**Difficulty**

*by Jonas Helsen*

When people talk about physics, and in particular the human side of it, the ‘doing’ physics, they will usually point out that there exist two main forms of physicists. There are experimentalists, who spend their days gathering data in labs or tinkering with huge particle accelerators. These physicists, although rarely actually wearing white lab coats – at least in my experience – seem to be the closest to the pop culture stereotype of a scientist: wedding a strong analytical spirit to a practical, do-it-yourself mindset and a work ethic that often borders on obsession. They form the majority of physics practitioners and often speak with mild disdain about the ‘other’ type of physicist: the theorist. Theorists differ from experimentalist in that they mostly do, well, theory. Their days are usually not spent tinkering with equipment or analysing data but rather studying literature and diving into the complicated mathematics needed to describe modern physics. They often eschew the practical in favour of a generalist, axiomatic mindset; using as few assumptions as possible to describe the largest possible piece of the physical puzzle.

Throughout history these two strands of physics were usually not distinct professions but merely reflected the interests of a singular physicist. Even Newton, the prototype of a theoretical physicist, regularly performed experiments using prisms and even built one of the earliest reflecting telescopes. In my understanding of the history of physics these two strands of physicist started splitting into true professions in the late 19th century and early 20th century in response to the ever growing complexity of physics. Over time they grew further apart until the present day where among many theorists it is considered a point of pride to have never performed any experiments at all. Entire careers can be wholly devoted to the understanding of ‘physical theories’ that are decades away from being subjected to experimental verification. On the other hand, as the scale and complexity of experiments has grown, many experimentalists find themselves spending most of their time not doing physics but the cutting edge engineering work necessary to perform modern experiments to begin with. This has lead both groups to develop language and practices which differ immensely and can lead to almost Babylonic misunderstandings in the occasions where theorists and experimentalists do meet.

## Theory at QuTech

At first glance quantum computing seems an experimental, possibly even a purely engineering endeavour. It might therefore surprise you that QuTech also has a sizeable theory section, of which I am part. Of course, theorists are a minority at QuTech and hence we spend a lot of our time in contact with experimental physicists. For me this was an interesting contrast with the group I spent my undergrad years in. I spent most of my undergrad toying with the idea of pursuing string theory or some supergravity related subject and most people I talked to on a daily basis actively spent their days thinking about these subjects. This made for somewhat of a dreamy atmosphere where very little, if any, thought was given to the actual observable consequences of the theory.

So when I started at QuTech and was suddenly surrounded by these very practical-minded experimentalists who not only performed experiments but also had clear plans, goals, and roadmaps for where they would be in five years this was sort of a culture shock to me. During my first year here I spent my time talking to many experimentalists and I realised how different our outlooks were and sometimes even the language we used was. We’d spend an hour debating some concept, only to then realise that we were talking about different things, or the other way around: we’d be confused and annoyed until we realised we were just using different words and concepts to describe the same fundamental thing.

As an example, it took me a long time to realise that when experimentalists talk about “pulses” they mean what theorists call quantum gates and when they talk about gates they talk about something completely different, namely the tuning component of a transistor. This might seem like a triviality in the grand scheme but I feel like many of the communication problems between theorists and experimentalists are caused fundamentally by little more than semantics.

## A quantum design

Of course you might ask yourself: why have a theory group in QuTech at all? Isn’t building quantum computer a hands-on practical task? You’d be forgiven for that thought since I’ve had it myself several times. But when I think about it I realise that many things in the theory of quantum computing are still very much unsolved even though the quantum mechanics it is based on is fairly well understood. As an example close to my heart, consider the theory of **unitary designs**.

Unitary designs are the objects that must be considered when one wants to do a *random operation* on a quantum system. This might be useful when one for instance wants to think about the *average error* of the operations performed by a quantum computer. The best way to quantify this is to pick a set of random operations, check how error prone they are and then average over the result. If you do this right you should be able to say something about how much error any operation produces on average (including all the possible ones you didn’t test). Now a problem here is how you pick this set in a way such that you come as close as possible to purely randomly selecting them. You want for instance to avoid the situation where you only perform a certain subtype of operations and don’t check any other cases that might show up. This is a general problem in statistics and is generally studied via *design theory* which deals with how to properly select subsets, called designs, of sets such that certain statistical properties (e.g. averages) of the full set are reproduced in the design subset. In general this is a hard problem and in particular for the set of quantum operations startlingly little is really known about their properties and how to reliably find designs. And even when we know of designs existing we often know very little about their internal structure.

This is not just idle theorising, since these designs (at least the known ones) are used literally every day in labs around the world in order to perform various tests on nascent quantum computers. Finding better designs or understanding the ones already being used thus has the potential to substantially improve the testing of new quantum systems. The upshot is that working with designs requires quite a bit of complex mathematics which is a subject that experimentalists often have precious little time for. This is of course where the theorist comes in, understanding the mathematical structures arising from quantum theory but also translating this understanding into usable advantages and guiding principles for experiments in the race to build actual quantum computers. If you still think this is not all that useful, remember then that a theorist is generally substantially cheaper than a dilution refrigerator and we (usually) come with a better sense of humour.

Jonas Helsen is an aspiring theorist in the Wehner group where he works on verifying quantum computers. In his free time he enjoys improvisational theater and pretending to be a superhero. He likes the Netherlands but wishes they wouldn’t put peanuts in everything.