So this is yet another interesting system added to the list of candidates for potential QC hardware.

Nevertheless, when it comes to the realization of scalable quantum computers, qubits decoherence time may very well be eclipsed by the importance of another time span: 20 years, the length at which patents are valid (in the US this can include software algorithms).

With D-Wave and Google leading the way, we may be getting there faster than most industry experts predicted. Certainly the odds are very high that it won't take another two decades for useable universal QC machines to be built.

But how do we get to the point of bootstrapping a new quantum technology industry? ** DK Matai **addressed this in a recent blog post, and identified five key questions, which I attempt to address below (I took the liberty of slightly abbreviating the questions, please check at the link for the unabridged version).

The challenges DK laid out will require much more than a blog post (or a LinkedIn comment that I recycled here), especially since his view is wider than only Quantum Information science. That is why the following thoughts are by no means comprehensive answers, and very much incomplete, but they may provide a starting point.

*1. How do we prioritise the commercialisation of critical Quantum Technology 2.0 components, networks and entire systems both nationally and internationally?*

The prioritization should be based on the disruptive potential: Take quantum cryptography versus quantum computing for example. Quantum encryption could stamp out fraud that exploits some technical weaknesses, but it won't address the more dominant social engineering deceptions. On the upside it will also facilitate iron clad cryptocurrencies. Yet, if Feynman’s vision of the universal quantum simulator comes to fruition, we will be able to tackle collective quantum dynamics that are computationally intractable with conventional computers. This encompasses everything from simulating high temperature superconductivity to complex (bio-)chemical dynamics. ETH’s ** Matthias Troyer** gave an excellent overview over these killer-apps for quantum computing in his recent Google talk, I especially like his example of nitrogen fixation. Nature manages to accomplish this with minimal energy expenditure in some bacteria, but industrially we only have the century old Haber-Bosch process, which in modern plants still results in 1/2 ton of CO

*2. Which financial, technological, scientific, industrial and infrastructure partners are the ideal co-creators to invent, to innovate and to deploy new Quantum technologies on a medium to large scale around the world? *

This will vary drastically by technology. To pick a basic example, a quantum clock per se is just a better clock, but put it into a Galileo/GPS satellite and the drastic improvement in timekeeping will immediately translate to a higher location triangulation accuracy, as well as allow for a better mapping of the earth's gravitational field/mass distribution.

**3. What is the process to prioritise investment, marketing and sales in Quantum Technologies to create the billion dollar “killer apps”?**

As sketched out above, the real price to me is universal quantum computation/simulation. Considerable efforts have to go into building such machines, but that doesn't mean that you cannot start to already develop software for them. Any coding for new quantum platforms, even if they are already here (as in the case of the D-Wave 2) will involve emulators on classical hardware, because you want to debug and proof your code before submitting it to the more expansive quantum resource. In my mind building such an environment in a collaborative fashion to showcase and develop quantum algorithms should be the first step. To me this appears feasible within an accelerated timescale (months rather than years). I think such an effort is critical to offset the closed sourced and tightly license controlled approach, that for instance Microsoft is following with its development of the LIQUi|> platform.

**4. How do the government agencies, funding Quantum Tech 2.0 Research and Development in the hundreds of millions each year, see further light so that funding can be directed to specific commercial goals with specific commercial end users in mind?**

This to me seems to be the biggest challenge. The amount of research papers produced in this field is enormous. Much of it is computational theory. While the theory has its merits, I think the governmental funding should try to emphasize programs that have a clearly defined agenda towards ambitious yet attainable goals. Research that will result in actual hardware and/or commercially applicable software implementations (e.g. the UCSB Martinis agenda). Yet, governments shouldn't be in the position to pick a winning design, as was inadvertently done for fusion research where ITER’s funding requirements are now crowding out all other approaches. The latter is a template for how not to go about it.

**5. How to create an International Quantum Tech 2.0 Super Exchange that brings together all the global centres of excellence, as well as all the relevant financiers, customers and commercial partners to create Quantum “Killer Apps”?**

On a grassroots level I think open source initiatives (e.g. a LIQUiD alternative) could become catalysts to bring academic excellence centers and commercial players into alignment. This at least is my impression based on conversations with several people involved in the commercial and academic realm. On the other hand, as with any open source products, commercialization won’t be easy, yet this may be less of a concern in this emerging industry, as the IP will be in the quantum algorithms, and they will most likely be executed with quantum resources tied to a SaaS offering.

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Paradoxically, while science is at the foundation of all our technological progress, it is like the eye at the center of the storm - the academic mode of operation has hardly changed over the last two centuries. And why not? An argument could be made not to fix what isn't broken. For instance, sometimes you hear the scientific process compared to the Open Source movement, arguing that both strive for a transparent meritocracy where openness ensure that mistakes will not survive for long. Unfortunately, this idealized view is a fallacy on more than one count.

There are lots of good reasons for the Open Source coding paradigm, but it does not give license to forgo quality control and code review, as for instance the heartbleed bug, or the most recent widespread (and ancient!) bash vulnerability, illustrated.

On the other hand, the scientific peer review process is not anything like the open communication that goes on in public forums and email lists of Open Source software like the Linux kernel. Peer review is completely closed off from public scrutiny, yet determines what enters the scientific discourse in the first place.

The main medium of communicating scientific results remains the publication of papers in scientific journals, some of which charge outrageous subscription fees that shut out poorer institutions and most individuals. But this isn't by far the worst impediment to open scientific exchange. Rather, it is the anonymous peer review process itself, which is by design not public. Authors are often given opportunities to correct a paper by re-submitting if the original one is rejected, but ultimately the peer reviewers serve as gatekeepers.

For a discipline that is the foundation of all our technology, the knowledge generating process of science has been surprisingly untouched, and due to the build in anonymity, it has also managed to escape any scrutiny. That would be all fine and good if it was actually working. But it is not. We know little about stellar papers that may have been rejected and now linger forever in obscurity in some pre-print archive, but we know all the trash that passed final approval for publications. For instance, we get sensational headlines like this, promising an entirely new take on dark energy, but if you actually read up on this you realize that the author of the underlying paper, who is just referred to as a University of Georgia professor, is actually not a physicist but a biologist. Now far be it from me to discourage a biologist from wanting to do physics, but if you bother to read his paper on the matter you will quickly realize that the man apparently doesn't grasp the basics of general and special relativity. Yet, this was published in PLOS One which supposedly follows a rigorous peer review process. They even bothered to issue a correction to an article that is just pseudo science. Mind boggling.

Now you may think, well, this is PLOS One, although a leading Open-Access journal, the underlying business model must surely imply that they cannot pay decent money for peer review. Surely more prestigious journals, published by an organization that is known for its ludicrous journal subscription prices, such as Elsevier, will have a much more rigorous peer review process. Unfortunately you would be wrong. May I present you this Rainbow and ~~Unicorns~~ Gravity paper. It has, of course, caused the predictable splash in the mainstream media. The paper should never have been published in this form. You don't have to take my word for it, you can read up on it in detail on the blog of Sabine Hossenfelder, whose 2004 paper on black hole production the authors listed as a reference. When challenged to write up a criticism to submit to the same journal, Sabine didn't mince words:

This would be an entire waste of time. See, this paper is one of hundreds of papers that have been published on this and similar nonsense, and it is admittedly not even a particularly bad one. Most of the papers on the topic are far worse that that. I have already tried to address these problems by publishing this paper which explicitly rules out all models that give rise to a modified dispersion relation of the same type that the authors use. But look, it doesn't make any difference. The model is ruled out - you'd think that's the end of the story. But that isn't how science works these days. People continue to publish papers on this by just ignoring it. They don't even claim there is something wrong with my argument, they just ignore it and continue with their nonsense.

I have wasted enough time on this. There is something really, really going wrong with theoretical physics and this is only one indication for it.

Later in the comment thread she also had this to say:

I have had to talk to students who work on related things (not exactly the same thing) and who were never told that there are any problems with this idea. Even though I know for sure their supervisor knows. Even though I have published half a dozen of comments and papers explicitly explaining what the problems are. Honestly, it's things like this that make me want to leave academia. This just isn't research any more this is only sales strategies and networking.

The problem goes beyond peer review and comes down to accountability, but because the peer review is anonymous by design, it is especially easily corrupted, and I know of cases that resulted in exactly what Sabine spelled out: Top talent leaving academia and theoretical physics. The more I look into this the more I believe that this process at the heart of the scientific endeavour is fundamentally broken, and urgently needs fixing.

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Spoiler alert, I will summarize some of the most interesting aspects of this talk as I finally found the time to watch it in its entirety.

The first 15 min you may skip if you follow this blog, he just gives a quick introduction to QC. Actually, if you follow the discussion closely on this blog, then you will find not much news in most of the presentation until the very end, but I very much appreciated the graph 8 minutes in, which is based on this Intel data:

Daniel, deservedly, spends quite some time on this, to drive home the point that classical chips have hit a wall. Moving from Silicon to Germanium will only go so far in delaying the inevitable.

If you don't want to sit through the entire talk, I recommend skipping ahead to the 48 minute mark, when error correction on the D-Wave is discussed. The results are very encouraging, and in the Q&A Daniel points out that this EC scheme could be inherently incorporated into the D-Wave design. Wouldn't be surprised to see this happen fairly soon. The details of the EEC scheme are available at arxiv, and Daniel spends some time on the graph shown below. He is pointing out that, to the extent that you can infer a slope, it looks very promising, as it get flatter as the problems get harder, and the gap between non-EEC and the error corrected annealing widens (solid vs. dashed lines). With EEC I would therefore expect D-Wave machines to systematically outperform simulated annealing.

Daniel sums up the talk like this:

- Is the D-Wave device a quantum annealer?
- It disagrees with all classical models proposed so far. It also exhibits entanglement. (I.e. Yes, as far as we can tell)

- Does it implement a programmable Ising model in a transverse field and solve optimization problems as promised?
- Yes

- Is there a quantum speedup?
- Too early to tell

- Can we error-correct it and improve its performance?
**Yes**

With regard to hardware implemented qubit EEC, we also got some great news from Martinis' UCSB lab, whom Google drafted for their quantum chip. The latest results have just been published in Nature (pre-print available at arxiv).

Martinis explained the concept in a talk I previously reported on, and clearly the work is progressing nicely. Unlike the EEC scheme for the D-Wave architecture, Martinis' approach is targeting a fidelity that not only will work for quantum annealing, but should also allow for non-trivial gate computing sizes.

Quantum Computing may not have fully arrived yet, but after decades of research we clearly are finally entering the stage where this technology won't be just the domain of theorists and research labs, and at this time, D-Wave is poised to take the lead.

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The US already only has observer status at CERN, so bailing on ITER would sideline the American physics community even more. Despite the cost overruns and irrespective of its commercialisation prospects, ITER will make for one of the most advanced testbeds for plasma physics. Should the US really shut itself out of having prime access to this machine once it is operational?

John's post provides an excellent round-up of the various approaches to fusion, and mentions the damage that cold fusion inflicted on the field, a story that deserves a separate article. But there is another plasma phenomenon that some hope could be exploited for nuclear fusion that goes unmentioned in John's otherwise exhaustive post. It shares some communality with the dubious cold fusion experiments: Abysmally bad replicability that severely damaged the reputation of one of the lead researchers in the field. This speculative approach to fusion was recently prominently featured in a surprisingly well researched gawker article (h/t Ed B.). It mentions some private outfits that are hanging their hat on sonoluminescence, and since the latter phenomenon is, after all, an actual plasma creating micro cavitation, these companies don't deserve to be lumped in with the more shady cold fusion hustlers.

However, it is quite apparent that none of these can produce neutrons at a significant rate, unlike PNL's High Yield Neutron Generator, an already commercially valuable technology. So there clearly is not much reason to get too excited about sonoluminescence unless one of the companies invested in this approach could replicate this feat.

On balance, the influx of private money into nuclear fusion start-ups is the story here, one that gives hope that humanity may find a way to break its self-defeating fossil fuel habit within our lifetime.

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At other times, a groundbreaking progress in increasing the efficiency of solar energy would have qualified, the key being that this can be done comparatively cheaply. Alas, the unprecedented drop in the price of oil is not only killing off the fracking industry, but also the economics for alternative energy. For a planet that has had its fill of CO** _{2}**, fossil fuel this cheap is nothing but an unmitigated disaster.

So while it was a banner year for quantum computing, in many respects 2014 was utterly dismal, seeing the return of religiously motivated genocide, open warfare in Europe, a resurgence of diseases that could be eradicated by now, and a pandemic that caused knee jerk hysterical reactions that taught us how unprepared we are for these kind of health emergencies. This year was so depressing it makes me want to wail along to my favorite science blogger's song about it (but then again I'd completely ruin it).

And there is another reason to not yet let go of the past, corrections:

- No, there isn't really any evidence for primordial gravity waves in the cosmic background radiation (
*h/t Sol Warda*). I was pretty careful in reporting on this originally, and the smack down kept on coming until this retraction has now gone mainstream. (Of course it's not like this is unprecedented). - Neither does the purported correlation of Beta decay with solar radiation hold up. This was always a far stretch, but one that would have been extremely exciting, so I am glad to see that there has been yet another independent follow-up. At this point, I think the matter has been settled.

With these corrections out of the way I will finally let go of 2014, but with the additional observation that in the world of quantum computing, the new year started very much in the same vein as the old, generating positive business news for D-Wave, which managed to just raise another 29 million dollars, while at the same time still not getting respect from some academic QC researchers.

I.H. Deutsch (please note, not *the *Deutsch but Ivan) states at the end of this interview:

^{[1]}The D-Wave prototype is not a universal quantum computer.^{[2]}It is not digital, nor error-correcting, nor fault tolerant.^{[3]}It is a purely analog machine designed to solve a particular optimization problem.^{[4]}It is unclear if it qualifies as a quantum device."

No issues with [1]-[3]. But how many times do classical algos have to be ruled out before D-Wave is finally universally accepted as a quantum annealing machine? This is getting into climate change denying territory. It shouldn't really be that hard to define what makes for quantum computation. So I guess we found a new candidate for D-Wave chief critic, after Scott Aaronson seems to have stepped down for good.

Then again, with a last name like Deutsch, you may have to step up your game to get some name recognition of your own in this field. And there's no doubt that controversy works.

So 2015 is shaping up to become yet another riveting year for QC news. And just in case you made the resolution that, this year, you will finally try to catch that rainbow, there's some new tech for you.

**Update**: Almost forgot about this epic fail of popular science reporting at the tail end of 2014. For now I leave it as an exercise to the reader to spot everything that's wrong with it. Of course most of the blame belongs to PLoS ONE which supposedly practices peer review.

For reasons known only to them, science news authors seem to have collectively decided to ignore that there are many competing approaches to quantum computing. This apparent inability to differentiate between architectures and computational models makes for a constant source of confusion, which is then augmented by the challenge to explain the conceptual oddities of quantum computing, such as entanglement.

For instance, most authors, even if they may already know this is wrong, run with the simplest trope about quantum computing, which has been repeated ad nauseum: The pretense that these machines can execute every possible calculation within their input scope in parallel. Hard to imagine a misconception that would be better designed to put up a goalpost that no man-made machine could ever reach. Scott Aaronson is so incensed by this nonsense that it even inspired the title of his new book. It is truly a sorry state of affairs when even Nature apparently cannot find an author who doesn't fall for it. Elizabeth Gibney's recent online piece on quantum computing was yet another case in point. It starts off promising, as the subtitle is spot on:

After a 30-year struggle to harness quantum weirdness for computing, physicists finally have their goal in reach.

But then the reader's mind is again poisoned with this nonsense:

Where a classical computer has to try each combination in turn, a quantum computer could process all those combinations simultaneously — in effect, carrying out calculations on every possible set of input data in parallel.

Part of the problem is that there exist no other easy concepts that a news author can quickly turn to when trying to offer up an explanation that a casual reader can understand, while at the same time having his mind blown. ('Wow, every possible combination at the same time!' It's like double rainbow all over again).

Here's my attempt to remedy this situation, a simple example to illustrate the extended capabilities of quantum computing versus classical machines. The latter are very fast, but when solving a complex puzzle, i.e. finding the lowest number in an unordered list, they have to take one stab at it at a time. It is like attacking an abstract problem-space the way ancient mariners had to fathom the depth of the sea. (Gauging the depth with a rope in this manner is the original meaning of the word 'fathom').

You may argue that having several guys fathoming at the same time will give you a 'parallelizing' speed-up, but you would have to be a Luddite to the core to convince yourself that this could ever measure up to echolocation. Just like the latter can perceive data from a larger patch of seafloor, quantum computing can leverage more than just local point data. But this comes at a price: The signal that comes back is not easy to interpret. It depends on the original set-up of the probing signal, and requires subsequent processing.

Like an echolocation system, a quantum computer doesn't magically probe the entire configuration space. It 'sees' more, but it doesn't provide this information in an immediately useful format.

The real challenge is to construct the process in a way that allows you to actually get the answer to the computational problem you are trying to solve. This is devilishly difficult, which is why there are so few quantum algorithms in existence. There are no simple rules to follow. In order to create one, it requires first and foremost inspiration, and is as much art as science. That is why, when I learned how Shor's algorithm worked, I was profoundly astounded and awed by the inordinate creativity it must have taken to think up.

Regardless, if this was the only problem with Elizabeth Gibney's article, that would just be par for the course. Yet, while reporting on Google's efforts to build their own quantum computing chip, she manages to not even mention the other quantum computer Google is involved with, and that despite D-Wave publishing in Nature in 2011 and just last year in Nature Communications.

Maybe if she hadn't completely ignored D-Wave, she may have thought to ask Martinis the most pressing question of all: What kind of chip will he build for Google? Everything indicates that it is yet another quantum annealer, but the quotes in the article make it sound as if he was talking about gate computing:

“It is still possible that nature just won't allow it to work, but I think we have a decent chance.”

Obviously he can not possibly be referring to quantum annealing in this context, since that clearly works just fine with fairly large numbers of qubits (as shown in the above mentioned Nature publication).

The current state of news reporting on quantum computing is beyond frustrating. There is a very real and fascinating race underway for the realization of the first commercially useful universal quantum computer. Will it be adiabatic or the gate model? Are quantum cellular automatons still in the running?

But of course in order to report on this, you must first know about these differences. Apparently, when it comes to science news reporting, this is just too much to expect.

The Nature article also contains this little piece of information:

... the best quantum computers in the world are barely able to do school-level problems such as finding the prime factors of the number 21. (Answer: 3 and 7.)

I guess the fact that the answer is provided gives us a hint as to what level of sophistication the author expects from her audience, which in turn must be terribly confused to see a headline such as "**New largest number factored on a quantum device is 56,153**".

This is of course not done with Shor's algorithm but via adiabatic computing (and also involves some slight of hand as the algorithm only works for a certain class of numbers and not all integers).

Nevertheless, adiabatic computing seems to have the upper hand when it comes to scaling the problem scope with a limited number of qubits. But the gate model also made some major news last month. The guinea pig Simon's algorithm (one of the first you will learn when being introduced to the field) has been demonstrated to provide the theoretically predicted quantum speed-up. This is huge news that was immediately translated to the rather misleading headline "**Simon's algorithm run on quantum computer for the first time—faster than on standard computer**".

Faster in this case means less processing iterations rather than actual elapsed time, but irrespective, having this theoretical prediction confirmed using the fairly recent one-way technique clearly bolsters the case that gate computing can deliver the goods.

No doubt, the race between the architectures to deliver the first commercial-grade universal quantum computer is on. It is still wide open, and makes for a compelling story. Now, if we could only get somebody to properly report on it.

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I am not aware of many examples of exploring alternative histories with regards to science, and by that I mean in more detail than what steampunk has to offer, although William Gibson and Bruce Sterling do a pretty good job of imagining a world in which Charles Babbage succeeded in introducing a mechanical computer to the world in their book "The Difference Engine". The subject matter is certainly a worthwhile topic for another post , especially when contrasted with the challenges now to go beyond the Turing machine by getting Quantum Computing to the market. (*h/t vznvzn*)

The untimely death I am contemplating here is that of William Kingdon Clifford. If you are not immersed in physics and math, you have probably never heard his name, because we live in a world where he died young.

That meant it fell to Gibbs and Heaviside to clean up the Maxwell equations, which gave us the insufferable cross-product that confused leagues of students by requiring them to distinguish between polar and axial vectors. It also meant that complex function theory got stuck in two dimensions, and that group theory was developed without the obvious geometric connection. Which in turn, once this approach started to take over, provoked older physicists, such as Schrödinger, to coin the term "Gruppenpest" (group pestilence). It also created a false symmetry between the electric and magnetic fields, motivating the quest for the ever elusive magnetic monopol. Last but not least, it led to the confused notion that spin is an intrinsically quantum mechanical property, something that is still taught in universities across the globe to this day.

It's impossible to do Geometric Algebra (GA) justice in one short blog post, but David Hestenes managed to do so in a fairly concise and highly readable paper, the 2002 Oersted Medal Lecture.

It is hard to overstate the profound effect this paper had on me. The only thing it compares to is when I first learned of Euler's formula many years ago in my first physics semester. And the similarities are striking, not only due to the power of bringing together seemingly disparate areas of mathematics by putting them into a geometric context. In the latter case, the key is the imaginary unit, which was originally introduced to solve for negative square roots, and thus allows for the fundamental theorem of algebra. In fact, it turns out that complex numbers can be neatly embedded into geometric algebra and are isomorphic to the 2d GA case. Also, Quaternion are part of the 3d geometric algebra and have a similarly satisfying geometric interpretation.

All this is accomplished by introducing a higher level concept of vector. For instance, rather than using a cross product, an outer product is defined that creates a bivector that can be thought of as a directed plane segment.

Hestenes makes a convincing case that geometric algebra should be incorporated into every physics curriculum. He wrote some excellent textbooks on the subject, and thankfully, numerous other authors have picked up the mantle (outstanding is John W. Arthur's take on electrodynamics and Chris Doran's ambitious and extensive treatment).

The advantages of geometric algebra are so glaring and the concepts so natural that one has to wonder why it took a century to be rediscovered. John Snygg puts it best in the preface to his textbook on differential geometry:

]]>Although Clifford was recognized worldwide as one of England’s most distinguished mathematicians, he chose to have the first paper published in what must have been a very obscure journal at the time. Quite possibly it was a gesture of support for the efforts of James Joseph Sylvester to establish the first American graduate program in mathematics at Johns Hopkins University. As part of his endeavors, Sylvester founded the American Journal of Mathematics and Clifford’s first paper on what is now known as Clifford algebra appeared in the very first volume of that journal.

The second paper was published after his death in unfinished form as part of his collected papers. Both of these papers were ignored and soon forgotten. As late as 1923, math historian David Eugene Smith discussed Clifford’s achievements without mentioning “geometric algebra” (Smith, David Eugene 1923). In 1928, P.A.M. Dirac reinvented Clifford algebra to formulate his equation for the electron. This equation enabled him to predict the discovery of the positron in 1931. (...)

Had Clifford lived longer, “geometric algebra” would probably have become mainstream mathematics near the beginning of the twentieth century. In the decades following Clifford’s death, a battle broke out between those who wanted to use quaternions to do physics and geometry and those who wanted to use vectors. Quaternions were superior for dealing with rotations, but they are useless in dimensions higher than three or four without grafting on some extra structure.

Eventually vectors won out. Since the structure of both quaternions and vectors are contained in the formalism of Clifford algebra, the debate would have taken a different direction had Clifford lived longer. While alive, Clifford was an articulate spokesman and his writing for popular consumption still gets published from time to time. Had Clifford

participated in the quaternion–vector debate, “geometric algebra” would have received more serious consideration.

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The ‘god particle’, aka the Higgs boson, received a lot of attention, not that this wasn’t warranted, but I can’t help but suspect that the justification of the CERN budget is partly to blame for the media frenzy. The gay particle, on the other hand, is no less spectacular - especially since its theoretical prediction by far pre-dates the Higgs boson. Of course, what has been discovered is, yet again, not a real particle but ‘only’ a pseudo particle similar to the magnetic monopol that has been touted recently. And as usual, most pop-science write-ups fail entirely to remark on this rather fundamental aspect (apparently the journalists don’t want to bother their audience with these boring details). In case you want to get a more complete picture this colloquium paper gives you an in-depth overview.

On the other hand, a pseudo particle quantum excitation in a 2d superconductor is exactly what the doctor ordered for topological quantum computing, a field that has seen tremendous theoretical progress as it has been generously sponsored by Microsoft. This research entirely hinges on employing these anyon pseudoparticles as a hardware resource, because they have the fantastic property of allowing for inherently decoherence-resistant qubits. This is as if theoretical computer science would have started writing the first operating system in the roaring twenties of the last century, long before there was a computer or even a transistor, theorizing that a band gap in doped semiconductors should make it possible to build one. If this analogy was to hold, we’d now be at the stage where a band gap has been demonstrated for the first time. So here's to hoping this means we may see the first anyon-based qubit within the decade.

In the here and now of quantum computing, D-Wave merrily stays the course despite the recent Google bombshell news. It has been reported that they now have 12 machines operational, used in a hosted manner by their strategic partners (such as 1Qbit). They also continue to add staff from other superconducting outfits i.e. recently Bill Blake left Cray to join the company as VP of R&D.

Last but not least, if you are interested in physics you would have to live under a rock not to have heard about the sensational news that numerical calculations presumably proofed that black holes cannot form and hence do not exist. Sabine Hossenfelder nicely deconstructs this. The long and short of it is that this argument has been going on for a long time, that the equations employed in this research has some counter-intuitive properties, and that the mass integral employed is not all that well-motivated.

Einstein would have been happy if this pans out, after all this research claims to succeed where he failed, but the critical reception of this numerical model has just begun. It may very well be torn apart like an unlucky astronaut in a strongly in-homogeneous gravitational field.

This concludes another quick round-up post. I am traveling this week and couldn't make the time for a longer article, but I should find my way back to a more regular posting schedule next week.

]]>Recently a friend of mine observed in an email discussion *"I must admit I find it a little difficult to keep up with the various definitions of quantum computing." *

A healthy sign for an enlightened confusion, because this already sets him apart from most people who still have yet to learn about this field, and at best think that all quantum computers are more or less equivalent.

As computers became an integral part of peoples everyday lives, they essentially learn the truth of Turing completeness - even if they have never heard the term. Now, even a child exposed to various computing devices will quickly develop a sense that whatever one computer can do, another should be able to perform as well, with some allowance for the performance specs of the machine. Older, more limited machines may not be able to run a current software for compatibility or memory scaling reasons, but there is no difference in principle that would prevent any computer from executing whatever has already been proven to work on another machine.

In the quantum computing domain, things are less clear cut. In my earlier post where I tried my hand at a quantum computing taxonomy, I focused on maturity of the technology, less so on the underlying theoretical model. However, it is the dichotomy in the latter that has been driving the heated controversy of D-Wave's quantumness.

When David Deutsch wrote his seminal paper, he followed in Turing's footsteps, thinking through the consequences of putting a Turing machine into quantum superposition. This line of inquiry eventually gave rise to the popular gate model of quantum computing.

D-Wave, on the other hand, gambled on adiabatic quantum computing, and more specifically, an implementation of quantum annealing. In preparation for this post I sought to look up these terms in my copy of Nielsen and Chuang's 'Quantum Computation and Quantum Information' textbook. To my surprise, neither term can be found in the index, and this is the 2010 anniversary edition. Now, this is not meant to knock the book, and if you want to learn about the gate model I think you won't find a better one. It just goes to show that neither the adiabatic nor annealing approach was on the academic radar when the book was originally written - the first paper on adiabatic quantum computation (Farhi et al.) was published the same year as the first edition of this standard QIS textbook.

At the time it was not clear how the computational powers of the adiabatic approach compared to the quantum gate model. Within a year, Vazirani et al. published a paper that showed that Grover Search can be implemented on this architecture with quantum speed-up. And although the notoriety of Shore's algorithm overshadows Grover's, the latter has arguably much more widespread technological potential. The Vazirani et al. paper also demonstrated that there will be problem instances that this QC model will not be able to solve efficiently, even though they can be tackled classically.

In 2004 a paper was submitted with a title that neatly sums it up: "Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation" (Lloyd et al.)

If D-Wave had aimed for universal adiabatic quantum computation, maybe it would not have experienced quite as much academic push-back, but they pragmatically went after some lower hanging fruit i.e, quantum annealing. (Notwithstanding, this doesn't stop MIT's Seth Lloyd from claiming that the company uses his ideas when pitching his own QC venture).

An adiabatic quantum computing algorithm encodes a problem into a cost, or in this case energy function, that is then explored for its absolute minimum. For instance, if you try to solve the traveling salesman problem your cost function would simply be distance traveled for each itinerary. A simple classical gradient descent algorithm over this energy 'landscape' will quickly get stuck in a local minimum (for an analog think of balls rolling down the hilly landscape collecting at some bottom close to were they started and you get the idea). A truly quantum algorithm, on the other hand, can exploit the 'spooky' quantum properties, such as entanglement and the tunnel effect . In essence, it is as if our rolling balls could somehow sense that there is a deeper valley adjacent to their resting place and "tunnel through" the barrier (hence the name). This gives these algorithms some spread-out look-ahead capabilities. But depending on your energy function, this may still not be enough.

The graph bellow illustrates this with a completely made-up cost function, that while entirely oversimplified, hopefully still somewhat captures the nature of the problem. To the extent that the look-ahead capabilities of an adiabatic algorithm are still locally limited, long flat stretches with a relative minimum (a 'plain' in the energy landscape) can still defeat it. I threw in some arbitrary Bell curves as a stand in for this local quantum 'fuzziness' (the latter incidentally the correct translation for what Heisenberg called his famous relation).

To the left, this fuzzy width doesn't stretch outside the bounds of the flat stretch (or rather, it is negligibly small outside any meaningful neighborhood of this local minimum).

On the other hand, further to the right there is some good overlap between the local minimum closest to the absolute one (overlayed with the bell curve in green). This is where the algorithm will perform well.D-Wave essentially performs such an algorithm with the caveat that it does not allow completely arbitrary energy functions, but only those that can be shoe-horned into the Ising model.

This was a smart pragmatic decision on their part because this model was originally created to describe solid state magnets that were imagined as little coupled elementary magnetic dipoles, and the latter map perfectly to the superconducting magnetic fluxes that are implemented on the chip.

In terms of complexity, even in a simple classical 2-d toy model, the amount of possible combinations is pretty staggering as the video below nicely demonstrates. The corresponding energy function (Hamiltonian in QM) is surprisingly versatile an can encode a large variety of problems.

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