John Watrous


Other writing

This page includes a collection of writings, mostly stories connected with my experiences as an educator and researcher. I prefer to treat them as works in progress and reserve the right to edit them at any point. I have no expectations concerning anyone’s interest in these stories — they’re just here for those that might find some value in them.

The worst TA ever

In my first semester as a graduate student, I taught introductory programming to around 25 undergraduates. This was just one of many, many sections of the same course. The hundreds of students enrolled were divvied up into small sections, and those sections were assigned to graduate student teaching assistants, many of whom (like me) had little or no teaching experience. I guess the reasoning was that if one section didn’t go well, only a small fraction of students would be affected. There was a weekly session for first-time teaching assistants, to provide guidance, discuss the curriculum, and so on — but it obviously wasn’t enough for me.

I performed abysmally. I didn’t take it seriously and didn’t particularly enjoy it. I wanted to be doing research instead. I remember uttering “I hate teaching” in class. Among other unforgivable transgressions, I provided an input set to a coding assignment that had a bug — I’d not even bothered to test it. How much frustration did that cause, I wonder?

I paid the price on the instructor evaluation at the end of the course, scoring at the very bottom of my entire department. I knew this because those scores were made public, including the names of the instructors. Everyone in my department would have looked at the bottom of the list and seen my name. “John is the worst TA I’ve ever had,” one student wrote. I don’t know why, but those evaluations were a huge shock at the time. Somehow I hadn’t realized that I was so bad.

So I begged for another shot, and was offered an 8am class the next semester to make amends. I believe I did, at least to a new batch of students. I took it seriously, worked hard, and kept the perspective of the students in mind and treated them with respect. I doubled my evaluation scores, and found that I actually enjoyed teaching.

I think of this experience as being formative. When I was a professor, I put a lot of work into being a good instructor, and this experience undoubtedly motivated that. I tried to put myself in the shoes of my students and never asked them to do something I hadn’t done myself to completion. I didn’t hide the day before the final exam, I held “all day” office hours from 9 to 5 instead — those were unusually fun office hours in my memory. I memorized the name of every student in my classes, partly as a challenge but I quickly learned how much it’s appreciated. Of course, I also did my best to explain the material. All in all, I would like to think that I straightened myself out, and have been led to believe that others have found value in my efforts.

But I’ll never get that first class back. And to those that took that class with me, I can only say that I am sorry.

A hard scooping

In science, getting scooped generally means that someone else announces a discovery, maybe by posting or publishing a paper, that steals the thunder from something you’re working on. Maybe they reached the same conclusions as you but got there quicker — or maybe they discovered something more interesting that trivializes your work. Sometimes it’s not so bad and you can still get something out of it, like quickly putting out a paper claiming an independent discovery, or perhaps publishing an alternative way to reach the same conclusion. Other times, there’s nothing to be salvaged — so you ditch everything and move on to something else. This is a story about a time I was scooped as a graduate student that falls into the second category.

I’d been working on something for a while — several months at least. It had to do with space-bounded quantum computation, but the details aren’t really important to the story. It was very technical, and I’d built up a lot of mathematical machinery to make it all work. I was nearly done with a paper about it, and I’d used the results I’d discovered as the basis for a thesis proposal that I had to submit and defend as a part of my PhD degree requirements. That part went fine and my thesis proposal was accepted.

A professor I worked with knew Peter Shor and had arranged for me to visit him for a couple of days. Peter was at AT&T Research at the time, before he moved to MIT. I prepared a talk on what I’d been working on and travelled to New Jersey. I was excited to share my results, and of course I also hoped to make a good impression. I got scammed by a limo driver on the way there, but that wasn’t my main concern (and in the end I just claimed the expense and it was reimbursed).

About an hour or two before my talk, one of the postdocs working with Peter showed me a new paper he’d just learned about: Reversible space equals deterministic space by Lange, McKenzie, and Tapp. The title alone struck fear into my heart. I quickly read the paper, which is both simple and beautiful, and it probably took me about 90 seconds to understand how it worked. And I saw that it was a fatal headshot to my work. This wasn’t a case where I could claim the independent discovery of something or salvage an alternative proof — everything I’d done was essentially trivialized by this work and no longer worth the paper I’d printed it on. It was pretty devastating, to be honest. As a graduate student, publishable results were few and far between and each felt precious. The fact that this was going to be the basis of my thesis made it that much worse.

So that was bad — but then I had to give the talk. The reality was that what I’d come prepared to speak about was now trivial and pointless, and I was basically just wasting everyone’s time. But I couldn’t give the talk I’d prepared and not tell them what I’d recently learned, so I explained the situation and went through what I’d prepared. The audience was mercifully small, but it did include Peter. Eric Rains was there as well. Eric moved on to other subjects, but his work on quantum information theory from this period is well known and had a significant impact on the field. Anyway, it was a hard talk to give, and it surely did not impress, but at least it ended.

I have a memory of flying home, feeling defeated and shell shocked. But after I returned home, I just went back to work and started something new. I never again touched that nearly completed paper. Now, decades later, I no longer seem to have it in my files. And everything turned out fine. I found new results and wrote a different thesis than what I’d proposed — and if anyone on my committee realized, they didn’t mention it.

I hope there’s some encouragement to be found in this story. Looking back now, I wouldn’t choose not to have had this experience. We tend to hide our failures and struggles as we focus on our successes and accomplishments, but we’re all subject to the luck of the draw — and things don’t always go as we might have hoped. In these situations, as long as putting one foot in front of the other and moving forward is an option, it’s a good one to take.

Good advisors and bad advisors

When I was a graduate student my advisor was Eric Bach. He was a great advisor! He didn’t work on quantum computing — very few people did back then — but I first learned about quantum computing through a reading group on it that Eric set up. He encouraged me to work on what I found to be interesting and gave me the freedom to do that. And though he didn’t work on quantum computing specifically, he knew a hell of a lot about mathematics and computation, and I always knew more when I left his office than when I’d entered.

Some graduate students are not so fortunate. In various roles I held as a professor, including being a graduate program director and the director of an institute, I sometimes interacted with students in distress over their advisor’s treatment of them. Often they would cry. While I believe most professors I worked with treated their students kindly, some evidently did not.

I don’t know why some professors treat their students the way they do. I suspect in some cases they’re just trying to replicate the experience they had as a student, but they may not be able to do that. Or maybe the problem is that they are, in fact, able. Some professors drive hard and expect that from their students in return, and forget that their students aren’t them. And some professors are just assholes.

In situations like this the power dynamic is completely imbalanced and students feel powerless. Switching to another advisor can be very difficult for multiple reasons, and there’s always the fear that the student isn’t going to be able to go anywhere without their advisor’s letter of support. The perception is that this person that’s making them miserable can end their career and everything they’ve worked for.

So what should you do if, as a student, you find yourself in this situation? I wish I had a good answer. My advice is to start by telling someone, like the program director for whatever degree program you’re enrolled in, or maybe an associate chair or dean in charge of graduate studies. Nobody can help you if they don’t know. Ask around — every program and department is different. Your department or school may have a graduate advocate or an ombudsperson with whom you can discuss the matter confidentially and can provide you with advice. Whatever happens, you don’t have to put up with it — there are many paths your career can take and your advisor doesn’t hold the keys to all of them.

And if you’re deciding whom to work with as a graduate student, be sure to talk to people before making a decision. The right answer is not necessarily to go with the advisor or school with the bigger name. Talk to your would-be advisor and ask questions, and talk to their students as well. The importance of having an advisor that supports and encourages you, and has your best interests in mind, should never be underestimated.

Some jobs will take everything you give them

From January to December of 2021, I served as the Interim Executive Director of the Institute for Quantum Computing (IQC) at the University of Waterloo. Interim means temporary: it was a one-year appointment. But all along there was an expectation that I would move into the role on a continuing basis, meaning a five-year term without the word interim to let people know not to take me too seriously. Initially I thought this was likely, and others at the institute thought the same.

IQC had been searching for a director for several years. At the beginning of the search, there had been great expectations and lofty visions of the hero and savior that would take on the role, but the search had failed repeatedly. When the pandemic hit and lockdowns followed, the need to appoint someone internally came sharply into focus. Discussions were had and I assume strings were pulled, and the outcome was that I was asked if I would take on the interim role by a senior leader at the university (which I would not describe as a kindly request). There was a part of me that wanted to do it and part of me that didn’t, but one thing is for sure: I had absolutely no idea what the job actually entailed. But I said yes anyway.

Once I started, I was quickly overwhelmed. I suddenly had 50 staff members under me, compared with zero at all points prior, and an annual budget with twice as many figures as I’d ever had to worry about. Believe it or not, this part actually wasn’t so bad because the senior staffers at the institute — true heroes in this story — mostly took care of those things. But there were a lot of other things on my plate, and I really didn’t know what I was doing. I had no training to draw on; I was trained to prove theorems, but there were no theorems involved. Mostly it was about money, building relationships with government and industry to get it, and fighting with others at the university about it. My days were packed with meetings. In the beginning, my goal was merely to get through each one without looking like a complete idiot. There were definitely a few for which I did not succeed.

But the real problems started once I gained my footing, because of how hard I leaned into the job. In fact, I gave it pretty much everything I had. I wanted to succeed, and that meant the institute succeeding — and it wasn’t long before there wasn’t really any difference between IQC and my life. By July, things had become completely insane — there was so much I needed to get done that there was no hope and no relief in sight. I hadn’t even thought about research in 6 months. Then I thought I’d lost a $25 million line of funding that the institute depended upon. I’d be the first director in nearly 20 years to fail to secure that support. As a result of it all, I guess you could say that I crashed and burned. I will spare you (really myself) the details — let’s just say that I was unable to continue on my current trajectory.

I briefly tried to hide what was going on, but that didn’t last long and I turned to my wife for help. She got in touch with my assistant, who wiped my calendar clean for a week so I could recover. A forced vacation, essentially, but also a welcome one. The weird thing is that I got the impression that my assistant had seen this sort of thing before. She was the assistant to a couple of directors before me and several department chairs prior to that, so there’s little doubt that she’d seen some things. I realized that, with the pandemic and everything else, I’d neglected to take any vacation in about 18 months, which must have been a contributing factor. So perhaps this is one moral to take away from this story: Sometimes you have to take a break. And if you don’t, you’ll have to take a break.

I did eventually recover, though it took longer than a week, and in the process I came to the realization that taking this job on a continuing basis was simply not something I could do to myself. I felt terrible about letting the institute down, just when it was finally about to get a new director, and it was very difficult to tell my colleagues that I would not be taking the job on a continuing basis. But to say that a weight had been lifted off my shoulders would be an understatement. There were more challenges and struggles to come in the second half of the year, and I wouldn’t say that I necessarily finished strong, but I completed the term I’d agreed to serve. Someone else stepped up, and I was able to hand the institute off to the next director in what I believe was a better state than when I had started. By the end, I’d lost about 15 pounds and half an eyebrow.

My communications director (and guardian angel throughout this experience) had warned me about this sort of thing right from the start. She said, “This job will take everything you give it.” That was wise advice and I should have listened.

Quantum interactions

When I was a graduate student, I worked on topics in quantum computing that were very much off-the-beaten-path, including quantum cellular automata, quantum finite automata, and space-bounded quantum computation. I was definitely interested in those things (and still am), but a big part of choosing to work on them was that others hadn’t so much, giving a student like me a fighting chance to contribute and discover something new. I published papers on this work and was invited to speak at quantum computing workshops from time to time, but I wanted to do something more relevant and of broader interest.

Then, when I graduated and began working as a postdoc at l’Université de Montréal in 1998, I started thinking about quantum interactive proof systems. In theoretical computer science, interactive proof systems are an abstract computational model involving an interaction between a hypothetical prover and verifier having different goals: the prover’s goal is to convince the verifier that some given statement is true (whether or not it actually is true), while the verifier’s goal is to check the validity of the prover’s argument — and to not be fooled into believing the statement is true if it happens to be false. It could be said that the practical importance of this model is open to debate, but there’s no questioning its theoretical importance: it’s played a truly salient role in the development of complexity theory and is also important in theoretical cryptography. To be clear, these are claims about the classical version of this model, whereas I was working on the quantum version of it, which previously hadn’t really been studied at all.

I discovered something interesting: ordinary (meaning classical) interactive proof systems could be parallelized by making the model quantum, in the sense that long conversations between a classical prover and verifier could be reduced down to just three quantum messages by a quantum interactive proof system. There’s no way to do this classically unless something unexpected in complexity theory happens: the polynomial-time hierarchy collapses. This is all to say that this was a bona fide interesting result illustrating a new way to take advantage of quantum information. I felt like my work had relevance for the first time. This was in the fall of 1998.

A short time later, I travelled to DePaul University for the AQIP ‘99 (Algorithms in Quantum Information Processing) workshop. The “A” for algorithms was later shed, and the workshop became the premier conference on the theory of quantum computing known as QIP — which is coincidentally the name of the complexity class associated with quantum interactive proof systems that I now had something to say about. I wasn’t invited to speak at the workshop, but I did bring some printed copies of a new paper explaining my results. I shared it with some people, and the organizers kindly squeezed in an extra talk slot for me to present it toward the end of the workshop. This likely wouldn’t happen now because QIP has become much more formal and competitive, but back then it wasn’t so unusual — there was no program committee and the organizers could invite whomever they chose to speak.

Among those I shared my paper with was Alexei Kitaev, a name that anyone who works in quantum computing recognizes immediately. He was already a legend, even back then, and this was the first time I’d met him. At the workshop he was giving a talk on the QMA-completeness of the local Hamiltonian problem, now a cornerstone result in quantum complexity theory. Given the subject matter of his talk, I was pretty sure he would be interested in my new work, so I gave him a copy of my paper. We talked for a bit in a short conversation that a few others joined and left in a typical coffee break sort of fashion.

The next morning brought another coffee break, and I was milling around when Kitaev came up to me. He’d been looking for me! He explained that he was very tired because he’d stayed up all night studying my paper, and he said that it was a beautiful result. I’m not exactly sure how much of that moment sunk in then and how much of it I came to appreciate later — but when I look back now it seems like it came out of a dream. One of the greatest minds of our time decided to stay up all night studying my work, and found beauty therein. Let’s just say this more than made up for getting scooped right before my talk at AT&T, which I wrote about in another story.

As it turns out, there really isn’t much point in reading that old paper any longer. Shortly after the workshop, Kitaev invited me to come to Caltech to work with him for a couple of weeks, and in that short time we were able to prove a great deal more about quantum interactive proof systems than I had on my own, completely subsuming my original result in the process. I was awed and humbled by the power of Kitaev’s brain, and without much fuss I came to the realization that I wasn’t actually all that smart after all. But the new ideas and techniques I’d learned about served me well and kicked off a new phase of my research: my days of studying quantum interactions, semidefinite programs, and operator norms had begun.