Quantum Bayesian Networks

December 5, 2017

The Toronto Quantum Meetup Supremos invite you to their next Meetup on Bill Gates and Bayesian networks

Filed under: Uncategorized — rrtucci @ 4:30 pm

The Toronto Quantum computing Meetup is the largest meetup in the world dedicated to quantum computing, so we claim the title of Quantum Meetup Supremacy, at least for now. (currently we have 873 Supremos as members. The second biggest club is in Austin with a paltry 630 Fajitas members)

We cordially invite you to our next meeting on Dec 15 . This meeting will start by addressing the question: “Was Bill Gates lying to the American people when he stated to the press that he doesn’t understand quantum computing?”. This question has cruelly split the American nation along party lines.

Consider the evidence:

  • Here are the beginning lines of an Oct 1996 article in the Los Angeles Times

    When Microsoft Senior Vice President Steve Ballmer first heard his company was planning to make a huge investment in an Internet service offering movie reviews and local entertainment information in major cities across the nation, he went to Chairman Bill Gates with his concerns.

    After all, Ballmer has billions of dollars of his own money in Microsoft stock, and entertainment isn’t exactly the company’s strong point.

    But Gates dismissed such reservations. Microsoft’s competitive advantage, he responded, was its expertise in “Bayesian networks.”

    Asked recently when computers would finally begin to understand human speech, Gates began discussing the critical role of “Bayesian” systems.

    Ask any other software executive about anything “Bayesian” and you’re liable to get a blank stare.

    Is Gates onto something? Is this alien-sounding technology Microsoft’s new secret weapon?

    Quite possibly.

  • But here are the beginning lines of a Nov 2017 article in MSN.com

    Bill Gates doesn’t completely understand quantum computing, the Microsoft Corp. co-founder and verified computer whiz told the Wall Street Journal Monday.

    “I know a lot of physics and a lot of math. But the one place where they put up slides and it is hieroglyphics, it’s quantum,” Gates said.

The host of the meeting, Henning Dekant, CEO of the company artiste-qb.net that I work for, will try to argue that Bill Gates is wrong. If only Gates realized that quantum computing languages can be written very intuitively as Bayesian Networks, the scales would fall from his eyes and he would recognize that the countenance of Quantum Computing is the same as that of his old love, Bayesian Networks.

Jesting aside, Henning will also speak about artiste-qb.net’s ongoing work to use quantum bayesian networks in quantum computing.

Mr. Gates, I never met Steve Jobs but I read his friking biography, and you, Mr. Gates, are no Steve Jobs, sir!

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December 3, 2017

You are invited to the wedding of Quantum Computing and TensorFlow

Filed under: Uncategorized — rrtucci @ 6:42 pm

The quantum computerization of TensorFlow (TF) is a quixotic dream that no doubt has crossed the minds of many, both technically and not technically savvy, people. Here at artiste-qb.net, we are very committed and well underway to achieving this goal. Since our company is fully committed to open source, it doesn’t really matter if we achieve this goal before anyone else. If someone else beats us to it, we will learn from their code and vice versa. That is, as long as they too deliver open source to the world. And if they don’t, we think that their software is doomed…quantum open source rules! How did Google vanquish, or at least de-fang, the Microsoft monopoly? To a large extent, by using Open Source. Open source rules the cloud and mobile.

So, let me tell you how we are using TF for quantum computing.

When Google first open sourced TF a mere 2 years ago, I wrote a blog post to mark the occasion. In that post, I called TF a platform for Fakesian networks instead of Bayesian networks. My beef was that TF had only deterministic nodes, which are standard in the field of artificial neural nets. It had no probabilistic nodes, which are standard in the 2 fields of classical Bayesian networks (BNets) and Hierarchical models (HM). But this past year, the open source community has fallen into the breach, filled in the gap, with a software library called Edward built on top of TF, that adds probabilistic nodes (the buzz word is “Probabilistic Deep Thinking”) to TF. And Edwards has been approved for integration into TF, so soon it will be seamless integrated into TF. Thus, soon, TF will combine artificial neural nets and BNets seamlessly. It will have superpowers!

Of course, in quantum mechanics, one must use complex amplitudes instead of probabilities for the nodes, and one must use an L2 norm instead of an L1 one with those amplitudes, so you can’t use Edward to do quantum mechanics just yet. Edward will have to be made “quantum ready”. By that we mean that one will have to rewrite parts of Edward so that it has a “quantum switch”, i.e. a parameter called ‘is_quantum’ which when True gives a quantum BNet and when False gives a classical BNet. That is precisely what artiste-qb.net’s open source program Quantum Fog already does, so our company is uniquely placed to make a quantum version of Edward.

Another obstacle to marrying TF and quantum computers is that the quantum BNets will have to be compiled into a sequence of elementary operations (SEO) such as control nots and single qubit rotations. Once again, our company artiste-qb.net is uniquely placed to accomplish this task. Our open source quantum simulator Qubiter is the only one in the business that includes a “quantum csd complier”, which is a tool that will help express quantum BNets as a SEO.

HMs are really a subset of BNets. However, the BNet and HM communities have historically grown somewhat independently. The BNet community is centered around pioneers like Judea Pearl (at UCLA), inventor of some of the most important BNet methods, whereas the HM community is centered around pioneers like Andrew Gelman (at Columbia), author of many great books and a great blog in the HM field. The HM tribe only uses continuous distributions for node probabilities, and they are very keen on MCMC (Markov Chain Monte Carlo). The BNet community uses both discrete (expressed as matrices or tensors) and continuous distributions for their node probabilities, and they use MCMC and other methods too, like the junction tree method, to do inferences.

Edward has a distinguished pedigree in both the BNet and HM communities. Edward originated in Columbia Univ. One of its main and original authors is Dustin Tran, currently a PhD student at Columbia. So you can be sure that the Edward people are in close communication and receive useful feedback from the Gelman tribe. Another distinguished author of Edward is Kevin Murphy, who has been working on BNets for more than a decade. Murphy wrote the oldie but goodie Bayes Net toolbox for Matlab. He has also written several books on bnets and machine learning. He previously worked as a prof at the Univ. of British Columbia but he now works at Google. He is one of the main organizers of the young (2 year old) Bayesian Deep Learning conference, which, by the way, will have its annual meeting in less than a week (Dec. 9, 2017).

Classical BNets are a very active field, both in academic research and in commerce. Judea Pearl won a Turing award for them. BNets are very popular in bioinformatics, for example. Whereas no qc company has yet broken-even financially, there are classical BNet companies that have lasted and been profitable for almost 2 decades, such as Bayesia, Hugin and Norsys/Netica.

Oh, and one last thing. It’s called TensorFlow, not TensorNetwork, for a very good reason. If you try to use TF to implement the “tensor networks” used in quantum computing, you will fail, unless you start using BNets instead of Tensor Networks and pretend these 2 are the same thing, which is probably what the Tensor Networks people will do. In TF (and BNets), the lines emanating out of a node carry in them a full tensor that they pass along to other nodes. In a Tensor Network, a Tensor does not Flow into the arrows emanating out of its node. The tensor just sits in the node. For more discussion about the important differences between a quantum BNet and a Tensor Network, see this blog post.
https://qbnets.wordpress.com/2015/03/26/tensor-networks-versus-quantum-bayesian-networks-and-the-winner-is/

November 24, 2017

The Era of the Gay Particle (a.k.a. Majorana Quasi Particle and Anyon) Begins

Filed under: Uncategorized — rrtucci @ 12:06 am

I first reported in this blog about a possible sighting of a Majorana quasi particle on Oct, 2014. In that blog post, I referred to them as gay particles because they are neither bosons nor fermions but something in between**. (I was making fun of Leon Lederman, who is credited with being the first person to refer to the Higgs boson particle as the God particle)

Check out this recent, excellent (very knowledgeable, clear and well written) article

Majorana Update by Stevan Nadj-Perge

recounting the amazing progress that has been made in the last 5 years on the gay particle front, going from an uncertain sighting of the elusive particle in 2012, to almost certain evidence of its existence just 2 weeks ago.

Most scientists believe that (gate model) quantum computing done using gay particles will have much lower error rates than quantum computing done using transmon superconductive circuits (the latter is the strategy being pursued by IBM, Google and many others).

The bad news is that Microsoft is the only major company in the world that has invested bigly in this technology and they have patented it to the hilt. The good news is that the MS quantum software is really crappy and closed source. Quantum open source will crush them like Linux and Android did before. As to the hardware, I predict that MS will try to use its patents to monopolize this technology in the US and Europe, but China will quickly duplicate the MS hardware, ignore the patents to a large extent, and offer this technology worldwide via the cloud.

**In case you are wondering, I am not gay. And the term “gay particle” is definitely not meant to be a homophobic slur. As I have said before in this blog, I have a lot of respect and admiration for many gay people, including two of mankind’s greatest heroes, Leonardo DaVinci and Alan Turing. And maybe Ettore Majorana too?

November 22, 2017

Dueling Quantum Computing Conferences, not to be missed by anyone who is anyone

Filed under: Uncategorized — rrtucci @ 1:41 am

These two “beauty contests” conferences are more exclusive than Davos. John Preskill, Paris Hilton, Kim Kardashian and Ivanka Trump are expected to fly in by helicopter. (We, the commoners, will be permitted to observe the proceedings from behind a cyclone fence)

West Coast – Dec 4-6, q2b Conference, http://www.q2b.us

East Coast – Dec 6-8, ThinkQ Conference,
https://www.research.ibm.com/ibm-q/thinkq/

November 18, 2017

Strange Connection Between ATOS corporation and Oak Ridge National Laboratory (ORNL) Quantum Computing Division

Filed under: Uncategorized — rrtucci @ 2:30 pm

The ATOS corporation, based in Bezons, France, has a really bad reputation in some countries like the UK. To see this, check out, for example, the “Controversy” section of the Wikipedia entry on ATOS.

On October 20, 2017, ORNL put out a press release entitled:
“Two ORNL-led research teams receive $10.5 million to advance quantum computing for scientific applications”

On Nov 13, 2017, ATOS put out the following press release: click here

This is very odd because a quantum simulator of 30 qubits is not considered leading edge nowadays. Google/ProjectQ have simulated 45 qubits and IBM has simulated 56 qubits. Furthermore, ORNL owns the Titan supercomputer, one of the largest supercomputers in the world. ORNL is at the forefront of HPC, so why did they buy an expensive albeit not very powerful French machine to do quantum simulations? Like selling coals to Newcastle, isn’t it? ATOS claims to offer a “Quantum Learning Machine” that runs a quantum language called aQasm, but their language is closed source. I haven’t found any tutorial, or examples, or open source software for it, no matter how hard I’ve looked. Why did ORNL, a DOE weapons lab in the very red #MAGA state of Tennessee, do something so un-MAGA and unpatriotic by MAGA standards, namely, to buy expensive French closed-source software and hardware when American companies like IBM and Google already provide an open-source quantum language and development kit and cloud usage of it for quantum simulations? Is this evidence of government waste, abuse or corruption, and does the government care?

November 8, 2017

Volkswagen’s Entangled Quantum State

Filed under: Uncategorized — rrtucci @ 5:26 am

Long, long ago (May 2013), in a galaxy far away (Silicon Valley), Google together with NASA bought a DWave quantum computer.

And then, just 7 months ago (Mar 2017), Volkswagen proudly announced that it was using a Dwaver quantum computer for traffic flow optimization in Beijing.

But yesterday, Volkswagen put out the following press release

https://www.volkswagenag.com/en/news/stories/2017/11/volkswagen-group-quantum-computing.html

announcing a grand partnership between Volkswagen and Google’s quantum computer group.

Some excerpts from yesterday’s Volkswagen press release: (Dwave was not mentioned directly.)

Neven: Google already has a high-performance quantum computer and the software it takes to run it.

Hofmann: One key focal point of our partnership will be optimizing traffic with the help of quantum computing. In this work, we will draw on the findings of our first research project with 10,000 taxis in China’s capital, Beijing.

Dieb-pickpocket.jpg

Hmm, has Google swiped their friend’s biggest client?

(art by Frankes )

November 6, 2017

Artiste-qb.net CEO will be a Featured Speaker at mini-summit to be held on Tuesday by the Toronto AI Meetup

Filed under: Uncategorized — rrtucci @ 5:33 am

The Toronto AI meetup, which currently has a whopping 1,694 members, will be holding a ‘mini-summit’ on Tuesday (1 day from now).

AI Summit 2017 – a micro-conference

Tuesday, Nov 7, 2017, 6:45 PM

5th floor, SAS Institute (Canada) Inc.
280 King Street East Toronto, ON

75 manifolds Attending

Welcome to the AI Summit.  This is a micro-conference on AI featuring some really great minds.  We are partnering with SAS on this event and co-hosting with the Toronto Women’s Data Group.  Hope to see you there – we may even give away a t-shirt at the event, maybe :)Helen Ngo – Ensemble methodsJane Illarionova – Deep Learning applied to brain …

Check out this Meetup →

The Univ. of Toronto, may I remind you, is the home of Geoffrey Hinton, one of world’s leading researchers in the field of artificial neural networks (he and 3 others invented, in a 1986 paper, the backpropagation method)

Tuesday’s summit will feature 5 speakers, 2 women and 3 men. One of the men will be Henning Dekant, the CEO of artiste-qb.net (the company I work for). Henning will be speaking on quantum computing AI. The venue for the meeting will be the 5th floor of the SAS Institute (Canada) Inc. Henning is scary ugly (he dresses as himself for Halloween). He isn’t as beautiful and brainy as the two women speakers, but he does have the home court advantage, having worked at the SAS Institute for many years before leaving it to lead artiste-qb.net.

October 23, 2017

Vicious Game of Battleship Currently Being Played in Quantum Computing Software World Between IBM and Google

Filed under: Uncategorized — rrtucci @ 4:48 pm

The competition between IBM and Google to hog the quantum computing limelight has been fairly intense this year. The following 2 high stakes games of Battleship are currently being played. Yikes. (Footnote: Google seems to have decided to marry the opaque, poorly designed software of ProjectQ so I lump them together below.)

original-battleship-game

Thanks son. You have crushed my spirit and now I will divorce your mom and leave you to her with no alimony.

October 18, 2017

One small step for Qubiter, one giant step for Alibaba

Filed under: Uncategorized — rrtucci @ 10:06 pm

In a previous blog post, I used the example of teleportation of a 1 qubit state to compare 3 popular quantum computer simulators: (1) artiste-qb.net’s Qubiter (of which I am the main author), (2) IBM’s Quantum Experience and (3) Microsoft’s Liqui|> sequel. I gave many reasons why I think Qubiter is much better than the other 2 (clearer, simpler, more logical design, more commands, open source under BSD license, Python, many Jupyter notebooks, includes translators from Qubiter’s qasm to IBM’s qasm and soon to Google’s qasm, …)

Today, I am proud to announce that Qubiter now has 2 of its Jupyter notebooks in both English and Chinese (translator: Dr. Tao Yin, CTO of artiste-qb.net, living in Shenzhen, China)

Alibaba must have heard about our Chinese notebooks and decided to match our move and better it by a smidgen. On Oct 10, 2017, they announced to the press that they are planning to spend $15B over the next 3 years on moonshot projects like AI and quantum computing. At the same time, they unveiled at a conference a quantum computing cloud service.

October 17, 2017

Hartmut Neven’s impeccable taste for fashion

Filed under: Uncategorized — rrtucci @ 4:37 pm

Hartmut Neven is the impresario of Google’s quantum computing effort (Martinis’ Pomeranian dog, Qubit, is the real scientific master mind behind the operation. Martinis and his mules just follow Qubit’s orders). As far back as 2013, I have jested about Neven’s faith in the Everett many-worlds-interpretation (MWI) of quantum mechanics, a religion which I find ridiculous, with no physical evidence or utility. Today I’ve read a somewhat gossipy quantum computing article in the Wall Street Journal that confirms my suspicion that Neven’s faith in MWI remains steadfast 4 years later. Luckily, Neven’s bad taste for interpretations of quantum mechanics is more than compensated by his superb sense of fashion. The same WSJ article informed me of something that I have long wanted to know, the provenance of Neven’s magical sneakers: they are “Christian Louboutin sneakers”. Gone are the Silicon Valley fashion-challenged days in which all serious Silicon Valley entrepreneurs wore jeans and a black turtle neck to emulate Steve Jobs.

Possible captions

  • Google should force this man to wear a tie and suit
  • Microsoft stands no chance against the owner of Joseph’s magical multicolored dreamcoat.
  • Google’s German Michael Jackson doing the Google Moonwalk
  • Google’s Nevenator wishes you an “Hasta la vista Baby”
  • Martinis’ antiparticle, Martinis when he lets his hair down.
  • Now I am become Neven, the creator of many worlds.

More of my Neven blog posts.

October 3, 2017

A Microsoft Quantum Computing language by any other name would smell as badly

Filed under: Uncategorized — rrtucci @ 3:31 am

On September 25-29, 2017, Microsoft held its IGNITE conference at Orlando, FL. Arstechnica reported about IGNITE here. They usually publish quantum computing articles that are more balanced and well informed than the average sci-tech popular journal. This time though, I think Arstechnica dropped the ball badly. This article sounds to me like a glorified infomercial for MS. However, I did learn a few curious facts from it.

The article reports that MS intends to release by the end of this year a “quantum programming language—as yet unnamed” for programming quantum computers. The language will be distributed with Visual Studio and available on Azure, the MS cloud service. Let me henceforth call it language Q?#. The article gives the following snapshot of a quantum teleportation circuit written in this marvelous new language. A Rube Goldberg machine language if I ever saw one. Also, sounds like this ugly baby is going to be CLOSED SOURCE, just like LiquiD. (Click image to enlarge)

Mysteriously, no mention is made of Liqui|>, MS’s previous “quantum programming language”. Since Q?# comes a short time after Liqui|> and Dave Wecker is the main author of both, it is safe to assume that Q?# is just a new wrapper with Liqui|> under the hood. (Some have gone so far as to suggest that the new language should be called LiquidShit#).

But friends, Romans, countrymen, lend me your ears. I have come here to bury Q?#, not to praise it. Next, I will show the code for the same quantum Teleportation 3 qubit circuit, but written instead in IBM’s qasm language and in Qubiter’s language.

IBM’s github repository called qiskit-tutorial has a Jupyter notebook for this same teleportation circuit. Here is a snapshot taken from the notebook showing IBM qasm for the teleportation circuit.

The Qubiter repo at github also has a Jupyter notebook for the same teleportation circuit. Here is a snapshot taken from the notebook showing Qubiter’s English and Picture files for the teleportation circuit.

And now, let me indicate a few reasons why I think Qubiter (which I wrote) is nicer than the other two.

  • Qubiter allows one to write controlled gates with any number of controls, and the controls can be of two types T or F. (T controls are usually represented in latex pictures of quantum circuits by a solid dot, F controls by a hollow dot). Qubiter also has subroutines that allow one to expand each gate with multiple controls into a sequence of gates with only one or zero controls, because those simpler gates are the only type of gates that most hardware devices can perform physically. IBM’s qasm so far only allows one or two controls of type T only. They have CNOT and CCNOT and that’s it.
  • Qubiter automatically generates an ASCII picture of the circuit at the same time that it generates its English qasm-like file. IBM’s q-software and LiquiD do not write a picture of the circuit automatically. If they draw a circuit, it requires a separate run to generate it and the picture is in Latex. Also, their circuit pictures have time running from left to right instead of downwards. Qubiter’s English and Picture files, on the other hand, have the highly desirable properties–especially desirable for long circuits–that (1) time runs downward in both English and Picture files, and (2) line number n in the English file corresponds to line number n in the Picture file.
  • IBM qasm and LiquiD distinguish between quantum and classical registers. Qubiter only has quantum registers. Classical registers are an unnecessary, ugly complication because the information stored in them can be stored in the memory of your pc.

Two other languages, Rigetti’s PyQuil and ProjectQ, are similar to IBM qasm and suffer from some of the same architectural design flaws mentioned above.

September 15, 2017

The Quantum Meetup Supremos Invite You to a Saturday Evening Meetup for shooting the breeze about Quantum AI

Filed under: Uncategorized — rrtucci @ 2:34 pm

As I mentioned in my previous blog post, Henning Dekant, CEO of artiste-qb.net, is currently attending, throughout this month of September, an intensive bootcamp/course on quantum machine learning and AI. This course is being offered by the Creative Destruction Lab of the Univ. of Toronto. At the end of the course, on Sept. 30, Henning will be hosting a Meetup were he will spill the beans about what he learned. Other participants in the course have been invited. Erudition + Gossip time! Come join us!

This course participant is currently programming the NYC Matrix:

September 7, 2017

Our Man In Toronto—at the CDL (Creative Destruction Lab) Quantum Machine Learning Program

Filed under: Uncategorized — rrtucci @ 5:55 am

Henning Dekant, CEO of our company artiste-qb.net, has been admitted to the exciting CDL (Creative Destruction Lab) Quantum AI Program. The program will culminate with sales pitches by the participants to prospective investors. But first, during most of September, Mon to Fri, 8 hrs per day, the participants will attend an intensive bootcamp, complete with problem sets for homework, presided by Peter Wittek, on quantum computing software, classical and quantum machine learning and related subjects.

Henning will be writing a series of blog posts reporting on his thoughts and experiences while attending this CDL program. Here is the first post of that series.

Henning is the dapper one wearing a white guayabera. He will be taking good course notes (including drawings of top secret quantum devices, such as the quantum Alexa, which looks suspiciously like a vacuum cleaner)

our-man-havana-poster

alec-guinness-our-man-in-havana

secret-vacuum-cleaner

August 15, 2017

Resistance is Futile: Jupyter Borg Threatens to Assimilate Quantum Computing Universe

Filed under: Uncategorized — rrtucci @ 5:00 pm

A week ago, IBM announced at its Quantum Experience usegroup that it had uploaded to github a large collection of jupyter notebooks exhibiting the use of their gate model quantum computer (previously 5 qubits, currently 16 qubits). I consider this an excellent addition to the quantum open source and free jupyter notebook universe and ecosystem. I’ve advocated for quantum open source and jupyter notebooks many times before in this blog, so it’s a pleasure for me to echo their announcement.

Pow! Right in the kisser of Microsoft’s Liqui|> software. Liqui|> is closed source software.

Google has announced that it will deliver by year’s end a 49 qubit gate model qc with accompanying open source software and cloud service. The jupyter ball is now in your court, Google.

Artiste-qb.net, the company that I work for, already provides a large and ever growing library of jupyter notebooks for both of its quantum open source offerings, Qubiter and Quantum Fog.

Rigetti’s PyQuil and ProjectQ are two other gate model qc simulators analogous to IBM quantum experience. So far these two have very few jupyter notebooks. Wimps! Laggards! Let them eat cake!

borg-cake

Borg Cake

jupyter-cake

Jupyter Cake

August 14, 2017

Quantum Computing Wrestlemania 2017-2018; Microsoft planning to buy Rigetti?

Filed under: Uncategorized — rrtucci @ 2:35 am

Whoneitral trapl be the contenders for the 2017-2018 Quantum Computing Wrestlemania Event? Google together with NASA bought a Dwave quantum computer, an annealer qc, on May 2013, and upon hiring Martinis in Sept 2014, Google told the press that it intended to build an annealer qc like DWave’s, but with error correction. However, since then, Google has changed plans and has promised a 49= 7X7 gate model, not annealer, qc, to be delivered by the end this year.

If you look at the Wikipedia article on superconducting quantum computing, it contains a table comparing 3 types of Josephson Junction (JJ) qubits: charge, flux and phase. Google’s 49 qubit device is going to be a charge JJ qc. The IBM and Rigetti qc’s are also charge JJ qc’s. Hence, it is now clear that a gladiator contest between Google (led by John Martinis and Hartmut Neven), IBM (led by Jerry Chow) and Rigetti (led by Chad Rigetti) is inevitable in the next few years. If Google and IBM are 800 pound gorillas in this contest, then Rigetti is an 8 pound one. Furthermore, another alpha male 800 pound gorilla is missing from this triad: Microsoft. Microsoft has the only large scale Majorana qc effort in the world, but this effort is much less advanced than the Google & IBM JJ qc efforts. Microsoft does not have any large JJ qc effort as far as I know. What it does have is a lot of moolah. So, in my opinion, it is quite possible that, in order to compete with their nemesis Google in the JJ qc arena, Microsoft will attempt to buy Rigetti. On the other hand, they may decide to sidestep Rigetti and buy some Rigetti imitator that is out there but is still too young to have registered in my radar screen.

(Sept. 14, 2017, Update: Just realized another option for Microsoft: instead of buying Rigetti, Microsoft could try to acquire QCI, a spin-off of the Yale Quantum Institute, which is also trying to build a charge JJ qc)

Besides JJ qc’s, another type of gate model qc that has garnered commercial funding is the trapped atoms qc. In that arena, there are two main contenders; IonQ (led by Chris Monroe, uses ions held place by Paul trap), and a Harvard-Russia group (led by Mikhail Lukin, uses neutral atoms held in place by optical tweezers).

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