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Learning Resources

I hold a passion for teaching quantum science and technology. Over the years, I’ve developed a significant collection of lecture notes and problem sets. This work has culminated in the creation of four unique educational offerings, detailed below.

These resources are readily available to all, with read-only links to Overleaf allowing for real-time updates as I continually refine these notes. My goal is to publish them as books in the future.

In all these courses, I utilize a blackboard or marker board for teaching. To put it another way, I believe that slides can detract from the learning experience. In addition, I integrate in situ problem-solving into the lecture content. 

Games to Teach Quantum Information and Cryptography

Level: Highschool and above
Lecture Notes: Games of Quantum: A Game-Based Introduction to Quantum Mechanics and Cryptography
Read-only Overleaf Link: available soon  

Introduction to Modern Quantum Algorithms

Level: 2nd year undergraduate, professional learners
Lecture Notes: Contemporary Quantum Algorithms

Resource: Read-Only Overleaf Link

Advanced Tensor Network Theory

Level: Research level
Lecture Notes: Elements of Tensor Network Theory
Resource: Read-Only Overleaf Link

Graphical Calculus in Quantum Information Processing

Level: Advanced undergraduate/beginning graduate
Lecture Notes: Visualising Quantum Information: A Guide to the Graphical Calculus of Tensor Networks
Resource: Read-Only Overleaf LinkDOI: 10.48550/arXiv.1912.10049

Hall of Fame

If you’re the first to identify a typo, your contribution will be acknowledged in the ‘Hall of Fame’ included in each set of notes. Overleaf versions are up-to-date. 

Course Description Summaries

Title: Games to Teach Quantum Information and Cryptography
Catalog Summary: This course introduces the principles of quantum theory by utilizing everyday household items to create experimental analogs of quantum effects. It covers topics such as quantum states and measurements, the distinction between quantum and probabilistic states, Bell’s inequality, and quantum cryptography.
Contact Hours: 8 hours of lectures, 8 hours of recitation and approximately 4 hours of independent study.

Title: Modern Quantum Algorithms
Catalog Summary: This course provides a comprehensive introduction to quantum computing, covering both theoretical foundations and practical applications. While exploring the fascinating world of quantum theory, students will develop an understanding of quantum algorithms, variational quantum algorithms, quantum optimization, and quantum cryptography. Through problem-driven learning and elegant calculations, students will gain the necessary skills to analyze quantum circuits and explore the potential of quantum computing.
Contact Hours: 16 hours of lectures, 16 hours of recitation, and approximately 8 hours of independent study.

Title: Advanced Tensor Network Theory
Catalog Summary: This course provides an introduction to the fundamental mathematical principles underlying tensor network theory, designed primarily for research active students and others interested in this field. Special attention is given to applications in quantum physics. The course content includes the foundational elements of tensor network theory, with a specific focus on parent Hamiltonian theory and the representation of quantum states using matrix product states. Additionally, it explores aspects of entanglement theory as they manifest within tensor network theory. Complementary subjects such as quantum circuits are also covered, alongside practical applications like employing tensor contraction to solve counting problem instances. This comprehensive approach equips students with a robust understanding of both the theoretical and practical aspects of tensor networks.
Contact Hours: 16 hours of lectures, 16 hours of recitation, and approximately 16 hours of independent study.

Title: Graphical Calculus in Quantum Information Processing
Catalog Summary: Graphical languages are widely utilized for reasoning and manipulation across various physical sciences. From quantum or classical circuits to graphs and even Feynman diagrams, the field of quantum information science extensively employs these graphical techniques. This course centers on the use of string diagrams as a graphical language, serving as a potent tool for reasoning about quantum circuits, quantum processes, and notably, open quantum systems. The course is crafted for those who already have a basic understanding of quantum information processing, forming a component of our ‘Modern Introduction to Quantum Algorithms.’ By focusing on the practical application of string diagrams, this course provides a thorough understanding of how these graphical techniques can be harnessed to effectively reason about complicated quantum systems.
Contact Hours: 16 hours of lectures, 16 hours of recitation, and approximately 16 hours of independent study.

Review Articles

Sections of my lecture notes have acted as the basis for various review articles, and vice versa. These notes can be accessed freely online:

Tensor networks in machine learning
R Sengupta, S Adhikary, I Oseledets and J Biamonte
European Mathematical Society Magazine 101, 4 (2022)
DOI: 10.4171/mag/101
ArXiv: 2207.02851

Complex networks from classical to quantum
J Biamonte, M Faccin and M De Domenico
Communications Physics 2, (2019)
DOI: 10.1038/s42005-019-0152-6
ArXiv: 1702.08459

Quantum techniques for stochastic mechanics [Book]
J Baez and J Biamonte
World Scientific Publishing Co Pte Ltd, 276 print pages (2018)
ISBN: 978-981-3226-96-8 (softcover), 978-981-3226-93-7 (hardcover)
ArXiv: 1209.3632

Charged string tensor networks
J Biamonte
Proceedings of the National Academy of Sciences 114, 2447 (2017)
DOI: 10.1073/pnas.1700736114
ArXiv: 1703.01302

Quantum machine learning
J Biamonte, P Wittek, N Pancotti, P Rebentrost, N Wiebe and S Lloyd
Nature 549, 195 (2017)
DOI: 10.1038/nature23474
ArXiv: 1611.09347

Tensor networks in a nutshell
J Biamonte and V Bergholm
ArXiv: 10.48550/arXiv.1708.00006