Quantum in Pictures
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
For a longer and more detailed but highly accessible explanation about the history and philosophy of ZX-calculus, please read “How ZX-calculus reveals the logic and processes of quantum mechanics to everyone” on the Quantinuum blog.
About Quantinuum
Quantinuum, the world’s largest integrated quantum company, pioneers powerful quantum computers and advanced software solutions. Quantinuum’s technology drives breakthroughs in materials discovery, cybersecurity, and next-gen quantum AI. With over 500 employees, including 370+ scientists and engineers, Quantinuum leads the quantum computing revolution across continents.
- The Sanger Institute illustrates the value of quantum computing to genomics research
- Quantinuum supports developments in a field that promises to deliver a profound and positive societal impact
Twenty-five years ago, scientists accomplished a task likened to a biological moonshot: the sequencing of the entire human genome.
The Human Genome Project revealed a complete human blueprint comprising around 3 billion base pairs, the chemical building blocks of DNA. It led to breakthrough medical treatments, scientific discoveries, and a new understanding of the biological functions of our body.
Thanks to technological advances in the quarter-century since, what took 13 years and cost $2.7 billion then can now be done in under 12 minutes for a few hundred dollars. Improved instruments such as next-generation sequencers and a better understanding of the human genome – including the availability of a “reference genome” – have aided progress, alongside enormous advances in algorithms and computing power.
But even today, some genomic challenges remain so complex that they stretch beyond the capabilities of the most powerful classical computers operating in isolation. This has sparked a bold search for new computational paradigms, and in particular, quantum computing.
Quantum Challenge: Accepted
The Wellcome Leap Quantum for Bio (Q4Bio) challenge is pioneering this new frontier. The program funds research to develop quantum algorithms that can overcome current computational bottlenecks. It aims to test the classical boundaries of computational genetics in the next 3-5 years.
One consortium – led by the University of Oxford and supported by prestigious partners including the Wellcome Sanger Institute, the Universities of Cambridge, Melbourne, and Kyiv Academic University – is taking a leading role.
“The overall goal of the team’s project is to perform a range of genomic processing tasks for the most complex and variable genomes and sequences – a task that can go beyond the capabilities of current classical computers” – Wellcome Sanger Institute press release, July 2025
Selecting Quantinuum
Earlier this year, the Sanger Institute selected Quantinuum as a technology partner in their bid to succeed in the Q4Bio challenge.
Our flagship quantum computer, System H2, has for many years led the field of commercially available systems for qubit fidelity and consistently holds the global record for Quantum Volume, currently benchmarked at 8,388,608 (223).
In this collaboration, the scientific research team can take advantage of Quantinuum’s full stack approach to technology development, including hardware, software, and deep expertise in quantum algorithm development.
“We were honored to be selected by the Sanger Institute to partner in tackling some of the most complex challenges in genomics. By bringing the world’s highest performing quantum computers to this collaboration, we will help the team push the limits of genomics research with quantum algorithms and open new possibilities for health and medical science.” – Rajeeb Hazra, President and CEO of Quantinuum
Quantum for Biology
At the heart of this endeavor, the consortium has announced a bold central mission for the coming year: to encode and process an entire genome using a quantum computer. This achievement would be a potential world-first and provide evidence for quantum computing’s readiness for tackling real-world use cases.
Their chosen genome, the bacteriophage PhiX174, carries symbolic weight, as its sequencing earned Fred Sanger his second Nobel Prize for Chemistry in 1980. Successfully encoding this genome quantum mechanically would represent a significant milestone for both genomics and quantum computing.
Sooner than many expect, quantum computing may play an essential role in tackling genomic challenges at the very frontier of human health. The Sanger Institute and Quantinuum’s partnership reminds us that we may soon reach an important step forward in human health research – one that could change medicine and computational biology as dramatically as the original Human Genome Project did a quarter-century ago.
“Quantum computational biology has long inspired us at Quantinuum, as it has the potential to transform global health and empower people everywhere to lead longer, healthier, and more dignified lives.” – Ilyas Khan, Founder and Chief Product Officer of Quantinuum
Every year, The IEEE International Conference on Quantum Computing and Engineering – or IEEE Quantum Week – brings together engineers, scientists, researchers, students, and others to learn about advancements in quantum computing.
This year’s conference from August 31st – September 5th, is being held in Albuquerque, New Mexico, a burgeoning epicenter for quantum technology innovation and the home to our new location that will support ongoing collaborative efforts to advance the photonics technologies critical to furthering our product development.
Throughout IEEE Quantum Week, our quantum experts will be on-site to share insights on upgrades to our hardware, enhancements to our software stack, our path to error correction, and more.
Meet our team at Booth #507 and join the below sessions to discover how Quantinuum is forging the path to fault-tolerant quantum computing with our integrated full-stack.
September 2nd
Quantum Software Workshop
Quantum Software 2.1: Open Problems, New Ideas, and Paths to Scale
1:15 – 2:10pm MDT | Mesilla
We recently shared the details of our new software stack for our next-generation systems, including Helios (launching in 2025). Quantinuum’s Agustín Borgna will deliver a lighting talk to introduce Guppy, our new, open-source programming language based on Python, one of the most popular general-use programming languages for classical computing.
September 3rd
PAN08: Progress and Platforms in the Era of Reliable Quantum Computing
1:00 – 2:30pm MDT | Apache
We are entering the era of reliable quantum computing. Across the industry, quantum hardware and software innovators are enabling this transformation by creating reliable logical qubits and building integrated technology stacks that span the application layer, middleware and hardware. Attendees will hear about current and near-term developments from Microsoft, Quantinuum and Atom Computing. They will also gain insights into challenges and potential solutions from across the ecosystem, learn about Microsoft’s qubit-virtualization system, and get a peek into future developments from Quantinuum and Microsoft.
BOF03: Exploring Distributed Quantum Simulators on Exa-scale HPC Systems
3:00 – 4:30pm MDT | Apache
The core agenda of the session is dedicated to addressing key technical and collaborative challenges in this rapidly evolving field. Discussions will concentrate on innovative algorithm design tailored for HPC environments, the development of sophisticated hybrid frameworks that seamlessly combine classical and quantum computational resources, and the crucial task of establishing robust performance benchmarks on large-scale CPU/GPU HPC infrastructures.
September 4th
PAN11: Real-time Quantum Error Correction: Achievements and Challenges
1:00 – 2:30pm MDT | La Cienega
This panel will explore the current state of real-time quantum error correction, identifying key challenges and opportunities as we move toward large-scale, fault-tolerant systems. Real-time decoding is a multi-layered challenge involving algorithms, software, compilation, and computational hardware that must work in tandem to meet the speed, accuracy, and scalability demands of FTQC. We will examine how these challenges manifest for multi-logical qubit operations, and discuss steps needed to extend the decoding infrastructure from intermediate-scale systems to full-scale quantum processors.
September 5th
Keynote by NVIDIA
8:00 – 9:30am MDT | Kiva Auditorium
During his keynote talk, NVIDIA’s Head of Quantum Computing Product, Sam Stanwyck, will detail our partnership to fast-track commercially scalable quantum supercomputers. Discover how Quantinuum and NVIDIA are pushing the boundaries to deliver on the power of hybrid quantum and classical compute – from integrating NVIDIA’s CUDA-Q Platform with access to Quantinuum’s industry-leading hardware to the recently announced NVIDIA Quantum Research Center (NVAQC).
Featured Research at the IEEE Poster Session:
Visible Photonic Component Development for Trapped-Ion Quantum Computing
Authors: Elliot Lehman, Molly Krogstad, Christopher DeRose and Michael Gehl
Scaling Up Trapped-Ion Quantum Processors with Integrated Photonics
Authors: Molly Andersen, Bryan DeBono, Sara Campbell, Kirk Cook, David Gaudiosi, Christopher Ertsgaard, Azure Hansen, Todd Klein, Molly Krogstad, Elliot Lehman, Gregory MacCabe, Duc Nguyen, Nhung Nguyen, Adam Ollanik, Daniel Ouellette, Brendan Paver, Michael Plascak, Justin Schultz and Johanna Zultak
Research Collaborations with the Local Ecosystem
In a partnership that is part of a long-standing relationship with Los Alamos National Laboratory, we have been working on new methods to make quantum computing operations more efficient, and ultimately, scalable.
Learn more in our Research Paper: Classical shadows with symmetries
Our teams collaborated with Sandia National Laboratories demonstrating our leadership in benchmarking. In this paper, we implemented a technique devised by researchers at Sandia to measure errors in mid-circuit measurement and reset. Understanding these errors helps us to reduce them while helping our customers understand what to expect while using our hardware.
Learn more in our Research Paper: Measuring error rates of mid-circuit measurements
From machine learning to quantum physics, tensor networks have been quietly powering the breakthroughs that will reshape our society. Originally developed by the legendary Nobel laureate Roger Penrose, they were first used to tackle esoteric problems in physics that were previously unsolvable.
Today, tensor networks have become indispensable in a huge number of fields, including both classical and quantum computing, where they are used everywhere from quantum error correction (QEC) decoding to quantum machine learning.
In this latest paper, we teamed up with luminaries from the University of British Columbia, California Institute of Technology, University of Jyväskylä, KBR Inc, NASA, Google Quantum AI, NVIDIA, JPMorgan Chase, the University of Sherbrooke, and Terra Quantum AG to provide a comprehensive overview of the use of tensor networks in quantum computing.
Standing on the shoulders of giants
Part of what drives our leadership in quantum computing is our commitment to building the best scientific team in the world. This is precisely why we hired Dr. Reza Haghshenas, one of the world’s leading experts in tensor networks, and a co-author on the paper.
Dr. Haghshenas has been researching tensor networks for over a decade across both academia and industry. Dr. Haghshenas did postdoctoral work under Professor Garnet Chan at Caltech, a leading figure in the use of tensor networks for quantum physics and chemistry.
“Working with Dr. Garnet Chan at Caltech was a formative experience for me”, remarked Dr. Haghshenas. “While there, I contributed to the development of quantum simulation algorithms and advanced classical methods like tensor networks to help interpret and simulate many-body physics.”
Since joining Quantinuum, Dr. Haghshenas has led projects that bring tensor network methods into direct collaboration with experimental hardware teams — exploring quantum magnetism on real quantum devices and helping demonstrate early signs of quantum advantage. He also contributes to widely used simulation tools like QUIMB, helping the broader research community access these methods.
Dr. Haghshenas’ work sits in a broad and vibrant ecosystem exploring novel uses of tensor networks. Collaborations with researchers like Dr. Chan at Caltech, and NVIDIA have brought GPU-accelerated tools to bear on the forefront of applying tensor networks to quantum chemistry, quantum physics, and quantum computing.
A powerful simulation tool
Of particular interest to those of us in quantum computing, the best methods (that we know of) for simulating quantum computers with classical computers rely on tensor networks. Tensor networks provide a nice way of representing the entanglement in a quantum algorithm and how it spreads, which is crucial but generally quite difficult for classical algorithms. In fact, it’s partly tensor networks’ ability to represent entanglement that makes them so powerful for quantum simulation. Importantly, it is our in-house expertise with tensor networks that makes us confident we are indeed moving past classical capabilities.
A theory of evolution
Tensor networks are not only crucial to cutting-edge simulation techniques. At Quantinuum, we're working on understanding and implementing quantum versions of classical tensor network algorithms, from quantum matrix product states to holographic simulation methods. In doing this, we are leveraging decades of classical algorithm development to advance quantum computing.
A topic of growing interest is the role of tensor networks in QEC, particularly in a process known as decoding. QEC works by encoding information into an entangled state of multiple qubits and using syndrome measurements to detect errors. These measurements must then be decoded to identify the specific error and determine the appropriate correction. This decoding step is challenging—it must be both fast (within the qubit’s coherence time) and accurate (correctly identifying and fixing errors). Tensor networks are emerging as one of the most effective tools for tackling this task.
Looking forward (and backwards, and sideways...)
Tensor networks are more than just a powerful computational tool — they are a bridge between classical and quantum thinking. As this new paper shows, the community’s understanding of tensor networks has matured into a robust foundation for advancing quantum computing, touching everything from simulation and machine learning to error correction and circuit design.
At Quantinuum, we see this as an evolutionary step, not just in theory, but in practice. By collaborating with top minds across academia and industry, we're charting a path forward that builds on decades of classical progress while embracing the full potential of quantum mechanics. This transition is not only conceptual but algorithmic, advancing how we formulate and implement methods utilizing efficiently both classical and quantum computing. Tensor networks aren’t just helping us keep pace with classical computing; they’re helping us to transcend it.