Building a quantum computer that offers advantages over classical computers is the goal of quantum computing groups worldwide. A competitive quantum computer must be “universal”, requiring the ability to perform all operations already possible on a classical computer, as well as new ones specific to quantum computing. Of course, that’s just the beginning – it should also be able to do this in a reasonable amount of time, to deal effectively with noise from the environment, and to perform computations to arbitrary accuracy.

This is a lot to get right, and over the years quantum computer scientists have described ways to solve these often-overlapping challenges. To deal with noise from the environment and achieve arbitrary accuracy, quantum computers need to be able to keep going even as noise accumulates on the quantum bits, or qubits, which hold the quantum information. Such fault-tolerance may be achieved using quantum error correction, where ensembles of physical qubits are encoded into logical qubits and those are used to counteract noise and perform computational operations called gates. Unfortunately, no single quantum error correction code plays well with the goal of universality because all codes lack a complete universal set of fault-tolerant gates (the technical reason for this comes down to the way quantum gates are executed between logical qubits – the native gate set on error-corrected logical qubits are known by experts as transversal gates, and they do not include all the gates needed for universal quantum computing).

The solution to this obstacle to universality is a magic state, a quantum state which provides for the missing gate when error correcting codes are used. High fidelity magic states are achieved by a process of distillation, which purifies them from other noisier magic states. It is widely recognized that magic state distillation is one of the totemic challenges on the path towards universal, fault-tolerant quantum computing. Quantinuum’s scientists, in close collaboration with a team at Microsoft, set out to demonstrate the distillation process in real-time using physical qubits on a quantum computer for the first time.

The results of this work are available in a new paper, Advances in compilation for quantum hardware -- A demonstration of magic state distillation and repeat until success protocols.

Magic state distillation

How does magic state distillation work? Imagine a factory, taking in many qubits in imperfect initial states at one end. Broadly speaking, the factory distills the imperfect states into an almost pure state with a smaller error probability, by sending them through a well-defined process over and over. In this case, the process takes in a group of five qubits. It applies a quantum error correcting code that entangles these five qubits, with four used to test whether the fifth, target qubit has been purified. If the process fails, the ensemble is discarded and the process repeats. If it succeeds, the newly distilled target qubit is kept and combined with four other successes to form a new ensemble, which then rejoins the process of continued purification. By undertaking this process many times, the purity of the magic state increases at each step, gradually moving towards the conditions required for universal, fault-tolerant quantum computing.

Despite being the subject of theoretical exploration over decades, real-time magic state distillation had never been realized on a quantum computer. In typical pioneering style, the Quantinuum and Microsoft team decided to take on this challenge. But before they could get started, they recognized that their toolset would have to be significantly sharpened up.

Creating new tools for quantum programming

At the heart of magic state distillation is a highly complex repeating process, which requires state-of-the-art protocols and control flow logic built on a best-in-class programming toolset. The research team turned to Quantum Intermediate Representation (QIR) to simplify and streamline the programming of this complex quantum computing process.

QIR is a is a quantum-specific code representation based on the popular open-sourced classical LLVM intermediate language, with the addition of structures and protocols that support the maturation and modernization of quantum computing. QIR includes elements that are essential in classical computing, but which are yet to be standardized in quantum computing, such as the humble programming loop.

Loops, which often take forms like "for...next" or "do...while," are central to programming, allowing code to repeat instructions in a stepwise manner until a condition is met. In quantum computing, this is a tough challenge because loops require control flow logic and mid-circuit measurement, which are difficult to realize in a quantum computer but have been demonstrated in Quantinuum’s System Model H1-1, Powered by Honeywell. Loops are essential for realizing magic state distillation and it’s well-understood that LLVM is great at optimizing complex control flow, including loops. This made magic state distillation a natural choice for demonstrating a valuable application of QIR and making for a great example of the use of a classical technique in a quantum context.

Result: demonstrating a magic state distillation protocol

The team used Quantinuum’s H1-1 quantum computer – benefiting from industry-leading components such as mid-circuit measurement, qubit reuse and feed-forward – to make possible the quantum looping required for a magic state distillation protocol, and becoming the first quantum computing team ever to run a real-time magic state distillation protocol on quantum hardware.

Four ways to achieve a quantum computer programmable loop

Building on this success, the team designed further experiments to assess the potential of four methods for exploring the use of a quantum protocol called a repeat-until-success (RUS) circuit to achieve a loop process. First, they hard-coded a loop directly into the extended OpenQASM 2.0, a widely used quantum assembly language, but which requires additional overhead to target advanced components on Quantinuum's very versatile H-Series quantum computer. Against this, they compared two alternative methods for coding a loop in a standard high-level programming language: controlled recursion, which was directed through both OpenQASM and through QIR; and a native for loop made possible within QIR.

The results were clear-cut: the hard-coded OpenQASM 2.0 loop performed as well as the theoretical prediction, maintaining high quality results after a number of loops, as did the natively-coded QIR for loop. The two recursive loops saw the quality of their results drop away fast as the loop limit was raised. But in a head-to-head between hard-coded OpenQASM and QIR, which converts high-level source code from many prominent and familiar languages into low-level machine code, QIR won hands-down on the basis of practicality.

Martin Roetteler, Director of Quantum Applications at Microsoft, shared: “This was a very exciting exploration of control flow logic on quantum hardware. In seeking to understand the capabilities of QIR to optimize programming structures on real hardware, we were rewarded with a clear answer, and an important demonstration of the capabilities of QIR.”

H2’s 32 qubits will power the next phase

In follow-up work, the team is now preparing to run a logical magic state protocol on the H2-1 quantum computer with its 32 high-fidelity qubits, and hopes to become the first group to successfully achieve logical magic state distillation. The features and fidelity offered by the H2 make it one of the best quantum computers currently capable of shooting for such a major milestone on the journey towards fault tolerance, while the current work demonstrates that, in QIR, the necessary control flow logic is now available to achieve it.

The paper discussed in this post was authored by Natalie C. Brown, John P. Campora III, Cassandra Granade, Bettina Heim, Stefan Wernli, Ciaran Ryan-Anderson, Dominic Lucchetti, Adam Paetznick, Martin Roetteler, Krysta Svore and Alex Chernoguzov.

Who is responsible for migrating your systems to quantum-safe algorithms? Is it your vendors or your cybersecurity team?  

The customers I speak to are not always clear on this question. But from my perspective, the answer is your cybersecurity team. They have the ultimate responsibility of ensuring your organization is secure in a post-quantum future. However, they will need a lot of help from your technology vendors.

This article outlines what you should expect (or demand) from your vendors, and what remains the responsibility of your cyber team.

What To Expect From General Vendors

A general vendor does not offer specific cryptographic services to you. Instead, they provide a business service that uses cryptography to maintain security and resilience.

Consider the accounting platform SAP. It is no doubt riddled with cryptography, yet its purpose is to manage your finances. Therefore, SAP’s focus will be on migrating their underlying cryptography to post-quantum technologies, while maintaining your business services without interruption.

You should expect a general vendor to share a quantum-safe migration roadmap with you, complete with timelines. They should explain the activities they will complete to address the quantum threat, and how they will impact you as a user.

Although your vendor will not begin migration until the NIST post-quantum algorithms are standardised next year, you should expect them to already have a roadmap in place. If they don’t, this is a cause for concern.

Some vendors may already offer a test version of their product, which uses post-quantum algorithms. This allows your cyber team to experiment with the impact on performance or interoperability.

What To Expect From Cryptographic Vendors

A cryptographic vendor provides you with services directly related to cryptography, such as network security, data encryption or key management.

The expectations that apply to general vendors also apply to cryptographic vendors. However, you will need more information from your cryptographic vendors to pull off a smooth migration.

Cryptographic vendors must provide you with detailed guidance on how to migrate between their current product suite and the new versions that use post-quantum algorithms. For instance, you might need to understand how to re-process legacy data so that it’s protected by the new algorithms. Similarly, network security vendors will need to provide detailed instructions on migrating traffic flows while maintaining uptime.

I would expect cryptographic vendors to be far more hands-on during your migration. Expect to have discussions of your deployment architecture with their account management teams, and don’t be afraid to ask the hard technical questions.

What Information You Should be Ready to Share

The flow of information will not be one-way. You should be prepared to share information with your vendors to help them help you.

Having your migration plan developed, at least at a high level, will be critical for meaningful conversations with your vendors. This will allow you to contrast their timelines for migration versus your expectations.

Vendors will also benefit from understanding how you use their products in conjunction with products from other vendors. The goal here is to spot edge cases, where you risk business downtime because the vendor wasn’t anticipating how you were using their product.

Finally, make sure you know the configuration of your deployment. The devil is in the details when it comes to planning migration, so be prepared to tell your vendor which features you are using and how you’ve configured product security settings.

What is Out of Scope for Your Vendor?

While your vendors should provide a lot of help and guidance, they are not responsible for everything.

Your cybersecurity team will be responsible for planning your overall migration strategy, including prioritising which systems to migrate first. This will involve understanding the relative importance of business systems, and the requirements for data security.

While vendors should provide some guidance for interoperability, ultimately the IT and cybersecurity teams are responsible for ensuring updates to one service do not impact another service.

Finally, you must ensure your IT and cyber teams are leading the conversation with your end users. You cannot rely on vendors to manage the communication with your customers and internal stakeholders.

What Should You Expect to See Today?

A good vendor will already be talking to you about their plans for quantum-safe migration.

For mass-market products, this might be via blog posts and thought-leadership articles. For products with a deeper client/vendor relationship, the topic of quantum-safe migration should already be appearing in quarterly business reviews.

For cryptographic vendors, you should also be expecting test versions to be available today, to allow for experimentation.

Overall, if any vendor is not able to talk about their plans for quantum-safe migration today, even at a high level, then you should flag this as a cause for concern.

Some of the more pressing and intractable problems in physics may be closer to being answered, such as the nature of superconductivity and other exotic properties, thanks to work done by a team at Quantinuum using the H2-1 trapped-ion quantum computer.  

Detailed in a scientific paper available on arXiv, the team used the H2-1 device to measure the “Loschmidt amplitude”, which quantifies how much a quantum system has changed after some time has passed (for the experts: this is the inner product between the time-evolved state and the initial state). Measuring the Loschmidt amplitude is central to several proposed quantum computing algorithms, including one described in the seminal work of Lu, Banuls and Cirac (2019). Their algorithm is a non-variational, hybrid quantum-classical scheme aimed at obtaining equilibrium properties of quantum systems. This is the first experimental demonstration of the quantum computation required for this algorithm.

To sweeten the pot, the research team measured the Loschmidt amplitude of a beloved, much-studied, and not-fully-understood model called the “Fermi-Hubbard” model. The Fermi-Hubbard model is used, among other things, to help scientists understand superconductivity, which is very challenging to explore fully with classical computing methods. When Richard Feynman “launched” the field of quantum computing with a famous talk in 1981, it was exactly this type of system he proposed we study with quantum computers: large quantum-mechanical systems that are difficult or impossible to effectively simulate classically. Using quantum computers to gain greater insights into the Fermi-Hubbard model could take us one step closer to understanding the behavior of high-temperature superconductors, a valuable goal with the potential to transform multiple industries.

A measurement of the Loschmidt amplitude is difficult because it is a “global observable”, meaning that any error in the quantum calculation will have an impact on the final results. This work highlights the outstanding precision of Quantinuum’s System Model H2 quantum computers. In particular, the trapped ion architecture allows for almost perfect state preparation and measurement, which is a necessary condition for such kind of calculations. Until now, this model had not been simulated with more than 16 qubits, in part because the gate operations applied are so complex. This paper explores the model on 32 qubits and includes a number of difficult elements; such as Schrodinger cat states, deep circuits, and complex Hamiltonians, making for a powerful demonstration of the H2-1 system capabilities. 

While this work is certainly a “NISQ”-era result, it shows that quantum computing can achieve interesting milestones without error correction – highlighting the fact that quantum methods may offer real advantages over classical methods in the near future. In addition, the team noted that while analog quantum simulators have made substantial progress in the study of exotic systems over the past decade, using a quantum computer to study these same systems allows for a wider exploration of the parameter space than Nature herself allows in laboratory simulations.

A more complex version of the algorithm will need to be implemented in the future to unlock the secrets of materials like superconductors, but in the meantime this work highlights the fact that Quantinuum is closing in on the answer to extremely relevant open questions, so far intractable with existing classical methods.

The IEEE International Conference on Quantum Computing and Engineering – or IEEE Quantum Week – is September 17 – 22 this year. Quantinuum is pleased to support IEEE’s efforts to bring engineers, scientists, researchers, students and others together to learn and encourage collaborations to advance quantum computing.

At the event, the Quantinuum team will be participating in a variety of sessions vital to the growth of the quantum ecosystem. Topics include photonics and fault tolerance strategies for scaling quantum computers, optimizing circuit compilation incorporating ZX-calculus as a simplification tool, and culture and policies.

Please see the complete list of sessions featuring Quantinuum team members below.

Tutorials

Quantum circuit compilation and classical control with TKET, Tuesday, Sept 19, 10:00am - 4:30pm, presented by Callum MacPherson, Technical support, training and outreach officer, and Lewis Wright, Quantum Algorithms Scientist

Quantum in Pictures in Practice, Wednesday, Sept 20, 10:00am – 4:30pm, presented by Lia Yeh, Research Engineer, Thomas Cervoni, Public Engagement and Academic Relations, and Harny Wang, Senior Research Fellow

Workshops

Quantum Computing Market Success Requires an Application-level Programming Model that Delivers Performance, Tuesday, Sept 19, 10:00am – 4:30pm, with Megan Kohagen, Lead Application Engineer

Quantum Computing for Natural Sciences: Technology and Applications, Wednesday, Sept 20, 10:00am – 4:30pm, with Lia Yeh, Research Engineer

Classical Control Systems for Quantum Computing, Wednesday, Sept 20, 10:00am – 4:30pm, with David Liefer, Chief Electrical Engineer

Emerging Technologies for Scaling Trapped-ion Quantum Systems, Thursday, Sept 21, 10:00am – 4:30pm, with Patty Lee, Chief Scientist for Hardware Technology Development

Quantum Algorithms for Financial Applications​, Friday, Sept 22, 10:00 – 4:30pm, with David Amaro, Senior Research Scientist

Technology Roadmapping for Quantum Computing​, Friday, Sept 22, 1:00 – 2:30pm, with Patty Lee, Chief Scientist for Hardware Technology Development

Panels

What’s in your photonics for quantum toolbox?, Monday, Sept 18, 10:00 – 11:30am, with Mary Rowe, Integrated Photonics Technical Manager

From the Capitol to the Laboratory: How Industry and Academia can Leverage National Policy for Funding of QIS, Wednesday, Sept 20, 3:00 – 4:30pm, with Ryan McKenney, Associate General Counsel, Compliance and Director of Government Relations

Real-Time decoding for in fault-tolerant era​, Thursday, Sept 21, 3:00 – 4:30pm, with Natalie Brown, Senior Advanced Physicist

Changing DEIA Culture and Environment in Industry​, Friday, Sept 22, 10:00 – 11:30am, with Sam Parsons, HR Director

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*All sessions are listed in Washington time, Pacific Time Zone

In a series of recent technical papers, Quantinuum researchers demonstrated the world-leading capabilities of the latest H-Series quantum computers, and the features and tools that make these accessible to our global customers and users.

Our teams used the H-Series quantum computers to directly measure and control non-abelian topological states of matter [1] for the first time, explore new ways to solve combinatorial optimization problems more efficiently [2], simulate molecular systems using logical qubits with error detection [3], probe critical states of matter [4], as well as exhaustively benchmark our very latest system [5].

Part of what makes such rapid technical and scientific progress possible is the effort our teams continually make to develop and improve workflow tools, helping our users to achieve successful results. In this blog post, we will explore the capabilities of three new tools in some detail, discuss their significance, and highlight their impact in recent quantum computing research.

Leakage Detection Gadget in pyTKET

“Leakage” is a quantum error process where a qubit ends up in a state outside the computational subspace and can significantly impact quantum computations. To address this issue, Quantinuum has developed a leakage detection gadget in pyTKET, a python module for interfacing with TKET, our quantum computing toolkit and optimizing compiler. This gadget, presented at the 2022 IEEE International Conference [6], acts as an error detection technique: it detects and excludes results affected by leakage, minimizing its impact on computations. It is also a valuable tool for measuring single-qubit and two-qubit spontaneous emission rates. H-Series users can access this open-source gadget through pyTKET, and an example notebook is available on the pyTKET GitHub repository. 

Mid-Circuit Measurement and Qubit Reuse (MCMR) Package

The MCMR package, built as a pyTKET compiler pass, is designed to reduce the number of qubits required for executing many types of quantum algorithms, expanding the scope of what is possible on the current-generation H-Series quantum computers. 

As an example, in a recent paper [4], Quantinuum researchers applied this tool to simulate the transverse-field Ising model and used only 20 qubits to simulate a much larger 128 site system (there is more detail below on this work). By measuring qubits early in the circuit, resetting them, and reusing them elsewhere, the package ingests a raw circuit and outputs an optimized circuit that requires fewer quantum resources. Previously, a scientific paper [7] and blog post on MCMR were published highlighting its benefits and applications. H-Series customers can download this package via the Quantinuum user portal.

Quantinuum H2-1 Emulator Release

To enable efficient use of Quantinuum’s 2^nd generation processor, the System Model H2, Quantinuum has released the H2-1 emulator to give users greater flexibility with noise-informed state vector emulation. This emulator uses the NVIDIA's cuQuantum SDK to accelerate quantum computing simulation workflows, nearly approaching the limit of full state emulation on conventional classical hardware. The emulator is a faithful representation of the QPU it emulates. This is accomplished by not only using realistic noise models and noise parameters, but also by sharing the same software stack between the QPU and the emulator up until the job is either routed to the QPU or the classical computing processors. Most notable is that the emulator and the QPU use the same compiler allowing subtle and time-dependent errors to be appropriately represented. The H2-1 emulator was initially released as a beta product alongside the System Model H2 quantum computer at launch. It runs on a GPU backend and an upgraded global framework now offering features such as job chunking, incremental resource distribution, mid-execution job cancellation, and partial result return. Detailed information about the emulator can be found in the H2 emulator product datasheet on the Quantinuum website. H-Series customers with an H2 subscription can access the H2-1 emulator via an API or the Microsoft Azure platform.

Enabling Recent Works

Quantinuum's new enabling tools have already demonstrated their efficacy and value in recent quantum computing research, playing a vital role in advancing the field and achieving groundbreaking results. Let's expand on some notable recent examples.

All works presented here benefited from having access to our H-Series emulators; of these two significant demonstrations were the “Creation of Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor” [1] and “Demonstration of improved 1-layer QAOA with Instantaneous Quantum Polynomial” [2]. These demonstrations involved extensive testing, debugging, and experiment design, for which the versatility of the H2-1 emulator proved invaluable, providing initial performance benchmarks in a realistic noisy environment. Researchers relied on the emulator's results to gauge algorithmic performance and make necessary adjustments. By leveraging the emulator's capabilities, researchers were able to accelerate their progress.

The MCMR package was extensively used in benchmarking the System Model H2 quantum computer’s world-leading capabilities [5]. Two application-level benchmarks performed in this work, approximating the solution to a MaxCut combinatorics problem using the quantum approximate optimization algorithm (QAOA) and accurately simulating a quantum dynamics model using a holographic quantum dynamics (HoloQUADS) algorithm, would have been too large to encode on H2's 32 qubits without the MCMR package. Further illustrating the overall value of these tools, in the HoloQUADS benchmark, there is a "bond qubit" that is particularly susceptible to errors due to leakage. The leakage detection gadget was used on this "bond qubit" at the end of the circuit, and any shots with a detected leakage error were discarded. The leakage detection gadget was also used to obtain the rate of leakage error per single-qubit and two-qubit gates, two component-level benchmarks.

In another scientific work [4], the MCMR compilation tool proved instrumental to simulating a transverse-field Ising model on 128 sites, using 20 qubits. With the MCMR package and by leveraging a state-of-the-art classical tensor-network ansatz expressed as a quantum circuit, the Quantinuum team was able to express the highly entangled ground state of the critical Ising model. The team showed that with H1-1's 20 qubits, the properties of this state could be measured on a 128-site system with very high fidelity, enabling a quantitatively accurate extraction of some critical properties of the model.

Key Takeaways

At Quantinuum, we are entirely devoted to producing a quantum hardware, middleware and software stack that leads the world on the most important benchmarks and includes features and tools that provide breakthrough benefit to our growing base of users.  In today's NISQ hardware, "benefit" usually takes the form of getting the most performance out of today’s hardware, continually pushing what is considered to be possible. In this blog we describe two examples: error detection and discard using the “leakage detection gadget” and an automated method for circuit optimization for qubit reuse. “Benefit” can also take other forms, such as productivity. Our emulator brings many benefits to our users, but one that resonates the most is productivity. Being a faithful representation of our QPU performance, the emulator is an accessible tool which users have at their disposal to develop and test new, innovative algorithms. The tools and features Quantinuum releases are driven by users’ feedback; whether you are new to H-Series or a seasoned user, please reach-out and let us know how we can help bring benefit to your research and use case.

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Footnotes:

[1] Mohsin Iqbal et al., Creation of Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor (2023), arXiv:2305.03766 [quant-ph]

[2] Sebastian Leontica and David Amaro, Exploring the neighborhood of 1-layer QAOA with Instantaneous Quantum Polynomial circuits (2022), arXiv:2210.05526 [quant-ph]

[3] Kentaro Yamamoto, Samuel Duffield, Yuta Kikuchi, and David Muñoz Ramo, Demonstrating Bayesian Quantum Phase Estimation with Quantum Error Detection (2023), arXiv:2306.16608 [quant-ph]

[4] Reza Haghshenas, et al., Probing critical states of matter on a digital quantum computer (2023),
arXiv:2305.01650 [quant-ph]

[5] S. A. Moses, et al., A Race Track Trapped-Ion Quantum Processor (2023), arXiv:2305.03828 [quant-ph]

[6] K. Mayer, Mitigating qubit leakage errors in quantum circuits with gadgets and post-selection, 2022 IEEE International Conference on Quantum Computing and Engineering (QCE), Broomfield, CO, USA, (2022), pp. 809-809, doi: 10.1109/QCE53715.2022.00126.

[7] Matthew DeCross, Eli Chertkov, Megan Kohagen, and Michael Foss-Feig, Qubit-reuse compilation with mid-circuit measurement and reset (2022), arXiv:2210.08039 [quant-ph]

In the last 6 months, Quantinuum H-Series hardware has demonstrated explosive performance improvement. Quantinuum’s System Model H1-1, Powered by Honeywell, has demonstrated going from 2¹⁴ = 16,384 quantum volume (QV) announced in February 2023 to now 2¹⁹ = 524,288, with all the details and data released on our GitHub repository for full transparency.  At a quantum volume of 524,288, H1-1 is 1000x higher than the next best reported quantum volume.

We set a big goal back in 2020 when we launched our first quantum computer, HØ. HØ was launched with six qubits and a quantum volume of 2⁶ = 64, and at that time we made the bold and audacious commitment to increasing the quantum volume of our commercial machines 10x per year for 5 years, equating to a quantum volume of 8,388,608 or 2²³ by the end of 2025. In an industry that is often accused of being over-hyped, a commitment like this was easy to forget. But we did not forget. Diligently, our scientists and engineers continued to achieve world-record after world-record in a tireless and determined pursuit to systematically improve the overall performance of our quantum computers.   As seen in Figure 1, from 2020 to early 2023, we have steadily been increasing the quantum volume to demonstrate that increased qubit count while reducing errors directly translates to more computational power.  Just within 2023 we’ve had multiple announcements of quantum volume improvements.  In February we announced that H1-1 had leapfrogged 2¹⁴ and achieved a quantum volume of 2¹⁵. In May 2023, we launched H2-1 with 32 qubits at a quantum volume of 2¹⁶.  Now we are thrilled to announce the sequential improvements of 2¹⁷, 2¹⁸, and 2¹⁹, all on H1-1.

Importantly, none of these results were “hero results”, meaning there are no special calibrations made just to try to make the system look better. Our quantum volume data is taken on our commercial systems interwoven with customer jobs. What we experience is what our customers experience. Instead of improving at 10x per year as we committed back in 2020, the pace of improvement over the past 6 months has been 30x, accelerating at least one year from our 5-year commitment. While these demonstrations were made using H1-1, the similarities in the designs of H1-2 (now upgraded with 20 qubits) and H2-1, our recently released second generation system, make it straightforward to share the improvements from one machine to another and achieve the same results.

In this young and rapidly evolving industry, there are and will be disagreements about which benchmarks are best to use. Quantum volume, developed by IBM, is undeniably rigorous.  Quantum volume can be measured on any gate-based machine. Quantum volume has been peer-reviewed and has well defined assumptions and processes for making the measurements.  Improvements in QV require consistent reductions in errors, making it likely that no matter the application, QV improvements translate to better performance. In fact, to realize the exponential increase in power that quantum computers promise, it is required to continue to reduce these error rates. The average two-qubit gate error with these three new QV demonstrations was 0.13%, the best in the industry.  We measure many benchmarks, but it is for these reasons that we have adopted quantum volume as our primary system-wide benchmark to report our performance.

Putting aside the argument of which benchmark is better, year-over-year improvements in a rigorous benchmark do not happen accidentally. It can only happen because the dedicated, talented scientists and engineers that work on H-Series hardware have a deep understanding of its error model and a deep understanding of how to reduce the errors to make overall performance improvements. Equally important the talented scientists and engineers have mastery of their domain expertise and can dream-up and then implement the improvements. These validated error models become the bedrock of future systems’ design, instilling confidence that those systems will have well understood error models, and the performance of those systems can also be systematically improved and ultimate performance goals achieved. Taking nothing away from those talented scientists and engineers, but having perfect, identical qubits and employing our quantum charge coupled device (QCCD) architecture does give us an advantage that all the other architectures and other modalities do not have.

What should potential users of H-Series quantum computers take away from this write-up (and what do current users already know)?

1. Quantinuum is committed to systematically improving the core performance of our quantum computing hardware. The better the fundamental performance, the lower the overhead will be when doing error mitigation, error detection, and ultimately error correction. This provides confidence in our ability to deliver fault-tolerant compute capabilities.
2. Progress on your research, use-case, or application can be accelerated by getting access to H-series technology because our quantum computers can do circuits that other technologies cannot. “It actually works!” exclaim excited first-time users.
3. Quantinuum intends to continue to be the quantum computing company that quietly over-delivers, even on big goals.

^1. https://github.com/CQCL/quantinuum-hardware-quantum-volume

^2. https://quantum-journal.org/papers/q-2022-05-09-707/