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IOP ebooks authors in profile: Paul Skrzypczyk

12 Dec 2023 by Cait Cullen

We recently reached out to some of our authors to hear about their experience in writing their book, advice they鈥檇 like to share with any of you considering writing a book and crucially, would they do it again?

The third author to feature in our collection of ebooks author experiences is Paul Skrzypczyk, Associate Professor and Royal Society University Research Fellow at the University of Bristol in the School of Physics. He certainly didn鈥檛 plan on writing a book but that鈥檚 what happened after finding there was no resource specific enough for his needs. A labour of love, he now remembers it fondly and may even do again. His book was published in March this year.

Paul’s author experience:

Trying to do something as well as possible 鈥 or optimisation as we often like to call it 鈥 is such a ubiquitous task that we do it all the time, often without even mentioning it explicitly. Optimisation arises across almost all academic disciplines, and as such, there is a rich and advanced mathematical theory of optimisation, going back for centuries.

In the context of quantum mechanics 鈥 the theory that describes nature at small scales 鈥 and in particular in the context of quantum information science, which aims to use quantum mechanics to process, store, and communicate information, there is a particular class of optimisation problems which turns out to be extremely prevalent. This class is known as semidefinite programs. Broadly speaking, these are problems where the variables being optimised are naturally associated with matrices, and should satisfy a number of constraints. These constraints, in particular, demand a certain natural property, a form a positivity. This is the meaning of the term 鈥渟emidefinite鈥, which refers to 鈥減ositive semidefinite matrices鈥.

Why does this class of problem arise so naturally in quantum information? Interestingly, the three main physical ingredients of the theory 鈥 states, measurements, and dynamics 鈥 are all represented mathematically by positive semidefinite matrices, and hence in many situations where we want to find, for example the best state, or best measurement, or best dynamics, subject to some constraints, then we naturally arrive at a semidefinite program. This fact was realised quite some time ago, and by now it is fair to say that semidefinite programming has become a major mathematical method, widely utilised on a daily basis, to make advances across the field.

I first learnt about semidefinite programming like many of my colleagues 鈥 not through any formal training as a physicist 鈥 but through reading the literature. When I decided I wanted to learn the topic properly, I turned to what has become the standard resource, sometimes referred to as the bible of the field, Convex Optimisation by Boyd and Vandenberge. This is no doubt a fantastic textbook, however its target audience is not a quantum information scientist, and this mismatch definitely put up barriers to mastering this fascinating topic.

One easy example is that in quantum mechanics, complex numbers are absolutely essential, while in many engineering contexts this isn鈥檛 the case. While this doesn鈥檛 pose a problem as far as semidefinite programming is concerned, Boyd and Vandenberge only discuss complex numbers in two exercises, demonstrating how little significance they put on an essential feature of almost all semidefinite programs that arise in quantum information.

I first started learning about semidefinite programs a decade ago, with a long-term collaborator of mine, Daniel Cavalcanti, when working on a topic in the foundations of quantum mechanics known as Einstein-Podolsky-Rosen steering. Once we started using semidefinite programs in our research on this topic there was no turning back, as we quickly realised how powerful and well-suited they were for the types of questions we were interested in. We became so enthusiastic about this that we ended up writing a review article on the topic. Not long after this, Dani was invited to give a series of lectures on semidefinite programs at the VII Paraty Quantum Information School. These series of lectures (which can be found on youtube), were very well received. Although a couple of resources had started to appear on semidefinite programming aimed at quantum information scientists 鈥 notably John Watrous鈥 lecture notes and subsequent textbook, as well as Jamie Sikora and Antonios Varvitsiotis鈥 lecture notes 鈥 there was still clearly a strong desire for an accessible introduction to the topic, aimed squarely at quantum information science.

That is why when Dani came to me after the School and suggested we could turn his tutorial into something bigger, I jumped at the idea. The only question was what should we turn it into? It wasn鈥檛 long before we realised that a textbook would be the most appropriate way forward.

We were keen that the book should be widely available. Luckily I had previously met an IOP commissioning manager at a workshop previously, and so reached out to him for a meeting. It became clear very quickly that the IOP ebooks series in Quantum Technology would be a perfect place to publish our proposed textbook, given that it would then be widely available to academics across the globe.

Thus at the end of 2019 Dani and I set off on our journey of writing our very first textbook together. We naively thought that with a little hard work we would have a first draft completed within a year. I was even all set to visit him in Barcelona in February of 2020 in order to spend an intense week getting the book off the ground properly. Unfortunately, like the rest of the world, the global pandemic took us by complete surprise, and completely upended both of our lives. With small children and home schooling, as well as preparing asynchronous teaching materials, and all the other stresses and strains of COVID, the book writing sadly took a back seat.

Time ticked by, but little by little we did manage to make progress here and there, mostly in small flurries of activity. I particularly enjoyed my two impromptu summer 鈥榳riting retreats鈥 鈥 at my parent-in-laws farmhouse, where I set up for intense weeks of focused writing. These really helped push the book forward, and get us close to the finish line.

I feel like I learnt many lessons writing this book. Scientifically, as I鈥檝e also found when writing lecture notes, trying to present something in a pedagogical way is extremely challenging, and really forces you to understand both the minute details, as well as the big picture. I genuinely learnt a huge amount during the writing of this book, and understood much better many aspects of semidefinite programming because of it. From a writing perspective, having never written something so big (and to be honest, the textbook is actually rather small compared to many), I was surprised at just how hard it is to keep the narrative of the book in mind, and to keep the book consistent and coherent. I learnt just how important it is to be immersed in the book to make this happen.

We finally finished writing the book in September 2022, a mere 17 months later than we had originally agreed to submit. I will admit that checking the proofs that we then received was a long and arduous, but very necessary task, which picked up many more typos than I would like to admit. It was a hugely joyous day when Semidefinite Programming in Quantum Information Science was published on 7th March 2023.

I鈥檝e felt quite a sense of trepidation since then, as this book feels decidedly personal, much more so than a research article, for some reason. Dani and I really hope that we managed to achieve the goal we set for ourselves 鈥 to write an accessible and useful textbook, that will convey the beauty of semidefinite programming, and allow others to pick it up and use it in their work and research. Only time will tell if we have indeed managed this.

Reflecting now upon everything, although there were definitely stressful moments, and it was a huge amount of work, I have no regrets, and am very proud of the final book we wrote. I might even be crazy enough to do it all over again one day, if the opportunity presents itself. Just not for a little while yet.

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