The Bachelor in Quantum Information Science and why it won’t happen

Jan Florjanczyk

Doubtlessly, quantum information has benefited by assimilating members trained in a wide array of sciences, predominantly physics, mathematics and computer science. However, with (im)perfect 20/20 hindsight, we can always speculate on what a specialized undergraduate degree in quantum information science may look like.

The transition from the undergraduate curriculum-led lifestyle to the graduate research-led one can be turbulent when headed for quantum information. Likely, students come from at most two of the above three constituent areas. As a graduate student you can always play the game of “picking things up as you go” but this is not a mentality that scales well to the average freshman. Learning to trace results up through their parent papers or even searching the Internet using correct terminology is tough to learn in a lecture hall. To students starting out, the field of knowledge ahead of them seems of an absolutely overwhelming size. Thus, to make a quantum information scientist from scratch we have to examine what is essential and what is superfluous in an undergraduate curriculum.

Personally, I come from a background in physics and mathematics so I can only speak from this vantage point. However, my recent foray into computer science has shown me very clearly what it is that I lacked (or likely still lack) in that field. Altogether, I’m looking to distill in this article the essentials from my undergraduate degree that now support my studies in quantum information.

The core of the mathematics required is a basic understanding of probability and a very strong foundation of linear algebra. With only these tools we already find ourselves with enough framework to begin proving some rudimentary results. However, a course in probability at the undergraduate level is likely to focus on a survey of distributions and characteristic functions. We can make due with Bayes’ rule and Markov’s inequality in our curriculum. Alongside a short survey of constructions such as cyclic groups, a thorough understanding of linear algebra plays the central role in quantum information theory. More particularly, it is essential to grasp tensor product structure early on and this is very easily overlooked in a math program. Also, I would urge to prescribe the full run of mathematical analysis courses. Knowing about metric spaces and measure theory has proven repeatedly useful. Finally, group theory, complex variables and PDEs belong in this program as well, but a thorough treatment is not necessary as a student can still follow along most of the material without them.

A “classical” physics program is also a little ill-at-ease in the shaping of a quantum information scientist. Newtonian and (I would claim) Hamiltonian mechanics simply never appear. Classical electromagnetism and optics can lead to quantum optics so perhaps they should be included. But what else is left? Statistical mechanics and quantum mechanics, both of which tend of play off each other a little. Quantum mechanics itself deserves the most attention. The practice is to divide a large survey of quantum mechanics into two or three successive courses. These begin with introductory topics such as the Schroedinger equation, potential wells, eigenstates and values (all strictly in one spatial dimension). Next, students find themselves solving the equations of the hydrogen atom. For this they need spin operators, variational methods and most importantly: perturbation theory. Density operators may make a brief appearance in the third course and although Bell measurements may be mentioned, the POVM formalism is generally ignored. The process of teaching successively complicated mathematical methods to support successively complicated physical scenarios makes sense to enforce a more phenomenological understanding of physics. However, this is the long way to get to what quantum information science really needs, that is, a foundational understanding that leads to the circuit model necessary for algorithm development.

Enter the third science. The most important computer science concepts I could have had coming into quantum information are definitely algorithm design and complexity theory. I am unashamed to say that as a student formerly bound for something closer to the study of general relativity, the word “algorithm” was once terrifying. Even the design of the simplest algorithms is not a “pick it up as you go” affair. It is just as practiced an art as any problem solving in mathematics and physics. The computer science component of this curriculum must also provide a course in information theory. This is essential because although you can sit down and read the classical background from Mike and Ike, there’s no way to develop intuition without practice.

The only missing piece is a course (or a few courses) in quantum information proper. Any of the textbooks suggested by Mark Wilde (above/below) could be suitable. However, if you try to solidify a point at which to teach quantum information with respect to its math, physics, and computer science requisites, you cannot do so honestly until very late in the program. For example, it is difficult to introduce the Hadamard gate without quantum states, which in turn cannot be introduced until a solid understanding of linear algebra is established. Whichever way you go about it, you would always end up pushing the quantum information content further and further back in the program until you reached something resembling more of a B.Sc. (Hons. in QIS) than a true Bachelor in Quantum Information Science.

Perhaps it is fortunate that diving immediately into quantum information out of high school is impossible. Students in their undergraduate years change direction very often. A program specific to quantum information would be restricting since it would provide only background required for QIS and lack in the overlap required for students to move subjects. Quantum information science also gains much by attracting diversely educated students. Every math, physics, and computer science course that was not mentioned here plays a vital role in shaping the individuals who make up the QIS community. Nor should it be forgotten that chemistry and engineering are also contributors to the rapidly spreading pool. All in all, a Bachelor in Quantum Information Science would accomplish nothing more than guide a student through the history of quantum information science but sadly leave them short-handed for research in the field.

For now we can just wait until the game-changer: a fully functioning quantum computer. At that point we can start to visit the exciting realm of the Bachelor in Quantum Engineering.

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Chloe’s mother is an avid gardener hailing from the south of France. Her backyard and kitchen are teeming with fresh sweet tomatoes, large meyer lemons, succulent fresh figs, carrots, lemon basil, lemon verbanna (for tea), tangelos, quince, kumquat, courgettes, eggplants and even her own bay leaf tree. There was little room on the kitchen counter piling over with fruits and vegetables. I’m bringing home some homemade marmelade too!

Saturday, Chloe and I headed down to Berkeley in search of pastries and good eats. We arrived at Messe Pastries 5 minutes after they closed but a bit of knocking on the door and pleading (“I came all the way from Canada!”) got us two small cakes that we saved for dessert. For dinner we headed to the Cheeseboard, a pizza co-op.

The Cheeseboard only makes one type of pizza per day and servings are accompanied by the salad of the day and the dessert of the day. A long line reaches around the block but it moves quickly as the only thing to order is size. Since it was Indian Independance Day, the pizza du jour was roasted curried potatoe slices, chives, garlic, mozzarella and olive oil. You think potatoe chips wouldn’t belong on a pizza but the Indian-fusion live jazz band made everything make sense.

Truth be told, I really wanna open up a pizza co-op near McGill and hire students on a day-to-day basis. You only really need one permanent chef who knows how to make good dough and interesting pizza toppings and the rest of the assembly is done on the fly by people whom you can train in about an hour. I think it’d be very successful.

We sat down to dig into our cakes from Messe. Chloe had mentioned this bakery long before I even came so expectations were high. And to raise the stakes even further we had talked about the pastry business with the baker/owner’s son, who told us that his father graduated from the Culinary Institute of America (CIA) and then spent 40 years building up the Messe name.

Why were these so crap then!?! They were both completely stale and the dough of the suposedly “rich” chocolate cake was throat-scratching. The pear-caramel mousse thingamacake was bland and bested by similar cakes in grocery superstores everywhere.

Thankfully, Chloe makes a mean pavolva and combined with fresh berries+peaches and fresh coulis, a much better dessert awaited us at home.

We drove to Napa the following day. We passed this guy. It was cool.

Napa was suposed to be all about driving around and going to free wine-tastings. However, we found only one winery that wouldn’t charge the exorbitant $10-$20 per two tastes. We therefore decided to befriend the people at Folie-à-Deux and buy their cheapest 2007 Chardonnay (Other cheap options included 2008 Red, 2008 White, and 2008 Rose, we felt that if you know what type of grape your wine is made of then that’s probably a better wine).

Our other purpose for visiting Napa was the Bouchon bakery in Yountville, a part of Thomas Keller’s empire which includes The French Laundry and newly opened Ad  Hoc (we walked in for a bit, it was really nice!). Here, unlike Messe, everything was fresh, textures were perfect, flavours were strong. Altogether we had the makings of a picnic,

The lemon tarte was silky, not eggy like you usually get. The crust was also delicious. The chocolate ganache tarte was definitely the most satisfying baked good I think I’ve had all trip. The flavour was an intense chocolate, like you get in fudge or mousse and the crust was similarily delicious.

Today is now Tuesday and I get back to Montreal in a couple hours. San Francisco is amazing, beautiful, friendly, colourful, delicious, and very very hilly. It doesn’t beat Montreal though, and it doesn’t feel like home.

There! You happy? I did it and I’m not going any closer, I have food to eat. So let’s get right into that. We walked down Chestnut street in Northbeach next where amongst the many specialty stores we found Miette Confiserie and Patisserie,

Everything really is as shiny and perfect as in this picture. It all screams of Willy Wonka but if Willy Wonka took flavour pairing seriously.

The advantage of bakery-hopping for two (an activity I will now trademark) is that you benefit from buying twice as much food and then sharing it. Chloe selected four very floral macaroons and I went for one these keylime meringue pies:

The macaroons were alright although the flower essences they were suposed to contain were completely hidden in buttercream and sugar. The pie was way more interesting. First, the crust is impecable. It is literally as if it was machined into shape out of the delicious honey-flavoured shortcrust. I thought I made a pretty good shortcrust but I’ve never made a crust of such deep a brown colour nor with so little crumbling. My guess is that they knead the dough much more than I do. The filling was fine, it’s really the meringue which bewildered both of us. As you can see, it’s quite silky and shiny and the detailing is added with broiling or a small torch. The consistency, though, is extremely soft but not runny and more sticky than gummy. This meant they had used a lot of powdered sugar and set the meringue with tartaric acid. Later that day we had a much more traditional and more difficult meringue.

We spent the rest of the day in the Mission district. I had an unphotographed burrito for lunch because I’ve been told before by Californians that I’ve deffinitely never eaten real Mexican food living on the east coast. Turns out they were right. West coast burritos win. I took Chloe to 826 Valencia (see last post) but we also stopped next door at a store called Paxton Gates. Imagine that Indiana Jones and Dr. Livingstone got together and opened a shop with all of their found treasures. Two curious items were on sale, first note the last line here,

If the archeologists aren’t even that confident, how am I suposed to be excited about sea turtle poo?

Also hanging in the doorway was what I assume is an inside joke for taxidermists,

It’s a goose with a croc head but Chloe and I both think it looks like a pterodactyl so I’m gonna call this one Pterogoose.

After some wandering we finally ended up at Tartine! Everyone agrees this is the best bakery in San Francisco. And they are right. From the first moment you walk in you smell the 5 o’clock sourdough bread batch, you’re overwhelmed by a crowd of people all eating, drinking, ordering, conversing. This feels like the most social bakery in the world. It has a very small collection of perfected products. Large cakes that sell for $68 or just a slice for $4. Seasonal tartes, gougères, quiches, open-faced sandwiches on fresh bread. We couldn’t stop ordering. Chloe had a slice of lemon-meringue cream cake which when in one peice is covered all over in beautiful browned meringue waves and folds. I had a seasonal fruit tarte topped with crumble.

Chloe’s cake was perfect, really, the cream, lemon, chiffon cake and meringue were in harmony. My tarte was also very good. Very rustic and simple although at the cost of being a little dry. A half-loaf of sourdough bread would keep us filled for the rest of the day. We also ordered a gougère. It is a puffed choux pastry with cheese and herbs. The flavours of herb and cheese are quite strong and unexpected in this buttery pastry. I’ve never made or had gougères, but I think I’ll be working on them from now on.

Currently, I’m in Davis where trips around Napa and plenty of wine tasting await!

What a beautiful day! I’m starting to orient myself around San Francisco without the use of maps and I’ve finally grown comfortable to the basic transit system… as well as the discomfort of having paper dollars (seriously America, you make no sense). Started at Caffe Trieste today. Their espressos go up to “Grande” size, which I can only assume is triple because I had one and I was buzzed for hours following. The cafe itself is also very nice, it even has its own crew of local dudes who discuss the news and whom the staff know by name.

Next I headed to find a curiosity which I came across on the internet only last week. Carte415 is supposed to be a fine-dining street cart in the atrium of a business building. Well then I guess I found it:

It wasn’t open when I got there so I looked at the fancy printouts of the menu while I waited. Organized just like a restaurant, there are salads as well as entrées and I chose the shrimp salad sandwich. As you can see below, it came with its own smaller box of garnish. I think the whole idea was very neat and the sandwich itself was also delicious.

I visited the Museum of Modern Art as well afterwards but there wasn’t anything to write about from there. Oh! Except one thing, from the top floor of the museum you can look onto the roof of a neighbouring building and if you look closely a life-size cutout of Waldo is standing behind an AC duct. Awesome.

Finally, two more places today both of which have won my heart. First Ike’s Place is a tiny tiny sandwich restaurant in the Mission district. They have a wide array of sandwiches and a similarly large selection of root beers and sodas. It’s unfortunate that just as I came, a San Francisco city employee was forcing Ike’s to take down their sidewalk tables and chairs due some regulation. No worries, I took my Thanksgiving-Turkey-and-Cranberry-Sauce sandwich (and complementary lollipop) to Mission Dolores park.

Yeah, that’s right, palm trees. How pimp is that? Too bad for Tom Colicchio because Ike’s sandwich is actually the best sandwich I’ve ever had now. They bake the bread they put your sandwich on, after you order your sandwich. It is absolutely delicious.

Finally, I went to 826 Valencia which is… wait for it… a pirate supply store. Apparently there’s plenty of these kinds of stores around the US including a superhero supply store in New York. I couldn’t choose a single thing to buy, they’re all quite funny, so instead I bought a catalog of all their products. Next time we meet up, ask me to show you. It’s genius.

This last picture obviously isn’t mine, I got it off Flickr

I headed next for the Ferry Building. On the way I found another small treasure of San Francisco, assigned scooter parking:

It’s like parking for babies! (or at least parking for Julien). The Ferry building looks like this:

And is by-and-large filled with very expensive specialty stores. I was able to grab a cup of New Orleans style iced tea from the famed Blue Bottle Company. It was nice to spend a bit of time somewhere not as grungy as Broadway street where the hostel is.

Finally, I set heading for ‘wichcraft, a restaurant by Tom Colicchio whom my roomates and I idolized because of his role as head judge on Top Chef. ‘wichcraft is cool too. You order at the counter and then they give you a small sign that you take to whatever table of your chosing. A waiter delivers your sandwich and takes away your sign. The whole place is very modern and feels like an upscale fast food joint. However, the sandwiches don’t feel that way at all:

The slow-roasted pork sandwich was both extremely simple, consisting of nothing more than pork, peppers, cabbage and mustard, and also highly memorable. This is something I expect is difficult for simple food to do. However, ‘wichcraft has my strong recommendation although the prices are little steep.
Of course I couldn’t walk any further without stepping into this store:

and trying out a $70,000 grand piano. The sound is impecable. Playing the low keys softly is alone immensely satisfying.
The rest of the afternoon was spent on a walking tour of Nob Hill with two friends I met at the hostel. Plenty of history was learned and expensive hotel lobbies visited. I even saw the room where Tony Bennett first sang “I left my heart in San Francisco”. Actually the whole of the hill screams of the era of crooners and jazz greats.
So unlike yesterday, when you travel the San Francisco of San Franciscans you get the real feeling of the city. When you *use* SF transit, pharmacies, sidewalks and restaurants you feel less like a tourist and more like a participant. I have so much to see on Thursday though. I haven’t even made it down to the Mission once and that’s a day and a half of exploring.

I wanna say so many things! This post may be quite long. I’m sitting in the window bed of an 8-person dorm room at the Green Tortoise Hostel in San Francisco. It looks like the picture above. I’ve been up for nearly 36 hours now and I’ve spent most of it sitting down and traveling. Just a few things from my flights: first, whoever finds the word CASEY in giant letters visible from space on google earth in mid-Colorado gets $5 because I saw it from a plane! Second, Denver airport is all about the Country style and they have a mini-subway system that plays a Country music riff when the doors open and close. Kudos to the guy who built that feature in. Furthermore, while flying over the rRckies I could only hear one song in my head.

But at last after landing in San Francisco today I was able to breath for having made it safely and with all my stuff across the continent. Or could I? I asked a wise-looking man at the airport information booth what the cheapest way to get downtown was and he told me to take the public transit bus, that is: samtrans, the San Mateo county bus. Little did I know that this was far from a bus for travelers but instead a bus who’s main function it was to displace actual residents of San Mateo and San Francisco. So I basically spent my first hour in California in a crowded bus full of airport employees.

And it was awesome! I could not have gotten a better first taste of California than by this accidental intrusion on the daily life of regular people. The biggest difference is that whereas Montreal has a large Middle-Eastern population, California has an even larger Latino population. When the bus finally made it’s way out of the giant airport compound one thing became immediately clear: California is bathed in relentless sunlight. Everywhere the faded rainbow pastel stucco stands out against sunburnt yellow grass and Savanah-like trees. From San Mateo and into the heart of San Francisco we wove around the bottoms of hills where low-income people kept old pickups in their yards and were watched by high-income people who lived in eco-friendly houses higher up.

So having just gotten in today, and not being in any position to hunt down the places I want to visit, I naively let San Francisco tell me what to do and where to go. I headed first for Fisherman’s Warf. It is unfortunately theme-parkish and completely overrun by tourist who have defaulted to enjoy a setting fit for their 5yr-old children. My advice, don’t even go to Pier 39. Worst fish’n'chips ever. and overpriced. However, they do have this curiosity:

Basically, tons of sealions on rafts: fun for the whole ecosystem. I chose next to head  to Chirardelli Square, hoping to find some eccentric chocolate and relieve my tongue of Helmann’s Tartar Sauce. On the way I saw this:

No, they’re not policemen, this is a guided tour. I love it. I want it as a placemat.

Enough distractions, when I reached the impossible to spell/pronounce Chirardelli Square I ordered a “Sea Salt and Caramel Hot Chocolate” from their specialty store. Let me tell you the secret to this seemingly amazing treat. First, you take regular hot chocolate, then you drop in a bar of whatever chocolate you want it to taste like. In my case: Sea Salt and Caramel. Don’t get me wrong, sea salt and caramel is an awesome combination and I’ve had a very satisfying macaroon of the same in Montreal. However, Chirardelli did not think to mix their chocolate bar into their own hot chocolate and I ended up with a mouthful of salt right at the bottom of my cup:

Finally, since Lombard street was on the way home, I went to check it out. Lombard street is the very steep very winding street that adorns almost every postcard of San Francisco. Getting there involved climbing up some steep hills. And here steep means steep. Just look at these people fooled into thinking that cablecar drivers take their job seriously:

This thing was accelerating down like a rollercoaster.

Turns out however, that I’m not the only person in the world who knows about Lombard street. What’s more, I’m not the only person in the world willing to exert himself uphill to gain the status of “having climbed Lombard”. As I climbed down, a lady passed me saying “this is almost as exhausting as when we did the Arc de Triomphe”. Nevermind her confusion about roundabouts and Parisian stairs, Lombard was an attraction, a monument, a museum. Yet we were walking by the doors of people who lived there. Big grates seperate the street from the front doors of these houses. Was it really worth it to turn someone’s home into a tourist spot? And why did we find these people’s homes so attractive a destination to begin with? A literal motorcade of SUVs is constantly rolling down Lombard as some other member of the family snaps pictures of their car on the famous street. It’s quite a disgusting spectacle:

The moral of the story is this: tourism sucks. That’s not what I’m here to do. I came here looking to try every pastry shop and cafe available and I have a plan to report back on some incredible findings, hopefully get inspired and maybe even link physics into the mix. I’m done doing the touristy stuff and tomorrow I’m headed to Caffe Trieste (which I just walked by and looks soooo amazing: think Cagibi in Montreal but Italian) and Steps of Rome and Stella Pastries. Best part: all of them are within a one block of this hostel. Oh! and I shouldn’t forget that on my way in this morning I saw a ‘wichcraft (Tom Colicchio’s sandwhich franchise) so I’m definitely getting a pulled pork sandwhich there !

Carrot-Ginger-Orange smoothie and Peach-Blueberry Muffin

I’ve have never, not once, been able to successfully incoorporate orange blossom water into a single dish. Today, I’m happy to say that the once vanilla substitute is in perfect harmony with carrots, ginger, and oranges in the smoothie above. Unfortunately I don’t think I can publish the muffin recipe as it is straight out of the Cook’s Illustrated 800-page tome I own. However, like everything I make recently, this muffin is loaded with cinnamon and cardamom.

Also! before I give the recipes, I’m happy to announce that my friend Adam’s blog is now hosted here . Go to escapingsuburbia.sublimesuperlemon.com to read his insights on Canadian history and the Ottawa region. Adam has been one of my closest friends for a very long time now and hopefully someday I can get www.adamcoombs.com (a birthday present I got him once) working properly to redirect to his site :S

Carrot-Ginger-Orange smoothie (makes 2 servings)

• 4 medium to large carrots, peeled and sliced thin
• fresh ginger, a lump of about 3 thumb-sizes, peeled and sliced thin
• 1.5 cups of water
• 2 oranges
• 500mL of plain frozen yoghurt
• a teaspoon of orange blossom water

1. Put all the sliced carrot and ginger in a blender and add half of the water. Liquify to your heart’s content. Strain through a seive into a cup or bowl and then return the pulp to the blender. Add the rest of the water and liquify again. Strain again (duh). At this point you can discard the pulp.
2. Squeeze the juice of the two oranges into the strained carrot-ginger juice and add the orange blossom water.
3. In a clean blender froth the juice and yoghurt.
4. Serve!

This recipe is pretty labour intensive. If you know of a method to juice carrots with less work, let me know in the comments!

Cream Cheese Chocolate Coffee Fudge

This recipe is super simple to make and as I found out yesterday goes extremely well with tea brewed from fresh mint leaves. I still need to work on getting a thicker texture though, maybe then I can stop calling this “fudge”

Cream Cheese Chocolate Coffee Fudge

• 500g of cream cheese
• 600g of baker’s chocolate
• 3/4 cup sugar
• 1/4 cup heavy cream
• a double shot of espresso or a cup of coffee reduced to 1/3 of the liquid
• Muslin or cheesecloth

1. Start a double boiler (a bowl set on top of a pot of boiling water, N.B.: don’t let the boiling water touch the bowl) and put all the chocolate in peices into the bowl.
2. Add the sugar to the cream cheese in a bowl and use a fork to incorporate. The cream cheese should get considerably softer after a bit of work.
3. Add the heavy cream to the cream cheese and work it in again
4. At this point the chocolate should be melted completely, add it and the coffee/espresso to the cream cheese and mix thoroughly
5. For the next part I used a muffin tin but any mold of any shape will work. Cut 6″ squares of the cheesecloth and place it in a muffin tin. Spoon in the mixture to the brim and then fold the remaining muslin over the mixture, covering it completely and creating a little package. Do this for the rest of the tins.
6. Place in your freezer and let set over night.

Note that alternatively you can add 1/2 cup of heavy cream instead of 1/4 cup and you will get a much softer consistency. In this case you can set the fudge in glasses and present it as a mousse.