Quantinuum’s H-Series hits 56 physical qubits that are all-to-all connected, and departs the era of classical simulation
The first half of 2024 will go down as the period when we shed the last vestiges of the “wait and see” culture that has dominated the quantum computing industry. Thanks to a run of recent achievements, we have helped to lead the entire quantum computing industry into a new, post-classical era.
Today we are announcing the latest of these achievements: a major qubit count enhancement to our flagship System Model H2 quantum computer from 32 to 56 qubits. We also reveal meaningful results of work with our partner JPMorgan Chase & Co. that showcases a significant lift in performance.
But to understand the full importance of today’s announcements, it is worth recapping the succession of breakthroughs that confirm that we are entering a new era of quantum computing in which classical simulation will be infeasible.
A historic run
Between January and June 2024, Quantinuum’s pioneering teams published a succession of results that accelerate our path to universal fault-tolerant quantum computing.
Our technical teams first presented a long-sought solution to the “wiring problem”, an engineering challenge that affects all types of quantum computers. In short, most current designs will require an impossible number of wires connected to the quantum processor to scale to large qubit numbers. Our solution allows us to scale to high qubit numbers with no issues, proving that our QCCD architecture has the potential to scale.
Next, we became the first quantum computing company in the world to hit “three 9s” two qubit gate fidelity across all qubit pairs in a production device. This level of fidelity in 2-qubit gate operations was long thought to herald the point at which error corrected quantum computing could become a reality. It has accelerated and intensified our focus on quantum error correction (QEC). Our scientists and engineers are working with our customers and partners to achieve multiple breakthroughs in QEC in the coming months, many of which will be incorporated into products such as the H-Series and our chemistry simulation platform, InQuanto™.
Following that, with our long-time partner Microsoft, we hit an error correction performance threshold that many believed was still years away. The System Model H2 became the first – and only – quantum computer in the world capable of creating and computing with highly reliable logical (error corrected) qubits. In this demonstration, the H2-1 configured with 32 physical qubits supported the creation of four highly reliable logical qubits operating at “better than break-even”. In the same demonstration, we also shared that logical circuit error rates were shown to be up to 800x lower than the corresponding physical circuit error rates. No other quantum computing company is even close to matching this achievement (despite many feverish claims in the past 12 months).
Pushing to the limits of supercomputing … and beyond
The quantum computing industry is departing the era when quantum computers could be simulated by a classical computer. Today, we are making two milestone announcements. The first is that our H2-1 processor has been upgraded to 56 trapped-ion qubits, making it impossible to classically simulate, without any loss of the market-leading fidelity, all-to-all qubit connectivity, mid-circuit measurement, qubit reuse, and feed forward.
The second is that the upgrade of H2-1 from 32 to 56 qubits makes our processor capable of challenging the world’s most powerful supercomputers. This demonstration was achieved in partnership with our long-term collaborator JPMorgan Chase & Co. and researchers from Caltech and Argonne National Lab.
Our collaboration tackled a well-known algorithm, Random Circuit Sampling (RCS), and measured the quality of our results with a suite of tests including the linear cross entropy benchmark (XEB) – an approach first made famous by Google in 2019 in a bid to demonstrate “quantum supremacy”. An XEB score close to 0 says your results are noisy – and do not utilize the full potential of quantum computing. In contrast, the closer an XEB score is to 1, the more your results demonstrate the power of quantum computing. The results on H2-1 are excellent, revealing, and worth exploring in a little detail. Here is the complete data on GitHub.
Better qubits, better results
Our results show how far quantum hardware has come since Google’s initial demonstration. They originally ran circuits on 53 superconducting qubits that were deep enough to severely frustrate high-fidelity classical simulation at the time, achieving an estimated XEB score of ~0.002. While they showed that this small value was statistically inconsistent with zero, improvements in classical algorithms and hardware have steadily increased what XEB scores are achievable by classical computers, to the point that classical computers can now achieve scores similar to Google’s on their original circuits.
In contrast, we have been able to run circuits on all 56 qubits in H2-1 that are deep enough to challenge high-fidelity classical simulation while achieving an estimated XEB score of ~0.35. This >100x improvement implies the following: even for circuits large and complex enough to frustrate all known classical simulation methods, the H2 quantum computer produces results without making even a single error about 35% of the time. In contrast to past announcements associated with XEB experiments, 35% is a significant step towards the idealized 100% fidelity limit in which the computational advantage of quantum computers is clearly in sight.
This huge jump in quality is made possible by Quantinuum’s market-leading high fidelity and also our unique all-to-all connectivity. Our flexible connectivity, enabled by our QCCD architecture, enables us to implement circuits with much more complex geometries than the 2D geometries supported by superconducting-based quantum computers. This specific advantage means our quantum circuits become difficult to simulate classically with significantly fewer operations (or gates). These capabilities have an enormous impact on how our computational power scales as we add more qubits: since noisy quantum computers can only run a limited number of gates before returning unusable results, needing to run fewer gates ultimately translates into solving complex tasks with consistent and dependable accuracy.
This is a vitally important moment for companies and governments watching this space and deciding when to invest in quantum: these results underscore both the performance capabilities and the rapid rate of improvement of our processors, especially the System Model H2, as a prime candidate for achieving near-term value.
So what of the comparison between the H2-1 results and a classical supercomputer?
A direct comparison can be made between the time it took H2-1 to perform RCS and the time it took a classical supercomputer. However, classical simulations of RCS can be made faster by building a larger supercomputer (or by distributing the workload across many existing supercomputers). A more robust comparison is to consider the amount of energy that must be expended to perform RCS on either H2-1 or on classical computing hardware, which ultimately controls the real cost of performing RCS. An analysis based on the most efficient known classical algorithm for RCS and the power consumption of leading supercomputers indicates that H2-1 can perform RCS at 56 qubits with an estimated 30,000x reduction in power consumption. These early results should be seen as very attractive for data center owners and supercomputing facilities looking to add quantum computers as “accelerators” for their users.
Where we go next
Today’s milestone announcements are clear evidence that the H2-1 quantum processor can perform computational tasks with far greater efficiency than classical computers. They underpin the expectation that as our quantum computers scale beyond today’s 56 qubits to hundreds, thousands, and eventually millions of high-quality qubits, classical supercomputers will quickly fall behind. Quantinuum’s quantum computers are likely to become the device of choice as scrutiny continues to grow of the power consumption of classical computers applied to highly intensive workloads such as simulating molecules and material structures – tasks that are widely expected to be amenable to a speedup using quantum computers.
With this upgrade in our qubit count to 56, we will no longer be offering a commercial “fully encompassing” emulator – a mathematically exact simulation of our H2-1 quantum processor is now impossible, as it would take up the entire memory of the world’s best supercomputers. With 56 qubits, the only way to get exact results is to run on the actual hardware, a trend the leaders in this field have already embraced.
More generally, this work demonstrates that connectivity, fidelity, and speed are all interconnected when measuring the power of a quantum computer. Our competitive edge will persist in the long run; as we move to running more algorithms at the logical level, connectivity and fidelity will continue to play a crucial role in performance.
“We are entirely focused on the path to universal fault tolerant quantum computers. This objective has not changed, but what has changed in the past few months is clear evidence of the advances that have been made possible due to the work and the investment that has been made over many, many years. These results show that whilst the full benefits of fault tolerant quantum computers have not changed in nature, they may be reachable earlier than was originally expected, and crucially, that along the way, there will be tangible benefits to our customers in their day-to-day operations as quantum computers start to perform in ways that are not classically simulatable. We have an exciting few months ahead of us as we unveil some of the applications that will start to matter in this context with our partners across a number of sectors.”
– Ilyas Khan, Chief Product Officer
Stay tuned for results in error correction, physics, chemistry and more on our new 56-qubit processor.
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.
From September 16th – 18th, Quantum World Congress (QWC) will bring together visionaries, policymakers, researchers, investors, and students from across the globe to discuss the future of quantum computing in Tysons, Virginia.
Quantinuum is forging the path to universal, fully fault-tolerant quantum computing with our integrated full-stack. Join our quantum experts for the below sessions and at Booth #27 to discuss the latest on Quantinuum Systems, the world’s highest-performing, commercially available quantum computers, our new software stack featuring the key additions of Guppy and Selene, our path to error correction, and more.
Wednesday, September 17th
Keynote with Quantinuum's CEO, Dr. Rajeeb Hazra
9:00 – 9:20am ET | Main Stage
At QWC 2024, Quantinuum’s President & CEO, Dr. Rajeeb “Raj” Hazra, took the stage to showcase our commitment to advancing quantum technologies through the unveiling of our roadmap to universal, fully fault-tolerant quantum computing by the end of this decade. This year at QWC 2025, join Raj on the main stage to discover the progress we’ve made over the last year in advancing quantum computing on both commercial and technical fronts and be the first to hear exciting insights on what’s to come from Quantinuum.
Panel Session: Policy Priorities for Responsible Quantum and AI
1:00 – 1:30pm ET | Maplewood Hall
As part of the Track Sessions on Government & Security, Quantinuum’s Director of Government Relations, Ryan McKenney, will discuss “Policy Priorities for Responsible Quantum and AI” with Jim Cook from Actions to Impact Strategies and Paul Stimers from Quantum Industry Coalition.
Fireside Chat: Establishing a Pro-Innovation Regulatory Framework
4:00 – 4:30pm ET | Vault Theater
During the Track Session on Industry Advancement, Quantinuum’s Chief Legal Officer, Kaniah Konkoly-Thege, and Director of Government Relations, Ryan McKenney, will take the stage to discuss the importance of “Establishing a Pro-Innovation Regulatory Framework”.
In the world of physics, ideas can lie dormant for decades before revealing their true power. What begins as a quiet paper in an academic journal can eventually reshape our understanding of the universe itself.
In 1993, nestled deep in the halls of Yale University, physicist Subir Sachdev and his graduate student Jinwu Ye stumbled upon such an idea. Their work, originally aimed at unraveling the mysteries of “spin fluids”, would go on to ignite one of the most surprising and profound connections in modern physics—a bridge between the strange behavior of quantum materials and the warped spacetime of black holes.
Two decades after the paper was published, it would be pulled into the orbit of a radically different domain: quantum gravity. Thanks to work by renowned physicist Alexei Kitaev in 2015, the model found new life as a testing ground for the mind-bending theory of holography—the idea that the universe we live in might be a projection, from a lower-dimensional reality.
Holography is an exotic approach to understanding reality where scientists use holograms to describe higher dimensional systems in one less dimension. So, if our world is 3+1 dimensional (3 spatial directions plus time), there exists a 2+1, or 3-dimensional description of it. In the words of Leonard Susskind, a pioneer in quantum holography, "the three-dimensional world of ordinary experience—the universe filled with galaxies, stars, planets, houses, boulders, and people—is a hologram, an image of reality coded on a distant two-dimensional surface."
The “SYK” model, as it is known today, is now considered a quintessential framework for studying strongly correlated quantum phenomena, which occur in everything from superconductors to strange metals—and even in black holes. In fact, The SYK model has also been used to study one of physics’ true final frontiers, quantum gravity, with the authors of the paper calling it “a paradigmatic model for quantum gravity in the lab.”
The SYK model involves Majorana fermions, a type of particle that is its own antiparticle. A key feature of the model is that these fermions are all-to-all connected, leading to strong correlations. This connectivity makes the model particularly challenging to simulate on classical computers, where such correlations are difficult to capture. Our quantum computers, however, natively support all-to-all connectivity making them a natural fit for studying the SYK model.
Now, 10 years after Kitaev’s watershed lectures, we’ve made new progress in studying the SYK model. In a new paper, we’ve completed the largest ever SYK study on a quantum computer. By exploiting our system’s native high fidelity and all-to-all connectivity, as well as our scientific team’s deep expertise across many disciplines, we were able to study the SYK model at a scale three times larger than the previous best experimental attempt.
While this work does not exceed classical techniques, it is very close to the classical state-of-the-art. The biggest ever classical study was done on 64 fermions, while our recent result, run on our smallest processor (System Model H1), included 24 fermions. Modelling 24 fermions costs us only 12 qubits (plus one ancilla) making it clear that we can quickly scale these studies: our System Model H2 supports 56 qubits (or ~100 fermions), and Helios, which is coming online this year, will have over 90 qubits (or ~180 fermions).
However, working with the SYK model takes more than just qubits. The SYK model has a complex Hamiltonian that is difficult to work with when encoded on a computer—quantum or classical. Studying the real-time dynamics of the SYK model means first representing the initial state on the qubits, then evolving it properly in time according to an intricate set of rules that determine the outcome. This means deep circuits (many circuit operations), which demand very high fidelity, or else an error will occur before the computation finishes.
Our cross-disciplinary team worked to ensure that we could pull off such a large simulation on a relatively small quantum processor, laying the groundwork for quantum advantage in this field.
First, the team adopted a randomized quantum algorithm called TETRIS to run the simulation. By using random sampling, among other methods, the TETRIS algorithm allows one to compute the time evolution of a system without the pernicious discretization errors or sizable overheads that plague other approaches. TETRIS is particularly suited to simulating the SYK model because with a high level of disorder in the material, simulating the SYK Hamiltonian means averaging over many random Hamiltonians. With TETRIS, one generates random circuits to compute evolution (even with a deterministic Hamiltonian). Therefore, when applying TETRIS on SYK, for every shot one can just generate a random instance of the Hamiltonain, and generate a random circuit on TETRIS at the same time. This simple approach enables less gate counts required per shot, meaning users can run more shots, naturally mitigating noise.
In addition, the team “sparsified” the SYK model, which means “pruning” the fermion interactions to reduce the complexity while still maintaining its crucial features. By combining sparsification and the TETRIS algorithm, the team was able to significantly reduce the circuit complexity, allowing it to be run on our machine with high fidelity.
They didn’t stop there. The team also proposed two new noise mitigation techniques, ensuring that they could run circuits deep enough without devolving entirely into noise. The two techniques both worked quite well, and the team was able to show that their algorithm, combined with the noise mitigation, performed significantly better and delivered more accurate results. The perfect agreement between the circuit results and the true theoretical results is a remarkable feat coming from a co-design effort between algorithms and hardware.
As we scale to larger systems, we come closer than ever to realizing quantum gravity in the lab, and thus, answering some of science’s biggest questions.
At Quantinuum, we pay attention to every detail. From quantum gates to teleportation, we work hard every day to ensure our quantum computers operate as effectively as possible. This means not only building the most advanced hardware and software, but that we constantly innovate new ways to make the most of our systems.
A key step in any computation is preparing the initial state of the qubits. Like lining up dominoes, you first need a special setup to get meaningful results. This process, known as state preparation or “state prep,” is an open field of research that can mean the difference between realizing the next breakthrough or falling short. Done ineffectively, state prep can carry steep computational costs, scaling exponentially with the qubit number.
Recently, our algorithm teams have been tackling this challenge from all angles. We’ve published three new papers on state prep, covering state prep for chemistry, materials, and fault tolerance.
In the first paper, our team tackled the issue of preparing states for quantum chemistry. Representing chemical systems on gate-based quantum computers is a tricky task; partly because you often want to prepare multiconfigurational states, which are very complex. Preparing states like this can cost a lot of resources, so our team worked to ensure we can do it without breaking the (quantum) bank.
To do this, our team investigated two different state prep methods. The first method uses Givens rotations, implemented to save computational costs. The second method exploits the sparsity of the molecular wavefunction to maximize efficiency.
Once the team perfected the two methods, they implemented them in InQuanto to explore the benefits across a range of applications, including calculating the ground and excited states of a strongly correlated molecule (twisted C_2 H_4). The results showed that the “sparse state preparation” scheme performed especially well, requiring fewer gates and shorter runtimes than alternative methods.
In the second paper, our team focused on state prep for materials simulation. Generally, it’s much easier for computers to simulate materials that are at zero temperature, which is, obviously, unrealistic. Much more relevant to most scientists is what happens when a material is not at zero temperature. In this case, you have two options: when the material is steadily at a given temperature, which scientists call thermal equilibrium, or when the material is going through some change, also known as out of equilibrium. Both are much harder for classical computers to work with.
In this paper, our team looked to solve an outstanding problem: there is no standard protocol for preparing thermal states. In this work, our team only targeted equilibrium states but, interestingly, they used an out of equilibrium protocol to do the work. By slowly and gently evolving from a simple state that we know how to prepare, they were able to prepare the desired thermal states in a way that was remarkably insensitive to noise.
Ultimately, this work could prove crucial for studying materials like superconductors. After all, no practical superconductor will ever be used at zero temperature. In fact, we want to use them at room temperature – and approaches like this are what will allow us to perform the necessary studies to one day get us there.
Finally, as we advance toward the fault-tolerant era, we encounter a new set of challenges: making computations fault-tolerant at every step can be an expensive venture, eating up qubits and gates. In the third paper, our team made fault-tolerant state preparation—the critical first step in any fault-tolerant algorithm—roughly twice as efficient. With our new “flag at origin” technique, gate counts are significantly reduced, bringing fault-tolerant computation closer to an everyday reality.
The method our researchers developed is highly modular: in the past, to perform optimized state prep like this, developers needed to solve one big expensive optimization problem. In this new work, we’ve figured out how to break the problem up into smaller pieces, in the sense that one now needs to solve a set of much smaller problems. This means that now, for the first time, developers can prepare fault-tolerant states for much larger error correction codes, a crucial step forward in the early-fault-tolerant era.
On top of this, our new method is highly general: it applies to almost any QEC code one can imagine. Normally, fault-tolerant state prep techniques must be anchored to a single code (or a family of codes), making it so that when you want to use a different code, you need a new state prep method. Now, thanks to our team’s work, developers have a single, general-purpose, fault-tolerant state prep method that can be widely applied and ported between different error correction codes. Like the modularity, this is a huge advance for the whole ecosystem—and is quite timely given our recent advances into true fault-tolerance.
This generality isn’t just applicable to different codes, it’s also applicable to the states that you are preparing: while other methods are optimized for preparing only the |0> state, this method is useful for a wide variety of states that are needed to set up a fault tolerant computation. This “state diversity” is especially valuable when working with the best codes – codes that give you many logical qubits per physical qubit. This new approach to fault-tolerant state prep will likely be the method used for fault-tolerant computations across the industry, and if not, it will inform new approaches moving forward.
From the initial state preparation to the final readout, we are ensuring that not only is our hardware the best, but that every single operation is as close to perfect as we can get it.