How we equip our users to unlock the full potential of H-Series Quantum Computers
Quantinuum is proud to introduce three new tools to help enterprise and academic users to make full use of the world-leading capabilities of the System Model H1 and H2 quantum computers
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 2nd 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.
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]
About Quantinuum
Quantinuum, the world’s largest integrated quantum company, pioneers powerful quantum computers and advanced software solutions. Quantinuum’s technology drives breakthroughs in materials discovery, cybersecurity, and next-gen quantum AI. With over 500 employees, including 370+ scientists and engineers, Quantinuum leads the quantum computing revolution across continents.
In a new paper in Nature Physics, we've made a major breakthrough in one of quantum computing’s most elusive promises: simulating the physics of superconductors. A deeper understanding of superconductivity would have an enormous impact: greater insight could pave the way to real-world advances, like phone batteries that last for months, “lossless” power grids that drastically reduce your bills, or MRI machines that are widely available and cheap to use. The development of room-temperature superconductors would transform the global economy.
A key promise of quantum computing is that it has a natural advantage when studying inherently quantum systems, like superconductors. In many ways, it is precisely the deeply ‘quantum’ nature of superconductivity that makes it both so transformative and so notoriously difficult to study.
Now, we are pleased to report that we just got a lot closer to that ultimate dream.
Making the impossible possible
To study something like a superconductor with a quantum computer, you need to first “encode” the elements of the system you want to study onto the qubits – in other words, you want to translate the essential features of your material onto the states and gates you will run on the computer.
For superconductors in particular, you want to encode the behavior of particles known as “fermions” (like the familiar electron). Naively simulating fermions using qubits will result in garbage data, because qubits alone lack the key properties that make a fermion so unique.
Until recently, scientists used something called the “Jordan-Wigner” encoding to properly map fermions onto qubits. People have argued that the Jordan-Wigner encoding is one of the main reasons fermionic simulations have not progressed beyond simple one-dimensional chain geometries: it requires too many gates as the system size grows.
Even worse, the Jordan-Wigner encoding has the nasty property that it is, in a sense, maximally non-fault-tolerant: one error occurring anywhere in the system affects the whole state, which generally leads to an exponential overhead in the number of shots required. Due to this, until now, simulating relevant systems at scale – one of the big promises of quantum computing – has remained a daunting challenge.
Theorists have addressed the issues of the Jordan-Wigner encoding and have suggested alternative fermionic encodings. In practice, however, the circuits created from these alternative encodings come with large overheads and have so far not been practically useful.
We are happy to report that our team developed a new way to compile one of the new, alternative, encodings that dramatically improves both efficiency and accuracy, overcoming the limitations of older approaches. Their new compilation scheme is the most efficient yet, slashing the cost of simulating fermionic hopping by an impressive 42%. On top of that, the team also introduced new, targeted error mitigation techniques that ensure even larger systems can be simulated with far fewer computational "shots"—a critical advantage in quantum computing.
Using their innovative methods, the team was able to simulate the Fermi-Hubbard model—a cornerstone of condensed matter physics— at a previously unattainable scale. By encoding 36 fermionic modes into 48 physical qubits on System Model H2, they achieved the largest quantum simulation of this model to date.
This marks an important milestone in quantum computing: it demonstrates that large-scale simulations of complex quantum systems, like superconductors, are now within reach.
Unlocking the Quantum Age, One Breakthrough at a Time
This breakthrough doesn’t just show how we can push the boundaries of what quantum computers can do; it brings one of the most exciting use cases of quantum computing much closer to reality. With this new approach, scientists can soon begin to simulate materials and systems that were once thought too complex for the most powerful classical computers alone. And in doing so, they’ve unlocked a path to potentially solving one of the most exciting and valuable problems in science and technology: understanding and harnessing the power of superconductivity.
The future of quantum computing—and with it, the future of energy, electronics, and beyond—just got a lot more exciting.
In an experiment led by Princeton and NIST, we’ve just delivered a crucial result in Quantum Error Correction (QEC), demonstrating key principles of scalable quantum computing developed by Drs Peter Shor, Dorit Aharonov, and Michael Ben-Or. In this latest paper, we showed that by using “concatenated codes” noise can be exponentially suppressed — proving that quantum computing will scale.
When noise is low enough, the results are transformative
Quantum computing is already producing results, but high-profile applications like Shor’s algorithm—which can break RSA encryption—require error rates about a billion times lower than what today’s machines can achieve.
Achieving such low error rates is a holy grail of quantum computing. Peter Shor was the first to hypothesize a way forward, in the form of quantum error correction. Building on his results, Dorit Aharanov and Michael Ben-Or proved that by concatenating quantum error correcting codes, a sufficiently high-quality quantum computer can suppress error rates arbitrarily at the cost of a very modest increase in the required number of qubits. Without that insight, building a truly fault-tolerant quantum computer would be impossible.
Their results, now widely referred to as the “threshold theorem”, laid the foundation for realizing fault-tolerant quantum computing. At the time, many doubted that the error rates required for large-scale quantum algorithms could ever be achieved in practice. The threshold theorem made clear that large scale quantum computing is a realistic possibility, giving birth to the robust quantum industry that exists today.
Realizing a legendary vision
Until now, nobody has realized the original vision for the threshold theorem. Last year, Google performed a beautiful demonstration of the threshold theorem in a different context (without concatenated codes). This year, we are proud to report the first experimental realization of that seminal work—demonstrating fault-tolerant quantum computing using concatenated codes, just as they envisioned.
The benefits of concatenation
The team demonstrated that their family of protocols achieves high error thresholds—making them easier to implement—while requiring minimal ancilla qubits, meaning lower overall qubit overhead. Remarkably, their protocols are so efficient that fault-tolerant preparation of basis states requires zero ancilla overhead, making the process maximally efficient.
This approach to error correction has the potential to significantly reduce qubit requirements across multiple areas, from state preparation to the broader QEC infrastructure. Additionally, concatenated codes offer greater design flexibility, which makes them especially attractive. Taken together, these advantages suggest that concatenation could provide a faster and more practical path to fault-tolerant quantum computing than popular approaches like the surface code.
We’re always looking forward
From a broader perspective, this achievement highlights the power of collaboration between industry, academia, and national laboratories. Quantinuum’s commercial quantum systems are so stable and reliable that our partners were able to carry out this groundbreaking research remotely—over the cloud—without needing detailed knowledge of the hardware. While we very much look forward to welcoming them to our labs before long, its notable that they never need to step inside to harness the full capabilities of our machines.
As we make quantum computing more accessible, the rate of innovation will only increase. The era of plug-and-play quantum computing has arrived. Are you ready?
Quantum computing companies are poised to exceed $1 billion in revenues by the close of 2025, according to McKinsey & Company, underscoring how today’s quantum computers are already delivering customer value in their current phase of development.
This figure is projected to reach upwards of $37 billion by 2030, rising in parallel with escalating demand, as well as with the scale of the machines and the complexity of problem sets of which they will be able to address.
Several systems on the market today are fault-tolerant by design, meaning they are capable of suppressing error-causing noise to yield reliable calculations. However, the full potential of quantum computing to tackle problems of true industrial relevance, in areas like medicine, energy, and finance, remains contingent on an architecture that supports a fully fault-tolerant universal gate set with repeatable error correction—a capability that, until now, has eluded the industry.
Quantinuum is the first—and only—company to achieve this critical technical breakthrough, universally recognized as the essential precursor to scalable, industrial-scale quantum computing. This milestone provides us with the most de-risked development roadmap in the industry and positions us to fulfill our promise to deliver our universal, fully fault-tolerant quantum computer, Apollo, by 2029.
In this regard, Quantinuum is the first company to step from the so-called “NISQ” (noisy intermediate-scale quantum) era towards utility-scale quantum computers.
Unpacking our achievement: first, a ‘full’ primer
A quantum computer uses operations called gates to process information in ways that even today’s fastest supercomputers cannot. The industry typically refers to two types of gates for quantum computers:
- Clifford gates, which can be easily simulated by classical computers, and are relatively easy to implement; and
- Non-Clifford gates, which are usually harder to implement, but are required to enable true quantum computation (when combined with their siblings).
A system that can run both gates is classified as universal and has the machinery to tackle the widest range of problems. Without non-Clifford gates, a quantum computer is non-universal and restricted to smaller, easier sets of tasks - and it can always be simulated by classical computers. This is like painting with a full palette of primary colors, versus only having one or two to work with. Simply put, a quantum computer that cannot implement ‘non-Clifford’ gates is not really a quantum computer.
A fault-tolerant, or error-corrected, quantum computer detects and corrects its own errors (or faults) to produce reliable results. Quantinuum has the best and brightest scientists dedicated to keeping our systems’ error rates the lowest in the world.
For a quantum computer to be fully fault-tolerant, every operation must be error-resilient, across Clifford gates and non-Clifford gates, and thus, performing “a full gate set” with error correction. While some groups have performed fully fault-tolerant gate sets in academic settings, these demonstrations were done with only a few qubits and error rates near 10%—too high for any practical use.
Today, we have published two papers that establishes Quantinuum as the first company to develop a complete solution for a universal fully fault-tolerant quantum computer with repeatable error correction, and error rates low enough for real-world applications.
This is where the magic happens
The first paper describes how scientists at Quantinuum used our System Model H1-1 to perfect magic state production, a crucial technique for achieving a fully fault-tolerant universal gate set. In doing so, they set a record magic state infidelity (7x10-5), 10x better than any previously published result.
Our simulations show that our system could reach a magic state infidelity of 10^-10, or about one error per 10 billion operations, on a larger-scale computer with our current physical error rate. We anticipate reaching 10^-14, or about one error per 100 trillion operations, as we continue to advance our hardware. This means that our roadmap is now derisked.
Setting a record magic state infidelity was just the beginning. The paper also presents the first break-even two-qubit non-Clifford gate, demonstrating a logical error rate below the physical one. In doing so, the team set another record for two-qubit non-Clifford gate infidelity (2x10-4, almost 10x better than our physical error rate). Putting everything together, the team ran the first circuit that used a fully fault-tolerant universal gate set, a critical moment for our industry.
Flipping the switch
In the second paper, co-authored with researchers at the University of California at Davis, we demonstrated an important technique for universal fault-tolerance called “code switching”.
Code switching describes switching between different error correcting codes. The team then used the technique to demonstrate the key ingredients for universal computation, this time using a code where we’ve previously demonstrated full error correction and the other ingredients for universality.
In the process, the team set a new record for magic states in a distance-3 error correcting code, over 10x better than the best previous attempt with error correction. Notably, this process only cost 28 qubits instead of hundreds. This completes, for the first time, the ingredient list for a universal gate setin a system that also has real-time and repeatable QEC.
Fully equipped for fault-tolerance
Innovations like those described in these two papers can reduce estimates for qubit requirements by an order of magnitude, or more, bringing powerful quantum applications within reach far sooner.
With all of the required pieces now, finally, in place, we are ‘fully’ equipped to become the first company to perform universal fully fault-tolerant computing—just in time for the arrival of Helios, our next generation system launching this year, and what is very likely to remain as the most powerful quantum computer on the market until the launch of its successor, Sol, arriving in 2027.