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/

Quantinuum’s recent announcement about its breakthrough on topological qubits garnered headlines across both the specialist scientific media as well as those more broadly interested in the advances that will make quantum computing useful more quickly than anticipated. However, hidden in the details was a reference to a technology that is as rare as it is valuable. The fact is that the topological qubit that was generated could only have been done via Quantinuum’s H-Series quantum processors due to their various qualities and functions of which measurement and ‘feed-forward’ is critical.

As we know, great advances are often built on the back of little-known utilities - functions and tools that rarely get mentioned. These are sometimes technological constructs that might seem simple on the surface, but which are difficult (in the case of feed-forward make that “very difficult” to create), and without which critical advances would remain merely theoretical.

As detailed in two manuscripts that have been uploaded onto the pre-print repository, arXiv, Quantinuum researchers and their collaborators successfully demonstrated, for the first time, a large-scale implementation of a long-standing theory in quantum information science; namely the use of measurement and feed-forward (see below for a detailed explanation of what this means) to efficiently generate long-range entangled states.

The two experiments, conducted with research partners at the California Institute of Technology, Harvard University, the University of Sydney, the Perimeter Institute for Theoretical Physics and the University of California, Davis, used Quantinuum’s trapped ion quantum computers, Powered by Honeywell, to show how feed-forward enables success by dramatically reducing the resources required to produce highly-entangled quantum states and topologically ordered phases, one of the most exciting areas of research in modern physics.

Feed-forward uses selective measurements during the execution of a quantum circuit and adapts future operations depending on those measurement results. To be successful in running an adaptive quantum circuit, several challenging requirements must be met: (1) a select group of qubits must be measured in the middle of a circuit with high fidelity, and without accidentally measuring other qubits, and (2) the measurement results must be sent to a classical computer and quickly processed to create instructions to be fed-forward to the quantum computer on the fly - all of which must be done fast enough to prevent the active qubits from decohering.

Once these requirements are met, the feed-forward capabilities let quantum computers create long-range entangled states which are emerging as central to various branches of modern physics such as quantum error correction codes and the study of spin liquids in condensed matter. It is also the essential component of topological order and could enable the simulation of quantum systems beyond the reach of classical computation.

In the paper “Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer”, Quantinuum, working with colleagues from the California Institute of Technology and Harvard University use feed-forward to explore topologically ordered phases of matter. 

Separately, a different team of scientists from Quantinuum, the University of Sydney, the Perimeter Institute for Theoretical Physics and the University of California, Davis, used feed-forward to explore adaptive quantum circuits in “Experimental Demonstration of the Advantage of Adaptive Quantum Circuits”. 

Two of Quantinuum’s physicists who worked on both experiments, Henrik Dreyer and Michael Foss-Feig, offered some observations on the work.

“While it has been clear to theorists that feed-forward would be a useful primitive, doing it with low errors has turned out to be very challenging. The H-Series systems have made it possible to use this primitive efficiently,” said Henrik, managing director and scientific lead at Quantinuum’s office in Munich, Germany.

Michael, who is based at Quantinuum’s world-leading quantum computing laboratory outside of Denver, Colorado, also described feed-forward and adaptive quantum circuits as a jump toward meaningful simulations.

“This capability speeds up the timeline for new scientific discoveries,” he said.

These successful experiments proved that feed-forward operations reduce the quantum resources required for certain algorithms and are a valuable building block for more advanced research.

"I am really excited by the opportunities opened up by this demonstration: using wave-function collapse is a very powerful tool for preparing very exotic entangled states further down the road, where there are no good scalable alternatives," said Dr. Ruben Verresen, a physicist at Harvard University and a co-author of the topological order paper.

The authors note that “the primary technical challenge in implementing adaptive circuits is the requirement to perform partial measurements of a subset of qubits in the middle of a quantum circuit with minimal cross-talk on unmeasured qubits, return those results to a classical computer for processing, and then condition future operations on the results of that processing in real time.”

The paper describes how quantum hardware has now reached a state where adaptive quantum circuits are possible and can outperform unitary circuits. The experiment detailed in the paper “firmly establishes that given access to the same amount of quantum computational resources with respect to available gates and circuit depth, adaptive quantum circuits can perform tasks that are impossible for quantum circuits without feedback.”

Henrik and Michael noted that the adaptive circuit research provides concrete evidence not only that feed-forward works, but that it now works well enough to achieve tasks that would not be possible without it.

“We were trying to find a metric by which somebody can look at our data produced by a shallow adaptive circuit, and convince themselves it could not have been produced with a unitary circuit of the same depth,” Michael said. The metric proposed in the adaptive circuits paper achieved exactly that.

A good match: Trapped ion architecture and feed-forward 

Demonstrating this technique required significant performance from the H1-1. 

“It's a huge challenge to implement this in a way that works well,” Michael said. 

Quantinuum’s H-Series has the capabilities that are crucial to this work: high fidelity gates, low state preparation and measurement (SPAM) error, low memory error, the ability to perform mid-circuit measurement, and all-to-all connectivity.

The feed-forward theory has been well-known for years but challenging to execute in practice, and as the paper states:

“While individual elements of this triad have been demonstrated in the context of error correction and topological order, combining all of these ingredients into one experimental platform has proven elusive since the inception of this idea more than a decade ago. Here, we demonstrate for the first time the deterministic, high-fidelity preparation of long-range entangled quantum states using a protocol with constant depth, using Quantinuum’s H-Series programmable Ytterbium ion trap quantum computer.”

The authors also note that “the all-to-all connectivity of the device was vital for the implementation of the periodic two-dimensional geometry and the conditional dynamics.”

In summary – these papers showcase state-of-the-art demonstrations of what can be done with quantum computers today but are only a preview of what will be done tomorrow.

Quantinuum has unveiled our new optics and electromechanical engineering laboratory space at our largest operating site, in Broomfield Colorado.

Not only is the new space more than twice as big as the space we occupy today, but it will also house a clean, quiet, temperature controlled, state-of-the-art laboratory that befits the excellence of the work we do here.

Our hardware engineering and teams are focused on optimizing, customizing, and miniaturizing the components that power the H-Series quantum computers, demanding that our teams blur the boundaries between discrete disciplines, such as bulk optics and micro photonics, or embedded software and control electronics. Getting the handover right between different deeply skilled experts requires proximity and an intimate understanding of how one workflow blends into the other.

This is why this new lab space will make such a powerful contribution to our hardware success: because it is built around the needs of deeply connected, multidisciplinary teams, entirely focused on our goal of designing and building the first truly useful, breakaway quantum computer.

Six things you need to know about Quantinuum’s new lab

1. State-of-the-Art Facility: Our new lab, with its state-of-the-art design and facilities, creates an environment for collaboration that will spur advances in the fields of optics, photonics, electromechanical engineering, and others.
   
   
2. Expansive and Efficient Space: The lab is not only going to be much larger than what we have today, it is also highly functional, with high ceilings and cloud superstructures over optics benches for better movement and workflow, which will afford our teams greater flexibility and access to every angle of the technology they are creating.
   
   
3. Advancing Micro and Nano Optics: As we aim to reduce our beam delivery size, we're drawing together the work of different teams, creating a dynamic environment where optics transitions into photonics, yielding new potential in terms of size, scale and performance. The location of certain teams will enable such cross-disciplinary workflows.
   
   
4. Custom Fabrication Capabilities: The new optics lab, together with our highly capable chip and trap fabrication capabilities, is designed to enable generational transitions from off-the-shelf, multipurpose optical components to fabricating more compact and fit-for-purpose devices: Think of moving from Functionality on a Table, through Functionality on a Chip, to Functionality on a Trap.
   
   
5. Greater Collaboration and Integration: The new laboratory layout improves the way some teams are co-located, with an eye always toward helping to enhance collaboration. For example, the new engineering space was designed to facilitate close cooperation between the electronics and software teams who design our control systems, as well as the mechanical teams who package the hardware and the test teams who validate it.  Such proximity between disciplines supports faster decision-making and more efficient resolution of interdisciplinary challenges, leading to a virtuous circle of accelerated design and development, faster innovation, and better quantum computers.
   
   
6. Ready for Future Expansion: As we prepare for the next stage of the journey towards fault-tolerant quantum computing, where demand for quantum compute will scale exponentially everywhere, this new laboratory space is fit for the future as well as meeting the demands of today.

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Quantinuum’s new H2-1 quantum computer proves that trapped-ion architecture, which is well-known for achieving outstanding qubit quality and gate fidelity, is also built for scale – and Quantinuum’s benchmarking team has the data to prove it. 

The bottom line: the new System Model H2 surpasses the H1 in complexity and qubit capacity while maintaining all the capabilities and fidelities of the previous generation – an astounding accomplishment when developing successive generations of quantum systems.

The newest entry in the H-Series is starting off with 32 qubits whereas H1 started with 10. H1 underwent several upgrades, ultimately reaching a 20-qubit capacity, and H2 is poised to pick up the torch and run with it. Staying true to the ultimate goal of increasing performance, H2 does not simply increase the qubit count but has already achieved a higher Quantum Volume than any other quantum computer ever built: 2¹⁶ or 65,536. 

Most importantly for the growing number of industrials and academic research institutions using the H-Series, benchmarking data shows that none of these hardware changes reduced the high-performance levels achieved by the System Model H1. That’s a key challenge in scaling quantum computers – preserving performance while adding qubits. The error rate on the fully connected circuits is comparable to the H1, even with a significant increase in qubits. Indeed, H2 exceeds H1 in multiple performance metrics: single-qubit gate error, two-qubit gate error, measurement cross talk and SPAM. 

Key to the engineering advances made in the second-generation H-Series quantum computer are reductions in the physical resources required per qubit. To get the most out of the quantum charge-coupled device (QCCD) architecture, which the H-Series is built on, the hardware team at Quantinuum introduced a series of component innovations, to eliminate some performance limitations of the first generation in areas such as ion-loading, voltage sources, and delivering high-precision radio signals to control and manipulate ions.

The research paper, “A Race Track Trapped-Ion Quantum Processor,” details all of these engineering advances, and exactly what impacts they have on the computing performance of the machine. The paper includes results from component and system-level benchmarking tests that document the new machine’s capabilities at launch. These benchmarking metrics, combined with the company’s advances in topological qubits, represent a new phase of quantum computing.

Advancing Beyond Classical Simulation

‍In addition to the expanded capabilities, the new design provides operational efficiencies and a clear growth path.

At launch, H2’s operations can still be emulated classically. However, Quantinuum released H2 at a small percentage of its full capacity. This new machine has the ability to upgrade to more qubits and gate zones, pushing it past the level where classical computers can hope to keep up.

Increased Efficiency in New Trap Design

This new generation quantum processor represents the first major trap upgrade in the H-Series. One of the most significant changes is the new oval (or racetrack) shape of the ion trap itself, which allows for a more efficient use of space and electrical control signals. 

One key engineering challenge presented by this new design was the ability to route signals beneath the top metal layer of the trap. The hardware team addressed this by using radiofrequency (RF) tunnels. These tunnels allow inner and outer voltage electrodes to be implemented without being directly connected on the top surface of the trap, which is the key to making truly two-dimensional traps that will greatly increase the computational speed of these machines. 

The new trap also features voltage “broadcasting,” which saves control signals by tying multiple DC electrodes within the trap to the same external signal. This is accomplished in “conveyor belt” regions on each side of the trap where ions are stored, improving electrode control efficiency by requiring only three voltage signals for 20 wells on each side of the trap.

The other significant component of H2 is the Magneto Optical Trap (MOT) which replaces the effusive atomic oven that H1 used. The MOT reduces the startup time for H2 by cooling the neutral atoms before shooting them at the trap, which will be crucial for very large machines that use large numbers of qubits. 

Industry-leading Results from 15 Benchmarking Tests

Quantinuum has always valued transparency and supported its performance claims with publicly available data. 

To quantify the impact of these hardware and design improvements, Quantinuum ran 15 tests that measured component operations, overall system performance and application performance. The complete results from the tests are included in the new research paper. 

The hardware team ran four system-level benchmark tests that included more complex, multi-qubit circuits to give a broader picture of overall performance. These tests were:

• Mirror benchmarking: A scalable way to benchmark arbitrary quantum circuits.
• Quantum volume: A popular system-level test with a well-established construction that is comparable across gate-based quantum computers.
• Random circuit sampling: A computational task of sampling the output distributions of random quantum circuits.
• Entanglement certification in Greenberger-Horne-Zeilinger (GHZ) states: A demanding test of qubit coherence that is widely measured and reported across a variety of quantum hardware.

H2 showed state-of-the-art performance on each of these system-level tests, but the results of the GHZ test were particularly impressive. The verification of the globally entangled GHZ state requires a relatively high fidelity, which becomes harder and harder to achieve with larger numbers of qubits. 

With H2’s 32 qubits and precision control of the environment in the ion trap, Quantinuum researchers were able to achieve an entangled state of 32 qubits with a fidelity of 82.0(7)%, setting a new world record.

In addition to the system level tests, the Quantinuum hardware team ran these component benchmark tests:

• SPAM experiment
• Single-qubit gate randomized benchmarking
• Two-qubit gate randomized benchmarking
• Two-qubit SU gate randomized benchmarking RB
• Two-qubit parameterized gate randomized benchmarking
• Measurement/reset crosstalk benchmarking 
• Interleaved transport randomized benchmarking
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The paper includes results from those tests as well as results from these application benchmarks:

• Hamiltonian simulation
• Quantum Approximate Optimization Algorithm 
• Error correction: repetition code
• Holographic quantum dynamics simulation 

For more than two decades, there has been a general consensus among physicists pursuing the development of universal, fault-tolerant quantum computers that non-Abelian topological states would offer a promising path to success, if the states could ever be created.

These states host exotic quasi-particles—called anyons—that allow the storage of quantum information in their internal states which can only be changed by "braiding" them around each other in spacetime. Small perturbations in the trajectory of these braids would then leave the topology of the braid unchanged, making this paradigm inherently robust. It is as if they are ‘deaf’ to the noise of a system.

The problem however, is that non-Abelian anyons have never yet been detected, much less controlled. 

Until now.

Now, Quantinuum scientists, in collaboration with researchers from Harvard University and Caltech, have turned years of theory regarding topological states into reality, using the unique capabilities of the new H2 trapped-ion processor to create and control non-Abelian anyons. Using a shallow adaptive circuit on the H2, the research team prepared a non-Abelian quantum state on 27 qubits with a fidelity per site exceeding 98.4%.

This demonstration hinges on crucial advances in theory and experiment. On the theory side, Dr. Ruben Verresen, Prof. Ashvin Vishwanath (Harvard) and Dr. Nathanan Tantivasadakarn (Caltech) have shown how to use mid-circuit measurement to significantly simplify the route towards this kind of non-Abelian state. On the experimental side, the increased qubit capacity of the H2 system allows for sufficient complexity to create collective non-Abelian particles, while keeping the extremely low gate and mid-circuit measurement errors of previous generations.

The achievement has set the stage for an accelerated path to fault-tolerant quantum computing while also paving the way for new fields of research within condensed matter physics and high-energy physics.

The paper documenting the research, "Creation of Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor," is posted in Nature. This research was one of several papers published at the launch of H2, the next generation in Quantinuum's H-Series quantum computer, Powered by Honeywell.  

Advancing the Hardware Roadmap

Quantinuum has been advancing this area of research in “stealth mode” for some considerable time.  

Ilyas Khan, Quantinuum’s Chief Product Officer said "I recall vividly discussing topological quantum computing with Henrik 7 years ago during a long hot summer when devices such as our H2 processor were hard to even dream about. This research represents a milestone that benefits the industry as a whole and yet again demonstrates our ability to not only be world leaders today but also long into the future.”

"Topological order is our best shot at creating a quantum computer with very low error rates," Henrik said. "We need to be able to operate on the system while keeping it protected from the environment," he said. "Topological order can offer that protection. This research demonstrates that the more exotic kind of topological state, the non-Abelian kind, can be created with today's devices on-demand and with high fidelity. One of next steps will be to demonstrate stability by repetitive error-correction, utilizing the same ingredients used to prepare the state in the first place."

According to Tony Uttley, President and COO of Quantinuum, this advance represents a breakaway moment for Quantinuum.  

"We've reached a point with our technology that we can build a quantum computer on top of a quantum computer," Tony said. "These non-Abelian topological qubits can layer on top of physical qubits without changing how our quantum computer operates. That accomplishment will accelerate our work on the path to fault-tolerant quantum computing."