The debate about decoherence and noise started by Bill Unruh is a red herring. The Born rule is metaphysical fluff and QM just gives expectations of observables. The idea that uncertainty leads to computational speedups is absurd. Paul Davies pointed out that a 400-qubit computer would even come into conflict with the cosmological information bound implied by the holographic principle. It’s not only that Turing-complexity arguments cannot be run backwards but that there is a major debate about the completeness of mathematical descriptions in quantum mechanics. The real point is that some argue QC people are just rediscovering analog computing.

David Hestenes: Quantum physicists claim that anticommutivity expresses incompatibility of spin measurements in orthogonal directions. On the contrary, I proposed that {σ1,σ2,σ3} is simply a frame of three orthonormal vectors; anticommutivity expresses orthogonality, and σ1σ2 represents a directed area, while σ1σ2σ3 = i is a pseudoscalar representing an oriented volume. How is it, I asked my father, that the great theoretical physicists and mathematicians Pauli, Dirac, Weyl, von Neumann—all failed to recognize the geometric import of the Pauli algebra. My father’s response is the greatest compliment I ever received: “You have learned the difference between a mathematical concept and its representation by symbols—many mathematicians never learn that!”

https://link.springer.com/content/pdf/10.1007/s00006-016-0664-z.pdf

http://geocalc.clas.asu.edu/pdf/SnarkPaper.pp.pdf