Journal | November 2018

Someone told me we need another child so we can cover all 7 colours of the rainbow. As they say in Australia: yeah, nah 😁

Eureka!

The big aha! moment was seeing how much school children love YouTube stars. OK, maybe I should say “stars”. And by “stars” I mean people that have at least one YouTube video with them in it.

So, I planned on going to McCallums Hill PS to read to the Stage 1 students and do some physics activities. It was a great time and we all had a lot of fun.

But, what I didn’t expect was for the teachers and students to do a little research on me before I arrived. At some point they came across this video from the Perimeter Institute.

And, that was it, they decide I was a YouTube star 😂 When I arrive they swarmed me asking, “Are you the author from YouTube?!” Then they took turns taking pictures with me. It was all very charming and amusing.

Reading!

Children’s Literature Recommendations

Doll-E 1.0 by Shanda McCloskey

Fun illustrations and story of the technology infused world of today’s children. It’ll fit great in any bedtime picture book rotation. It also works to motivate the tinkerer in young listeners.

Ada Lace is on the Case by Emily Calandrelli and Renaee Kurilla

One of the few “first chapter books” that isn’t all about problems encountered at school. Ada, the main character, has to investigate and solve a neighborhood mystery that had my kids thinking and guessing along the way. Whereas many STEM-inspired fiction in this reading category resort to science fiction, Ada Lace sticks to real science and engineering.

Amulet 2 & 3 by Kazu Kibuishi

We continued reading the Amulet graphic novel series. It only gets better! We definitely recommend this for any age. Again, reading aloud a graphic novel may seem counterintuitive, but it definitely works!

Adult Literature September Reads

This Idea Is Brilliant: Lost, Overlooked, and Underappreciated Scientific Concepts Everyone Should Know by John Brockman

This is such a great book to have lying around. It is so easy to dip in and out of. Each chapter is a unique description of a new scientific idea. While they are on the shallow side (think: somewhere between a tweet and a TED talk), the book makes up for it in quantity. I really enjoyed learning about so many new scientific ideas.

Free to Learn: Why Unleashing the Instinct to Play Will Make Our Children Happier, More Self-Reliant, and Better Students for Life by Peter Gray

Read this book whether you have children or not. It’s not just a story about children and schooling, but one of Western society more generally. It really sharpened my observations of my own children’s experience in the school system. There is plenty of advice in here for parents.

Currently reading: Woo’s Wonderful World of Maths by Eddie Woo

Writing!

Wow! 8 Little Planets was named Best Children’s Book 2018 for ages 0-2 by Amazon!

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Next year, some books on engineering topics will be released. Here is the final version of the first cover! It’s ABCs of Engineering with my amazing co-author, engineer and lasers-in-space physicist, Dr Sarah Kaiser.

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It’s been a while in the making but the first translations of the new versions of the book are available. First up we have Italian! Available now are Ingegneria spaziale and Relatività generale. Next April, Ottica fisica and Fisica Quantistica will arrive.

Molto buona! I did an interview with the Italian publisher, which you can find here. (Google will do a great job translating it from Italian as well 😁)

Arithmetic! (academic news)

All this exciting children’s book news sure illustrates how slow academia moves! Of course, when trying to prove fundamental truths about the world, we are happy to take our time 😉

This month I’ve been dealing with reports from referees. Criticism is a necessary part of science and in many cases referees have provided crucial insight. But, you also have to develop a fairly thick skin.

This rather is rather timely since a podcast recorded last month with Sc-gasm about peer review just aired.

Events!

  • ACEMS 2018 Retreat Keynote titled “All your Bayes are Belong to Us”.

  • I spent a couple days in Perth talking about the children’s books and reading to a great crowd.

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Perth! You're awesome ♥️

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  • MathsCraft is workshop for high-schoolers which encourages them to “think like a research mathematician”. Each workshop brings together students, teachers, and mathematicians guide the students in their “play” at maths. It was a great experience and fun to watch the students explore their curiosity with maths.

Up next!

December in Australia combines the holiday season and summer. You’ll find me at the beach!

Journal | October 2018

Happy Halloween! We escaped the cold in Canada and are now back in Australia, ready for second summer 😁

Eureka!

The big aha! moment was seeing how much stories resonate with parents! Over the past year and a half, I’ve been reading from Rocket Science for Babies and doing some paper activities (paper airplanes, demonstrating lift, etc.). It’s been great and I think the children have lots of fun. But because it’s mostly an interaction between me and the children, perhaps some parents feel left out? Or, maybe they are just happy to sit back let their children take the lead.

This month, though, I started reading 8 Little Planets at events as well, and the response from the parents was amazing! Nothing like a good story to excite the imaginative child in all of us, I guess 😁

This month I also got some hilarious feedback on social media. Here are a few highlights:

Reading!

Children’s Literature Recommendations

What do you do with a problem by Kobi Yamada, Illustrated by Mae Besom

Inspirational story about a young person tackling a problem head on and finding beauty in it. It’s a bit abstract, meaning it might take a while for a child to “get it”, but the illustrations are beautiful and the pace was right for a bedtime read.

The Atlas Obscura Explorer’s Guide for the World’s Most Adventurous Kid by Dylan Thuras and Rosemary Mosco

I think adults will find this more amusing than children. My guess is that these real places are suppose to be surprisingly, well, obscure. But, to a child, these are just slightly less fantastic than what they can dream up in their own imagination. It can still keep a child’s attention and led to some interesting questions.

Amulet: The Stonekeeper by Kazu Kibuishi

I was skeptical about reading a graphic novel aloud, especially the pages with no words! But, it actually worked quite well. Even the non-readers could understand the plot. The story itself is amazing. We all can’t wait to continue the series.

Adult Literature September Reads

Scale: The Universal Laws of Life, Growth, and Death in Organisms, Cities, and Companies by Geoffrey West

This one is about the science of complexity and some simple rules that govern how things (from animals to suburbia) scale. There are lots of interesting tidbits in here. My favorite is an understanding, using scaling laws, for why every species of mammal has the same number of heartbeats over their lifetime, from the tiny shrew to the enormous blue whale. It can get a bit wordy and repetitive, but still worth a read.

Currently reading: This Idea Is Brilliant: Lost, Overlooked, and Underappreciated Scientific Concepts Everyone Should Know by John Brockman

Writing!

Big news this month was the release of 8 Little Planets! It’s super-fun and has amazing illustrations by Lizzy Doyle.

Next up is Blockchain for Babies by my UTS colleague, and blockchain expert, Marco Tomamichel. Just in time for the new year and next Bitcoin boom. HODL on for this one! It’s due 1 Jan 2019.

In terms of writing, I am working on a new ABC’s book. I don’t want to give away the details yet, but here’s a hint: it’s not a STEM topic!

Arithmetic! (academic news)

Last week I attended Quantum Gates, Jumps, and Machines, which was a workshop in honor of Gerard Milburn’s 60th birthday. If you ever get a chance to go to a “birthday workshop”, do it. The talks have great science alongside hilarious anecdotes and roasts of the guest of honor. Barry Sanders documented much of it on Twitter.

University of Technology Sydney will soon offer some undergraduate credit subjects in Quantum Computing. We’ve been having some high level discussion about organizing that and getting it approved through all the bureaucratic channels. There may even be some associated online content! Keep your eyes peeled next Spring term!

After submitting their papers, the students in the group are learning hands on the joys of peer review, including what to do about “interesting” referee reports! Look out for some publications soon.

An Honors student at the University of New South Wales submitted a thesis that I co-supervised. This was my first time officially supervising an undergraduate. It was a very rewarding process as the student was from outside of the field and wrote a thesis on quantum learning applications in statistics.

Events!

  • I read and signed some books at the Vancouver Public Library to some excited preschoolers.

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Fun at the Vancouver Public Library!

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  • Byrne and Wade from Sci-gasm Podcast came by the office and we recorded a not-so-family-friendly interview. Stay tuned for that—you might even win a signed copy of Quantum Computing for Babies.
  • Where the Wild Things Are bookshop in Brisbane hosted an event where I read and did some activities with some West Enders. I always have a good time in Brissie!
  • I joined a panel at UTS about Communicating as a researcher: Strategies for building value and reputation. It was quite interesting to contrast my fake-it-before-you-make-it style with one that was more structured, and another that was goal-oriented. Perhaps there is a useful middle ground?

Up next!

In November I’ll be visiting Melbourne and Perth. Come on out and get your science on 6 Nov!

Journal | September 2018

It was a busy month of extra-curriculars, making the most of our last weeks in Canada before returning to greet the Aussie summer.

Eureka!

The big aha! moment was finally understanding the pleas to remove “for babies” from the titles of the Baby University books. On 17 September I visited two elementary schools in the suburbs of Chicago: Rollins Elementary School and May Watts Elementary.

I had a great time at both, but I knew I had to carefully navigate “for babies”. So, I did read the title and immediately asked, “are there any babies here?” “No!” was the expected and resounding answer. I think I won them over with that. But when the cover image popped up on screen I still heard a few “hey! It says for babies” from the audience. The school avoided the “for babies” problem by selling my two picture books, Goodnight Lab and Scientist, Scientist, Who do you See?.

I can sympathize with teachers and librarians when they tell me about the difficulty in reading the “for babies” books. I am also honored that my baby books want a wider audience! In the meantime, while we figure out a solution to the “for babies” problem in the classroom, I think I’ll stick to reading the picture books at schools.

Reading!

Children’s Literature Recommendations

Twinkle Twinkle Little Star, I Know Exactly What You Are by Julia Kregenow and Carmen Saldaña

Filled with rhyming facts about stars that can be sung to the cadence of the classic nursery rhyme. Easy to read and look at for all ages.

How Did I Get Here? by Philip Bunting

Adorable illustrations accompany the history of the universe from the Big Bang, through conception (yep), until now. Easy for the the kids to listen to and point at.

Adult Literature September Reads

Humility Is the New Smart by Edward D. Hess and Katherine Ludwig

I found this difficult to read because it is heavy on repeating buzzwords and technobabble. There are some great nuggets of wisdom in here which are drawn from well-laid-out examples of people and companies that have put humility ahead of arbitrary measures of merit.

How not to be Wrong by Jordan Ellenberg

This book is about math applied to real life. Some of the explanations are abstract and others follow closely with recent, and mostly quirky, stories. I thoroughly enjoyed it. However, I suspect that the author demands a little too much from the casual reader.

Currently reading: Scale by Geoffrey West

Writing!

We are in the final editorial stages of ABC’s of Engineering, Robotics for Babies, and Neural Networks for Babies, all co-authored by my friend Sarah Kaiser. Look for these in January of 2019. They are going to be awesome. Conversations about them included the sentence, “I hate to have to tell you this… but we can’t rickroll babies.”

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One of the questions I get most is are you working on any books for older kids? Yes, yes I am. But at the moment it is too early to give anything away. Stay tuned!

I completed a few more early manuscripts in the Red Kangaroo Physics series. Next year, they will begin to be translated (or untranslated 😄) and available in English. If this is news to you, this is a series of picture books each of which discusses a topic in physics. The story follows a dialogue between me and a curious Red Kangaroo. The first 15 are available now in Chinese.

Arithmetic! (academic news)

Both my students recently submitted their first papers and presented them at an international conference this month. Congrats to Maria and Akram!

I finally got the advertisements up for two postdoctoral positions which are funded by a $3 million grant from the Australian government. This is a collaboration with Gerardo Paz Silva, Howard Wiseman, and Andrea Morello that I am keen to get going.

Mostly an exercise in catharsis, I am reminding myself to say no to every invitation to chair, organise, or join a committee. My future self won’t heed this warning—so here’s hoping it is another thing that gets easier and less time consuming with practice.

Events!

Lots of great opportunities this past month. I met many great people and learned a lot!

  • I gave a public lecture at the Institute for Quantum Computing on 13 September call Big Ideas for Little Minds. I won’t say too much about it as it will be posted online soon. I also gave the same talk at Google on 19 September, which will also appear on Talks at Google.

  • I finally met (in person) Cara Florance my co-author of ABC’s of Biology, Organic Chemistry for Babies, and Evolution for Babies! We did a joint event at the MIT Coop bookstore. How did it go? Well, Cara built a DIY cloud chamber and had a Geiger counter—’nuff said. I also met an MIT professor that bought a copy of Statistical Physics for Babies for every student in his class 😳!
  • I joined Nikola Tesla for some reading, banter, and science demonstrations at the Rochester Museum and Science Center. This was the first time I read 8 Little Planets and was really pleased with the response from both the children and parents! The science centre itself was awesome and I even got a private showing of musical Tesla coils!

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Just hanging out in a Faraday cage ⚡⚡⚡

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  • I got to visit Sourcebooks headquarters in Chicago. It was great to meet all the people behind the scenes that make the children’s books possible. Everyone I met was so passionate about making books, especially the amazing Dominique Raccah!
  • Check out a quick discussion about Baby University on Global TV’s The Morning Show. It’s a great opportunity to reach a large television audience. Too bad the time is so short and the questions so quick!
  • I did some reading and activities at the Oxford County Library in Ingersoll on 6 September. It was amazing to see how close members of a small community are with their library. The librarians even knew the interests of the children! Very eye opening as this has not been my experience in Sydney.

Up next!

October is going to be another busy month. We need to get settled back into Sydney and I don’t even want to think about the backlog of administration I have been ignoring at the uni. But I am also really excited for Quantum Gates, Jumps, and Machines and of course the release of 8 Little Planets!

New papers dance!

Two new papers were recently posted on the arXiv with my first two official PhD students since becoming a faculty member! The earlier paper is titled Efficient online quantum state estimation using a matrix-exponentiated gradient method by Akram Youssry and the more recent paper is Minimax quantum state estimation under Bregman divergence by Maria Quadeer. Both papers are co-authored by Marco Tomamichel and are on the topic of quantum tomography. If you want an expert’s summary of each, look no further than the abstracts. Here, I want to give a slightly more popular summary of the work.

Efficient online quantum state estimation using a matrix-exponentiated gradient method

This work is about a practical algorithm for online quantum tomography. Let’s unpack that. First, the term work. Akram did most of that. Algorithm can be understood to be synonymous with method or approach. It’s just a way, among many possibilities, to do a thing. The thing is called quantum tomography. It’s online because it works on-the-fly as opposed to after-the-fact.

Quantum tomography refers to the problem of assigning a description to physical system that is consistent with the laws of quantum physics. The context of the problem is one of data analysis. It is assumed that experiments on this to-be-determine physical system will be made and the results of measurements are all that will be available. From those measurement results, one needs to assign a mathematical object to the physical system, called the quantum state. So, another phrase for quantum tomography is quantum state estimation.

The laws of quantum physics are painfully abstract and tricky to deal with. Usually, then, quantum state estimation proceeds in two steps: first, get a crude idea of what’s going on, and then find something nearby which satisfies the quantum constraints. The new method we propose automatically satisfies the quantum constraints and is thus more efficient. Akram proved this and performed many simulations of the algorithm doing its thing.

Minimax quantum state estimation under Bregman divergence

This work is more theoretical. You might call it mathematical quantum statistics… quantum mathematical statistics? It doesn’t yet have a name. Anyway, it definitely has those three things in it. The topic is quantum tomography again, but the focus is different. Whereas for the above paper the problem was to devise an algorithm that works fast, the goal here was to understand what the best algorithm can achieve (independent of how fast it might be).

Work along these lines in the past considered a single figure of merit, the thing the defines what “best” means. In this work Maria looked at general figures of merit called Bregman divergences. She proved several theorems about the optimal algorithm and the optimal measurement strategy. For the smallest quantum system, a qubit, a complete answer was worked out in concrete detail.

Both Maria and Akram are presenting their work next week at AQIS 2018 in Nagoya, Japan.

One is the loneliest prime number

You can’t prove 1 is, or is not, prime. You have the freedom to choose whether to include 1 as a prime or not and this choice is either guided by convenience or credulity.

I occasionally get some cruel and bitter criticism from an odd source. I’m putting my response here for two reasons: (1) so I that I can simply refer them to it and not have to repeat myself or engage in the equally impersonal displeasure of internet arguments, and (2) I think there is something interesting to be learned about mathematics, logic, and knowledge more generally.

It all started when I wrote a very controversial book about an extremely taboo topic: mathematics. In my book ABCs of Mathematics, “P is for Prime”. The short, child-friendly description I gave for this was:

A prime number is only divisible by 1 and itself.

I thought I did a pretty good job of reducing the concept and syllables down to a level palatable by a young reader. Oh, boy, was I wrong. Enter: the angriest group of people I have met on the internet.

You see, by the given definition, I had to include 1 as a prime number since, as we should all agree, it is divisible only by 1 and itself.

Big mistake. Because, apparently, it has been drilled into people’s heads that this is a grave error, a misconception that can eventually lead young impressionable minds to a life of crime and possibly even death! It might even end up on a list of banned books!

By a vast majority, people love the book. I am generally happy with the reponse. The baby books I write are not for everyone—I get that. And I do try to take advice from all the feedback I receive on my books. There is always room for improvement. But the intense emotions some people have with the idea of 1 being a prime number is truly perplexing. Here are some examples:

I actually love the book, but there is a big mistake. The number 1 is not a prime number! The book should not be sold like this and needs to be reprinted.

and

1 IS NOT PRIME! How could a supposed math book have an error like this in it? I am disgusted!

Yikes. So what gives? Is 1 prime, or not? The answer is: that’s not a valid question.

Let me explain.

First, let’s look at a typical definition. Compare to, for example, Wikipedia’s entry on prime numbers:

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

Much more precise—no denying that. It’s grammatically correct, but probably hard to parse. I wanted to avoid negative definitions as much as I could in my books. But that’s beside the point. The reason 1 is not a prime is that the definition of prime itself is contorted to exclude it!

OK, so why is that? Well, the answer is probably not as satisfying as you might like: convenience. By excluding 1 as prime, one can state other theorems more concisely. Take the Fundamental Theorem of Arithmetic, for example:

Every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, up to (except for) the order of the factors.

Now, this statement would not be true if 1 were a prime since, for example, 6 = 2 × 3 but also 6 = 2 × 3 × 1 and also 6 = 2 × 3 × 1 × 1, etc. That is, if 1 were prime, the representation would not be unique and the theorem would be false.

However, if we do chose to include 1 as a prime number, all is not lost. Then the Fundamental Theorem of Arithmetic would still be true if it were stated as:

Every integer is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, up to (except for) the order of the factors and the number of 1’s.

Which version do you prefer? In either case, both the definition and theorem treat 1 as a special number. I’d argue that in this context, the number 1 is more of an annoyance that gets in the way of the deeper concept behind the theorem. But in mathematics you must be precise with your language. And so 1 must be dealt with as an awkward special case no matter which way you slice it.

So, is 1 prime, or not? Well, it depends on how you define it. But in the end it doesn’t really matter, so long as you are consistent. And understanding that is a much bigger lesson than memorizing some fact you were told in grade school.

The definition given in ABCs of Mathematics is not wrong” any more than all of the other simplifications and analogies I have made are “wrong”. But, in case you were wondering, the second printing will be modified with the hope that everyone can enjoy the book. Even the angry people on the internet deserve to be happy.

Quantum computing worst case scenario: we are Lovelace and Babbage

As we approach the peak of the second hype cycle of quantum computing, I thought it might be useful to consider the possible analogies to other technological timelines of the past. Here are three.

Considered Realism

We look most like Lovelace and Babbage, historical figures before their time. That is, many conceptual, technological, and societal shifts need to happen before—hundreds of years from now—future scientists say “hey, they were on to something”.

Charles Babbage is often described as the “father of the computer” and he is credited with inventing the digital computer. You might be forgiven, then, if you thought he actually built one. The Analytical Engine, Babbage’s proposed general purpose computer, was never built. Ada Lovelace is credited with creating the first computer program. But, again, the computer didn’t exist. So the program is not what you are currently imagining—probably, like, Microsoft Excel, but with parchment?

By the time computing began in earnest, Lovelace and Babbage were essentially forgotten. Eventually, historians restored them to their former glory—and rightfully so as they were indeed visionaries. Lovelace anticipated many ideas in theoretical computer science. However, the academic atmosphere at the time lacked the language and understanding to appreciate it.

Perhaps the same is true of quantum computation? After all, we love to tout the mystery of it all. Does this point to a lack of understanding comparable to that in computing 200 years ago?

This I see as the worst case scenario for quantum computation. We are missing several conceptual—and possibly societal—ideas to articulate this thing which obviously has merit. Eventually, humanity will have a quantum computer. But, will that future civilisation look at us as their contemporaries or a bunch of idiots mostly interested in killing each other while a few of our social elite played with ideas of quantum information?

Cautious Optimism

We are on the cusp off a quantum AI winter. We’re in for a long calm before any storm.

This is probably where most academic quantum scientists sit. We’ve seen 10-year roadmaps, 20-year roadmaps, even 50-year roadmaps. The truth is that every “scalable” proposal for quantum technology contains a little magic. We really don’t know what secret sauce is going to suddenly scale us up to a quantum computer.

On the other hand, very very few scientists believe quantum computing to be impossible—it’s going to happen eventually. At the same time, most would also not bet their own money on it happening any time soon. And, if most scientists are correct, the hype doesn’t match reality and we’re headed for a crash—a crash in funding, a crash in interest, and—worst of all—a crash in trust.

Some would argue that there are too many basic science questions unanswered before we harness the full potential of this theory that even its practitioners continue to call strange, weird, and counterintuitive. The science will march on anyway, though. Memes with truth and merit have a habit of slow and steady longevity. The ideas will evolve and—much like AI—eventually become mainstream, probably in our lifetime.

Unabated Opportunism

We will follow the same steady forward march that digital computers did the past 50 years.

If you are involved with a start-up company with an awkwardly placed “Q” in its name, this is where you sit. You believe our current devices are “quantum ENIAC machines”. Following the historical trajectory of classical computers, we just need some competitive players making a steady stream of breakthroughs and—voila!—quantum iPads for your alchemy simulations in no time. Along the way, we will reap continuing benefits from the spin-offs of quantum tech.

This is the quantum tech party line: quantum supremacy (yep, that’s a term of art now) is near. We are on the precipice of a technological—no, societal—revolution. It’s a new space race with equally high stakes. Get your Series A while the gettin’s good.

Like it or not, this is the best case scenario for the field. Scientists like to argue about what the “true” resource for quantum computation is. Turns out, it was money all along. Perhaps the hype will create a self-fulfilling prophecy that draws the the hobbyists and tinkerers that fueled much of the digital revolution. Can we engineer such a situation? I think we better find that out sooner rather than later.

 

 

Estimation… with quantum technology… using machine learning… on the blockchain

A snarky academic joke which might actually be interesting (but still a snarky joke).

Abstract

A device verification protocol using quantum technology, machine learning, and blockchain is outlined. The self-learning protocol, SKYNET, uses quantum resources to adaptively come to know itself. The data integrity is guaranteed with blockchain technology using the FelixBlochChain.

Introduction

You may have a problem. Maybe you’re interested in leveraging the new economy to maximize your B2B ROI in the mission-critical logistic sector. Maybe, like some of the administration at an unnamed university, you like to annoy your faculty with bullshit about innovation mindshare in the enterprise market. Or, maybe like me, you’d like to solve the problem of verifying the operation of a physical device. Whatever your problem, you know about the new tech hype: quantum, machine learning, and blockchain. Could one of these solve your problem? Could you really impress your boss by suggesting the use of one of these buzzwords? Yes. Yes, you can.

Here I will solve my problem using all the hype. This is the ultimate evolution of disruptive tech. Synergy of quantum and machine learning is already a hot topic1. But this is all in-the-box. Now maybe you thought I was going outside-the-box to quantum agent-based learning or quantum artificial intelligence—but, no! We go even deeper, looking into the box that was outside the box—the meta-box, as it were. This is where quantum self-learning sits. Self-learning is protocol wherein the quantum device itself comes to learn its own description. The protocol is called Self Knowing Yielding Nearly Extremal Targets (SKYNET). If that was hard to follow, it is depicted below.

hypebox
Inside the box is where the low hanging fruit lies—pip install tensorflow type stuff. Outside the box is true quantum learning, where a “quantum agent” lives. But even further outside-the-meta-box is this work, quantum self-learning—SKYNET.

Blockchain is the technology behind bitcoin2 and many internet scams. The core protocol was quickly realised to be applicable beyond digital currency and has been suggested to solve problems in health, logistics, bananas, and more. Here I introduce FelixBlochChain—a data ledger which stores runs of experimental outcomes (transactions) in blocks. The data chain is an immutable database and can easily be delocalised. As a way to solve the data integrity problem, this could be one of the few legitimate, non-scammy uses of blockchain. So, if you want to give me money for that, consider this the whitepaper.

Problem

 

99probs
Above: the conceptual problem. Below: the problem cast in its purest form using the formalism of quantum mechanics.

The problem is succinctly described above. Naively, it seems we desire a description of an unknown process. A complete description of such a process using traditional means is known as quantum process tomography in the physics community3. However, by applying some higher-order thinking, the envelope can be pushed and a quantum solution can be sought. Quantum process tomography is data-intensive and not scalable afterall.

The solution proposed is shown below. The paradigm shift is a reverse-datafication which breaks through the clutter of the data-overloaded quantum process tomography.

fuckyeahquantum
The proposed quantum-centric approach, called self-learning, wherein the device itself learns to know itself. Whoa. 

It might seem like performing a measurement of \{|\psi\rangle\!\langle \psi|, \mathbb I - |\psi\rangle\!\langle \psi|\} is the correct choice since this would certainly produce a deterministic outcome when V = U. However, there are many other unitaries which would do the same for a fixed choice of |\psi\rangle. One solution is to turn to repeating the experiment many times with a complete set of input states. However, this gets us nearly back to quantum process tomography—killing any advantage that might have been had with our quantum resource.

Solution

quantumintensifies
Schematic of the self-learning protocol, SKYNET. Notice me, Senpai!

This is addressed by drawing inspiration from ancilla-assisted quantum process tomography4. This is depicted above. Now the naive looking measurement, \{|\mathbb I\rangle\!\langle\mathbb I |, \mathbb I - |\mathbb I\rangle\!\langle \mathbb I|\}, is a viable choice as

|\langle\mathbb I |V^\dagger U \otimes \mathbb I |\mathbb I\rangle|^2 = |\langle V | U\rangle|^2,

where |U\rangle = U\otimes \mathbb I |\mathbb I\rangle. This is exactly the entanglement fidelity or channel fidelity5. Now, we have |\langle V | U\rangle| = 1 \Leftrightarrow U = V, and we’re in business.

Though |\langle V | U\rangle| is not accessible directly, it can be approximated with the estimator P(V) = \frac{n}{N}, where N is the number of trials and n is the number of successes. Clearly, \mathbb E[P(V)] = |\langle V | U\rangle|^2.

Thus, we are left with the following optimisation problem:
\min_{V} \mathbb E[P(V)] \label{eq:opt},

subject to V^\dagger V= \mathbb I. This is exactly the type of problem suitable for the gradient-free cousin of stochastic gradient ascent (of deep learning fame), called simultaneous perturbation stochastic approximation6. I’ll skip to the conclusion and give you the protocol. Each epoch consists of two experiments and a update rule:

V_{k+1} = V_{k} + \frac12\alpha_k \beta_k^{-1} (P(V+\beta_k \triangle_k) - P(V-\beta_k \triangle_k))\triangle_k.

Here V_0 is some arbitrary starting unitary (I chose \mathbb I). The gain sequences \alpha_k, \beta_k are chosen as prescribed by Spall6. The main advantage of this protocol is \triangle_k, which is a random direction in unitary-space. Each epoch, a random direction is chosen which guarantees an unbiased estimation of the gradient and avoids all the measurements necessary to estimation the exact gradient. As applied to the estimation of quantum gates, this can be seen as a generalisation of Self-guided quantum tomography7 beyond pure quantum states.

To ensure integrity of the data—to make sure I’m not lying, fudging the data, p-hacking, or post-selecting—a blochchain-based solution is implemented. In analogy with the original bitcoin proposal, each experimental datum is a transaction. After a set number of epochs, a block is added to the datachain. Since this is not implemented in a peer-to-peer network, I have the datachain—called FelixBlochChain—tweet the block hashes at @FelixBlochChain. This provides a timestamp and validation that the data taken was that used to produce the final result.

Results

results
SKYNET finds a description of its own process. Each N is a different number of bits per epoch. The shaded region is the interquartile range over 100 trials using a randomly selected “true” gate. The solid black lines are fits which suggest the expected 1/\sqrt{N} performance.

Speaking of final result, it seems SKYNET works quite well, as shown above. There is still much to do—but now that SKYNET is online, maybe that’s the least of our worries. In any case, go download the source8 and have fun!

Acknowledgements

The author thanks the quantum technology start-up community for inspiring this work. I probably shouldn’t say this was financially supported by ARC DE170100421.


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  8. The source code for this work is available at https://gist.github.com/csferrie/1414515793de359744712c07584c6990