BOOK REVIEW

Quantum Machine Learning and Optimisation in Finance

by Antoine Jacquier and Oleksiy Kondratyev

reviewed by Ariel Neufeld (NTU Singapore)

The book called Quantum Machine Learning and Optimisation in Finance written by Antoine Jacquier and Oleksiy Kondratyev targets the emerging topic of quantum computing while focusing on the financial applications. The book is written for (financial) mathematicians as well as quants with a solid mathematical background.

While quantum computing has grown huge interest both in the industry and in academia in the fields of physics and computer science, only a few papers from the mathematical finance and quant finance community have been developed so far, despite its relevance. Therefore, I see this book as a great source where researchers from the mathematical finance and quantitative finance community can learn the theory of quantum computing. Hereby, it helps that the authors put a lot of efforts to present the book in a way to address mathematicians and quants by writing it in a mathematical clear way and highlighting its applications in finance.

The authors, Antoine Jacquier and Oleksiy Kondratyev, are definitely among the strongest quants in academia (Antoine Jacquier) and industry (Oleksiy Kondratyev) and among the very few from these communities who have already published several papers in the field of quantum computing in finance. This makes them ideal authors of this book which encourages colleagues to also doing research in that direction.

The structure of the book is the following. In the first chapter the authors present the mathematical notions and concepts of quantum computing in detail which are necessary to understand quantum computing and its applications in finance. Hereby the authors nicely introduce the notions in a mathematical way without requiring the reader the have any knowledge of quantum mechanics or quantum computing, but only a solid knowledge of complex linear algebra. Then, the book is presented in two major parts; (I) Analog Quantum Computing–Quantum Annealing, and (II) Gate Model Quantum Computing. In Part (I), the authors present in several chapters the important concepts of Adiabatic Quantum Computing, Quadratic Unconstrained Binary Optimisation, and Quantum Boosting, where they carefully explain the quantum advantages compared to analog classical (i.e. non-quantum) computing methods, as well as highlight their direct applications and benefits in finance. In Part (II), the authors first introduce to the reader the concept of Qubits and Quan-
tum Logic gates. Then, they focus on parameterized quantum circuits leading to Quantum neural networks as well as to quantum circuit born machines which is one of the most important (class of) example for quantum generative models which can create quantum advantages on so-called NISQ devices. Next, the authors present at the end of Part (II) variational quantum eigensolvers and quantum approximate
Optimization Algorithm (QAVA) to train, for example, these quantum generative models by approximately solving corresponding optimization problems. Hereby the authors well-present these methods while highlighting their direct potential impact in quantitative finance, both from an academic and also from a practitioners point of view. Finally, they present NISQ-compatible algorithms and concepts such as quan-
tum kernel methods, quantum generative Adversarial networks (GANs), or Bayesian Quantum Circuits, while discussing the potentials and advantages of quantum computing, also compared to classical methods.

Overall, the book is a pleasure to read. It is one of the first and only books who addresses people from the community of mathematical finance and quantitative finance by presenting the material using their (mathematical) language without requiring any pre-knowledge in quantum computing. It also highlights its connection and fusion to machine learning, making it an excellent book also for data scientists
which are particularly interested in financial applications. The book is well-written and teaches the readers all the important concepts from scratch, no pre-knowledge up to basic complex-linear algebra is necessary. Therefore, the book is especially well-suited for mathematicians, quants, and data scientists both from academia and from industry who are newly interested in the theory and applications of quantum computing and its applications in finance.

I can highly recommend this book to everyone who is genuinely interested in learning quantum computing and its applications in finance. I personally hope that this book will inspire other researchers to follow the authors’ passion for the topic so that in the near future more research results in this field will emerge.