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ҹɫֱ�� has today published , 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 ҹɫֱ��'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 ҹɫֱ��, 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 ҹɫֱ��'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 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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For a longer and more detailed but highly accessible explanation about the history and philosophy of ZX-calculus, please read on the ҹɫֱ�� blog.

kicked off in Santa Clara, CA where ҹɫֱ�� presented among important influencers in the quantum computing industry. Our experts presented on a range of topics including industry trends, use cases for quantum hardware, middleware and software and technology updates for an audience of global top academics, industry end users, government representatives and quantum computing vendors. Here’s a recap of ҹɫֱ�� presentations:

Industry Trends:

Great Mashups: Steady Progress meets Exponential‍

President and COO Tony Uttley‍

Watch here ->

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Across the Pond: How UK-US partnerships are delivering on the promise of Quantum Computing

President and COO Tony Uttley

Watch here ->

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Quantum Computing Innovation: The 2023 International State of Play

Chief Legal Officer and Chief Compliance Officer, Kaniah Konkoly-Thege��

Watch here ->

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Use Cases for Automotive, Computational Chemistry, Finance, and More:

Entangling the Ecosystem: 5 Diverse Stories of Quantum Collaborations,

Technical Solutions Specialist, Mark Wolf, Ph.D.

Watch here -> ��

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Computational chemistry on near-term quantum computers and beyond

Scientific Project Manager, Michal Krompiec

Watch here ->

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Quantum Computing Technology:

ҹɫֱ�� H-Series features and capabilities powered through Azure Quantum hybrid quantum computing stack

Sr. Director of Offering And Program Management, Jennifer Strabley and Microsoft’s Principal PM Lead, Azure Quantum, Fabrice Frachon

Watch here -> ��

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If you’d like to learn more about these presentations and topics, please reach out.��

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ҹɫֱ�� also celebrated its first anniversary with attendees. At Q2B 2021, ҹɫֱ�� announced the combination of Cambridge Quantum Computing and Honeywell Quantum, so it was only fitting to celebrate its one-year anniversary at the 2022 event.��

From ҹɫֱ��’s launch in late 2021 as the world’s first fully integrated quantum tech company, its momentum quickly continued with the launches of and , achieving 20 fully connected qubits, expanding our work with major partners, and reaching a quantum volume of 8192, just to name a few milestones. Learn more about ҹɫֱ�� in its first year below.

When we launched InQuanto™, our computational chemistry platform for quantum computing, we explained that its origins lay at least as much with our industrial partners as it did with us. We revealed that its development was the culmination of many important scientific collaborations with some of the world’s leading industrial names in energy, automotive, pharmaceuticals, industrial materials, and other sectors.

Today, we announce the next version of our state-of-the-art platform. Just as before, it is important to us that InQuanto 2.0, while being more versatile, more extensible, and more applicable for those who have not yet explored the use of quantum computers, is the result of precisely the same spirit of collaboration.

In close collaboration with our industrial partners, we have designed, developed, and discovered methods using InQuanto for exploring the application of near-term quantum technology to material and molecular problems that remain challenging or intractable for even the most powerful classical computers.

What’s inside InQuanto 2.0?

InQuanto continues to be built around the latest quantum algorithms, advanced subroutines, and chemistry-specific noise-mitigation techniques. In the new version, we have added new features to enhance efficiency, such as new protocol classes that can speed up vector calculations by an order of magnitude, and integral operator classes that exploit symmetries and can reduce memory requirements.

We have introduced new tools for developing custom ���Բ�ä�ٳ���, new embedding techniques and novel hybrid methods to improve efficiency and precision, which in some cases have only recently been described in the scientific literature. And these rapid advances are supported by new ways for computational chemists to build InQuanto into their workflow, whether that is by improving visualization and interoperability with other chemistry packages, or by demonstrating the ability to run it in the cloud, for example, through a .

The most exciting progress, of course, is reflected in the diverse work of our partners. We know that some of the work being done today will be reflected in future methods and techniques incorporated into InQuanto, fulfilling the ever more advanced needs of our partners tomorrow.

Please book a demonstration of InQuanto 2.0 today.

InQuanto 2.0 brings together a range of new features that continue to make it the right choice for computational chemists on quantum computers:

Efficiency

• Workflow improvements in protocol classes for more efficient small test calculations — up to 10x speed-ups in some state vector calculations
• Symmetry-exploiting integral operator classes for efficient handling of the two-electron integral for a chemistry Hamiltonian using ~50% less memory
• Optimized computables for n-particle reduced density matrices

Algorithms

• Wide range of restructured ���Բ�ä�ٳ��� to support multi-reference calculations to enable new types of variational quantum algorithms — with improved custom ansatz development tools
• Generalised variational quantum solvers to perform imaginary and real-time evolution simulations
• Added Fragment Molecular Orbital embedding method
• New QRDM-NEVPT2 method to measure 4-particle reduced density matrices and add corrections to VQE energy

User Experience

• FCIDUMP read/write for improved integration with other quantum chemistry packages
• Unit cell visualization extensions, and support for trotterization in the operator level
• Improved resource cost estimation on H-Series quantum computers, Powered by Honeywell��

What to read next:

Ford battery researchers used ���Բϳܲ��Գٴ�™ to study how quantum computers could be used to model lithium-ion batteries.

Among other research, the Global Technology Applied Research (GTAR) Center at JPMorgan Chase is experimenting with quantum algorithms for constrained optimization to perform Natural Language Processing (NLP) for document summarization, addressing various application points across the firm.��

Marco Pistoia, Ph.D., Managing Director, Distinguished Engineer, and Head of GT Applied Research recently led the research effort around a constrained version of the Quantum Approximate Optimization Algorithm (QAOA) that can extract and summarize the most important information from legal documents and contracts. This work was recently published in Nature Scientific Reports () and deemed the “largest demonstration to date of constrained optimization on a gate-based quantum computer.”��

JPMorgan Chase was one of the early-access users of the ҹɫֱ�� H1-1 system when it was upgraded from 12 qubits with 3 parallel gating zones to 20 qubits with 5 parallel gating zones. The research team at JPMorgan Chase found the 20-qubit machine returned significantly better results than random guess without any error mitigation, despite the circuit depth exceeding 100 two-qubit gates. The circuits used were deeper than any quantum optimization circuits previously executed for any problem. “With 20 qubits, we could summarize bigger documents and the results were excellent,” Pistoia said. “We saw a difference, both in terms of the number of qubits and the quality of qubits.”

JPMorgan Chase has been working with ҹɫֱ��’s quantum hardware since 2020 (pre-merger) and Pistoia has seen the evolution of the machine over time, as companies raced to add qubits. “It was clear early on that the number of qubits doesn't matter,” he said. “In the short term, we need computers whose qubits are reliable and give us the results that we expect based on the reference values.”����

Jenni Strabley, Sr., Director of Offering Management for ҹɫֱ��, stated, “Quality counts when it comes to quantum computers. We know our users, like JPMC, expect that every time they use our H-Series quantum computers, they get the same, repeatable, high-quality performance. Quality isn’t typically part of the day-to-day conversation around quantum computers, but it needs to be for users like Marco and his team to progress in their research.”

More broadly, the researchers claimed that “this demonstration is a testament to the overall progress of quantum computing hardware. Our successful execution of complex circuits for constrained optimization depended heavily on all-to-all connectivity, as the circuit depth would have significantly increased if the circuit had to be compiled to a nearest-neighbor architecture.”

Describing the experiment��

The objective of the experiment was to produce a condensed text summary by selecting sentences verbatim from the original text. The specific goal was to maximize the centrality and minimize the redundancy of the sentences in the summary and do so with a limited number of sentences.��

The JPMorgan Chase researchers used all 20 qubits of the H1-1 and executed circuits with two-qubit gate depths of up to 159 and two-qubit gate counts of up to 765. The team used IBM’s Qiskit for circuit manipulation and noiseless simulation. For the hardware experiments, they used to optimize the circuits for H1-1’s native gate set. They also ran the quantum circuits in an emulator of the H1-1 device.

The JPMorgan Chase research team tested three algorithms: L-VQE, QAOA and XY-QAOA. L-VQE was easy to execute on the hardware but difficult to find good parameters for. Regarding the other two algorithms, it was easier to find good parameters, but the circuits were more expensive to execute. The XY-QAOA algorithm provided the best results.��

Looking ahead and across industries

Dr. Pistoia mentions that constrained optimization problems, such as extractive summarization, are ubiquitous in banks, thus finding high-quality solutions to constrained optimization problems can positively impact customers of all lines of business. It is also important to note that the optimization algorithm built for this experiment can also be used across other industries (e.g., transportation) because the underlying algorithm is the same in many cases.����

Even with the quality of the results from this extractive summarization work, the NLP algorithm is not ready to roll out just yet. “Quantum computers are not yet that powerful, but we're getting closer,” Pistoia said.�� “These results demonstrate how algorithm and hardware progress is bringing the prospect of quantum advantage closer, which can be leveraged across many industries.”