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ҹɫֱ��’s H-Series team has hit the ground running in 2023, achieving a new performance milestone. The H1-1 trapped ion quantum computer has achieved a Quantum Volume (QV) of 32,768 (2¹⁵), the highest in the industry to date.

The team previously increased the QV to 8,192 (or 2¹³) for the System Model H1 system in September, less than six months ago. The next goal was a QV of 16,384 (2¹⁴). However, continuous improvements to the H1-1's controls and subsystems advanced the system enough to successfully reach 2¹⁴ as expected, and then to go one major step further, and reach a QV of 2¹⁵.

The Quantum Volume test is a full-system benchmark that produces a single-number measure of a quantum computer’s general capability. The benchmark takes into account qubit number, fidelity, connectivity, and other quantities important in building useful devices.��While other measures such as gate fidelity and qubit count are significant and worth tracking, neither is as comprehensive as Quantum Volume which better represents the operational ability of a quantum computer.

Dr. Brian Neyenhuis, Director of Commercial Operations, credits reductions in the phase noise of the computer’s lasers as one key factor in the increase.

"We've had enough qubits for a while, but we've been continually pushing on reducing the error in our quantum operations, specifically the two-qubit gate error, to allow us to do these Quantum Volume measurements,” he said.��

The ҹɫֱ�� team improved memory error and elements of the calibration process as well.��

“It was a lot of little things that got us to the point where our two-qubit gate error and our memory error are both low enough that we can pass these Quantum Volume circuit tests,” he said.��

The work of increasing Quantum Volume means improving all the subsystems and subcomponents of the machine individually and simultaneously, while ensuring all the systems continue to work well together. Such a complex task takes a high degree of orchestration across the ҹɫֱ�� team, with the benefits of the work passed on to H-Series users.��

To illustrate what this 5-digit Quantum Volume milestone means for the H-Series, here are 5 perspectives that reflect ҹɫֱ�� teams and H-Series users.

Perspective #1:��How a higher QV impacts algorithms

Dr. Henrik Dreyer is Managing Director and Scientific Lead at ҹɫֱ��’s office in Munich, Germany. In the context of his work, an improvement in Quantum Volume is important as it relates to gate fidelity.��

“As application developers, the signal-to-noise ratio is what we're interested in,” Henrik said. “If the signal is small, I might run the circuits 10 times and only get one good shot. To recover the signal, I have to do a lot more shots and throw most of them away. Every shot takes time."

“The signal-to-noise ratio is sensitive to the gate fidelity. If you increase the gate fidelity by a little bit, the runtime of a given algorithm may go down drastically,” he said. “For a typical circuit, as the plot shows, even a relatively modest 0.16 percentage point improvement in fidelity, could mean that it runs in less than half the time.”

To demonstrate this point, the ҹɫֱ�� team has been benchmarking the System Model H1 performance on circuits relevant for near-term applications. The graph below shows repeated benchmarking of the runtime of these circuits before and after the recent improvement in gate fidelity. The result of this moderate change in fidelity is a 3x change in runtime.��The runtimes calculated below are based on the number of shots required to obtain accurate results from the benchmarking circuit – the example uses 430 arbitrary-angle two-qubit gates and an accuracy of 3%.

Perspective #2:��Advancing quantum error correction

Dr. Natalie Brown and Dr, Ciaran Ryan-Anderson both work on quantum error correction at ҹɫֱ��. They see the QV advance as an overall boost to this work.��

“Hitting a Quantum Volume number like this means that you have low error rates, a lot of qubits, and very long circuits,” Natalie said. “And all three of those are wonderful things for quantum error correction. A higher Quantum Volume most certainly means we will be able to run quantum error correction better. Error correction is a critical ingredient to large-scale quantum computing. The earlier we can start exploring error correction on today’s small-scale hardware, the faster we’ll be able to demonstrate it at large-scale.”

Ciaran said that H1-1's low error rates allow scientists to make error correction better and start to explore decoding options.

“If you can have really low error rates, you can apply a lot of quantum operations, known as gates,” Ciaran said. "This makes quantum error correction easier because we can suppress the noise even further and potentially use fewer resources to do it, compared to other devices.”

Perspective #3: Meeting a high benchmark

“This accomplishment shows that gate improvements are getting translated to full-system circuits,” said Dr. Charlie Baldwin, a research scientist at ҹɫֱ��.��

Charlie specializes in quantum computing performance benchmarks, conducting research with the Quantum Economic Development Consortium (QED-C).

“Other benchmarking tests use easier circuits or incorporate other options like post-processing data. This can make it more difficult to determine what part improved,” he said. “With Quantum Volume, it’s clear that the performance improvements are from the hardware, which are the hardest and most significant improvements to make.”��

“Quantum Volume is a well-established test. You really can’t cheat it,” said Charlie.

Perspective #4:��Implications for quantum applications

Dr. Ross Duncan, Head of Quantum Software, sees Quantum Volume measurements as a good way to show overall progress in the process of building a quantum computer.

“Quantum Volume has merit, compared to any other measure, because it gives a clear answer,” he said.��

“This latest increase reveals the extent of combined improvements in the hardware in recent months and means researchers and developers can expect to run deeper circuits with greater success.”��

Perspective #5:��H-Series users

ҹɫֱ��’s business model is unique in that the H-Series systems are continuously upgraded through their product lifecycle. For users, this means they continually and immediately get access to the latest breakthroughs in performance. The reported improvements were not done on an internal testbed, but rather implemented on the H1-1 system which is commercially available and used extensively by users around the world.

“As soon as the improvements were implemented, users were benefiting from them,” said Dr. Jenni Strabley, Sr. Director of Offering Management. “We take our Quantum Volume measurement intermixed with customers’ jobs, so we know that the improvements we’re seeing are also being seen by our customers.”

Jenni went on to say, “Continuously delivering increasingly better performance shows our commitment to our customers’ success with these early small-scale quantum computers as well as our commitment to accuracy and transparency. That’s how we accelerate quantum computing.”

Supporting data from ҹɫֱ��’s 2¹⁵ QV milestone

This latest QV milestone demonstrates how the ҹɫֱ�� team continues to boost the performance of the System Model H1, making improvements to the two-qubit gate fidelity while maintaining high single-qubit fidelity, high SPAM fidelity, and low cross-talk.

The average single-qubit gate fidelity for these milestones was 99.9955(8)%, the average two-qubit gate fidelity was 99.795(7)% with fully connected qubits, and state preparation and measurement fidelity was 99.69(4)%.

For both tests, the ҹɫֱ�� team ran 100 circuits with 200 shots each, using standard QV optimization techniques to yield an average of 219.02 arbitrary angle two-qubit gates per circuit on the 2¹⁴ test, and 244.26 arbitrary angle two-qubit gates per circuit on the 2¹⁵ test.

The ҹɫֱ�� H1-1 successfully passed the quantum volume 16,384 benchmark, outputting heavy outcomes 69.88% of the time, and passed the 32,768 benchmark, outputting heavy outcomes 69.075% of the time. The heavy output frequency is a simple measure of how well the measured outputs from the quantum computer match the results from an ideal simulation. Both results are above the two-thirds passing threshold with high confidence. More details on the Quantum Volume test can be found .

Heavy output frequency for H1-1 at 2¹⁵ (QV 32,768)

Heavy output frequency for H1-1 at 2¹⁴ (QV 16,384)��

Quantum Volume data and analysis code can be accessed on . Contemporary benchmarking data can be accessed at .

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If you’re a software developer, the best way to show your work is to post your code on . The site serves as a host for code repositories and a tool for software version control. It’s a straightforward and popular way for developers to share code, collaborate and spread the word about new languages and technical projects. Community members can download code, contribute to open source software projects, or develop their own projects.��

ҹɫֱ�� has used this open platform to make it easier for developers and everyone in the quantum ecosystem to understand the performance of the company’s H-Series quantum computers. The team posts to GitHub characterization data of System Model H1 quantum computer performance and also benchmarking data on Quantum Volume.

The ҹɫֱ�� team prioritizes transparency and published the data behind the System Model H1 data sheets in a publicly available place to back up performance claims with data. Anyone who is curious about how the hardware team achieved 32,768 quantum volume in February can . This repository contains the raw data along with the analysis code.

Charlie Baldwin, a lead physicist at ҹɫֱ��, said the GitHub postings make it easy to understand how the hardware team measures errors.

“Algorithm developers and anyone interested in quantum computing also can use the data to verify our stated error rates,” he said. “Both the single- and two-qubit error rates are among the lowest--if not the lowest--available on a commercial system.”

The publicly available data from ҹɫֱ��’s H-Series, Powered by Honeywell, is the most comprehensive set shared by a quantum computing company, as it includes circuits, raw data, gate counts and error rates. ҹɫֱ�� shares this data for users who need to understand exactly what a quantum computer’s performance metrics represent when they are analyzing or publishing their results. Posting the verification data for any performance metric is a best practice of how quantum hardware providers can promote more transparency in the performance of their hardware.

The team also has posted data sheets for the System Model H1 and for the System Model H1 Emulator on the company website. The System Model H1 is a generation of quantum computers based on ions trapped in a single linear geometry. Currently the ҹɫֱ�� H1-1 and H1-2 are available to customers. Many Fortune 500 companies use the System Model H1 for quantum research and development.

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��

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