Quantum in Pictures

February 7, 2023

Quantinuum has today published Quantum in Pictures, a new book that promises to make the fields of quantum physics and quantum computing more inclusive and open to anyone, regardless of their mathematical or scientific background.

By introducing readers of all levels of expertise – from school children, parents and general science enthusiasts to businesspeople and educators – to the central concepts of quantum theory, Quantum in Pictures helps to grow public understanding of quantum computing, and the scientific theory that lies behind it.

Quantum in Pictures will encourage people from all backgrounds to seriously consider quantum physics or quantum computing in their professional careers, and for younger readers, to consider the study of physics, quantum theory or, as the subject grows in popularity, quantum computing.

Making quantum theory more inclusive

Quantum in Pictures is the brainchild of Quantinuum's chief scientist Professor Bob Coecke and Dr Stefano Gogioso at Oxford University. The book introduces a formalism for quantum mechanics based on using “ZX-calculus” (or “ZX”), to describe quantum processes. 

ZX-calculus, was originally introduced around 15 years ago by Bob and Ross Duncan, the head of quantum software at Quantinuum, when they were colleagues in the Oxford University Computing Laboratory (now the Computer Science Department). ZX  is based on a novel system of pictures instead of formal, traditional mathematics.

ZX has, over the past few years, become a complete system for reasoning in quantum theory, particularly as it is applied in quantum computing. It is now widely used in the quantum computing industry.

ZX-calculus is active within the heart of Quantinuum's TKET compiler and software development kit, now downloaded over 900,000 times, and is used by many of the world's quantum computing companies for tasks such as error correction, lattice surgery and circuit optimization.

ZX-calculus was also recently described in a scientific paper co-authored by Peter Shor at MIT, one of the founding fathers of quantum computing, as having “become of more interest than ever in fault-tolerant quantum computation and quantum compiler theory because it can explicitly visualize properties of circuits and entanglement in an intuitive manner”.

Quantum in Pictures explains some of the most important results in quantum mechanics and how they are used in quantum computing. It uses 5 rules from ZX-calculus to present such principles as teleportation, entanglement and uncertainty, and essential aspects of quantum computing, such as CNOT gates and Hadamard gates. These concepts are explained in a fun, game-like way that combines mathematical rigor with inclusivity.

Quantum in Pictures will help to ensure that large numbers of people, perhaps everyone, can feel confident when they consider learning about quantum physics and quantum computing, and a forthcoming video series that will accompany the book should help further this objective.

A very Brief Explanation of ZX-calculus as it is used in Quantum in Pictures

ZX-calculus come equipped with all the necessary mathematical rules required to handle quantum mechanics. 

However, “doing” the mathematics of quantum mechanics with ZX-calculus is very different from the way it is generally taught today. ZX uses a method known as picturalism, which means manipulating shapes, connected by lines, according to a set of rules. 

ZX-calculus has been proven mathematically to be universal, sound, and complete — in other words, you can reason about and calculate quantum processes as effectively as if you had a university-level of prior mathematical training and were calculating solutions to complex quantum mechanical problems.

The 5 ZX rules used in Quantum in Pictures

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Kaniah Konkoly-Thege

Kaniah is Chief Legal Counsel and SVP of Government Relations for Quantinuum. In her previous role, she served as General Counsel, Honeywell Quantum Solutions. Prior to Honeywell, she was General Counsel, Honeywell Federal Manufacturing and Technologies, LLC, and Senior Attorney, U.S. Department of Energy. She was Lead Counsel before the Civilian Board of Contract Appeals, the Merit Systems Protection Board, and the Equal Employment Opportunity Commission. Kaniah holds a J.D. from American University, Washington College of Law and B.A., International Relations and Spanish from the College of William and Mary.

Jeff Miller

Jeff Miller is Chief Information Officer for Quantinuum. In his previous role, he served as CIO for Honeywell Quantum Solutions and led a cross-functional team responsible for Information Technology, Cybersecurity, and Physical Security. For Honeywell, Jeff has held numerous management and executive roles in Information Technology, Security, Integrated Supply Chain and Program Management. Jeff holds a B.S., Computer Science, University of Arizona. He is a veteran of the U.S. Navy, attaining the rank of Commander.

Matthew Bohne

Matthew Bohne is the Vice President & Chief Product Security Officer for Honeywell Corporation. He is a passionate cybersecurity leader and executive with a proven track record of building and leading cybersecurity organizations securing energy, industrial, buildings, nuclear, pharmaceutical, and consumer sectors. He is a sought-after expert with deep experience in DevSecOps, critical infrastructure, software engineering, secure SDLC, supply chain security, privacy, and risk management.

Todd Moore

Todd Moore is the Global Vice President of Data Encryption Products at Thales. He is responsible for setting the business line and go to market strategies for an industry leading cybersecurity business. He routinely helps enterprises build solutions for a wide range of complex data security problems and use cases. Todd holds several management and technical degrees from the University of Virginia, Rochester Institute of Technology, Cornell University and Ithaca College. He is active in his community, loves to travel and spends much of his free time supporting his family in pursuing their various passions.

John Davis

Retired U.S. Army Major General John Davis is the Vice President, Public Sector for Palo Alto Networks, where he is responsible for expanding cybersecurity initiatives and global policy for the international public sector and assisting governments around the world to prevent successful cyber breaches. Prior to joining Palo Alto Networks, John served as the Senior Military Advisor for Cyber to the Under Secretary of Defense for Policy and served as the Acting Deputy Assistant Secretary of Defense for Cyber Policy.  Prior to this assignment, he served in multiple leadership positions in special operations, cyber, and information operations.