Quantum Volume reaches 5 digits for the first time
5 perspectives on what it means for quantum computing
Quantinuum’s H-Series team has hit the ground running in 2023, achieving a new performance milestone. The H1-1 trapped ion quantum computer has achieved a Quantum Volume (QV) of 32,768 (215), the highest in the industry to date.
The team previously increased the QV to 8,192 (or 213) for the System Model H1 system in September, less than six months ago. The next goal was a QV of 16,384 (214). However, continuous improvements to the H1-1's controls and subsystems advanced the system enough to successfully reach 214 as expected, and then to go one major step further, and reach a QV of 215.
The Quantum Volume test is a full-system benchmark that produces a single-number measure of a quantum computer’s general capability. The benchmark takes into account qubit number, fidelity, connectivity, and other quantities important in building useful devices.1 While other measures such as gate fidelity and qubit count are significant and worth tracking, neither is as comprehensive as Quantum Volume which better represents the operational ability of a quantum computer.
Dr. Brian Neyenhuis, Director of Commercial Operations, credits reductions in the phase noise of the computer’s lasers as one key factor in the increase.
"We've had enough qubits for a while, but we've been continually pushing on reducing the error in our quantum operations, specifically the two-qubit gate error, to allow us to do these Quantum Volume measurements,” he said.
The Quantinuum team improved memory error and elements of the calibration process as well.
“It was a lot of little things that got us to the point where our two-qubit gate error and our memory error are both low enough that we can pass these Quantum Volume circuit tests,” he said.
The work of increasing Quantum Volume means improving all the subsystems and subcomponents of the machine individually and simultaneously, while ensuring all the systems continue to work well together. Such a complex task takes a high degree of orchestration across the Quantinuum team, with the benefits of the work passed on to H-Series users.
To illustrate what this 5-digit Quantum Volume milestone means for the H-Series, here are 5 perspectives that reflect Quantinuum teams and H-Series users.
Perspective #1: How a higher QV impacts algorithms
Dr. Henrik Dreyer is Managing Director and Scientific Lead at Quantinuum’s office in Munich, Germany. In the context of his work, an improvement in Quantum Volume is important as it relates to gate fidelity.
“As application developers, the signal-to-noise ratio is what we're interested in,” Henrik said. “If the signal is small, I might run the circuits 10 times and only get one good shot. To recover the signal, I have to do a lot more shots and throw most of them away. Every shot takes time."
“The signal-to-noise ratio is sensitive to the gate fidelity. If you increase the gate fidelity by a little bit, the runtime of a given algorithm may go down drastically,” he said. “For a typical circuit, as the plot shows, even a relatively modest 0.16 percentage point improvement in fidelity, could mean that it runs in less than half the time.”
To demonstrate this point, the Quantinuum team has been benchmarking the System Model H1 performance on circuits relevant for near-term applications. The graph below shows repeated benchmarking of the runtime of these circuits before and after the recent improvement in gate fidelity. The result of this moderate change in fidelity is a 3x change in runtime. The runtimes calculated below are based on the number of shots required to obtain accurate results from the benchmarking circuit – the example uses 430 arbitrary-angle two-qubit gates and an accuracy of 3%.
Perspective #2: Advancing quantum error correction
Dr. Natalie Brown and Dr, Ciaran Ryan-Anderson both work on quantum error correction at Quantinuum. They see the QV advance as an overall boost to this work.
“Hitting a Quantum Volume number like this means that you have low error rates, a lot of qubits, and very long circuits,” Natalie said. “And all three of those are wonderful things for quantum error correction. A higher Quantum Volume most certainly means we will be able to run quantum error correction better. Error correction is a critical ingredient to large-scale quantum computing. The earlier we can start exploring error correction on today’s small-scale hardware, the faster we’ll be able to demonstrate it at large-scale.”
Ciaran said that H1-1's low error rates allow scientists to make error correction better and start to explore decoding options.
“If you can have really low error rates, you can apply a lot of quantum operations, known as gates,” Ciaran said. "This makes quantum error correction easier because we can suppress the noise even further and potentially use fewer resources to do it, compared to other devices.”
Perspective #3: Meeting a high benchmark
“This accomplishment shows that gate improvements are getting translated to full-system circuits,” said Dr. Charlie Baldwin, a research scientist at Quantinuum.
Charlie specializes in quantum computing performance benchmarks, conducting research with the Quantum Economic Development Consortium (QED-C).
“Other benchmarking tests use easier circuits or incorporate other options like post-processing data. This can make it more difficult to determine what part improved,” he said. “With Quantum Volume, it’s clear that the performance improvements are from the hardware, which are the hardest and most significant improvements to make.”
“Quantum Volume is a well-established test. You really can’t cheat it,” said Charlie.
Perspective #4: Implications for quantum applications
Dr. Ross Duncan, Head of Quantum Software, sees Quantum Volume measurements as a good way to show overall progress in the process of building a quantum computer.
“Quantum Volume has merit, compared to any other measure, because it gives a clear answer,” he said.
“This latest increase reveals the extent of combined improvements in the hardware in recent months and means researchers and developers can expect to run deeper circuits with greater success.”
Perspective #5: H-Series users
Quantinuum’s business model is unique in that the H-Series systems are continuously upgraded through their product lifecycle. For users, this means they continually and immediately get access to the latest breakthroughs in performance. The reported improvements were not done on an internal testbed, but rather implemented on the H1-1 system which is commercially available and used extensively by users around the world.
“As soon as the improvements were implemented, users were benefiting from them,” said Dr. Jenni Strabley, Sr. Director of Offering Management. “We take our Quantum Volume measurement intermixed with customers’ jobs, so we know that the improvements we’re seeing are also being seen by our customers.”
Jenni went on to say, “Continuously delivering increasingly better performance shows our commitment to our customers’ success with these early small-scale quantum computers as well as our commitment to accuracy and transparency. That’s how we accelerate quantum computing.”
Supporting data from Quantinuum’s 215 QV milestone
This latest QV milestone demonstrates how the Quantinuum team continues to boost the performance of the System Model H1, making improvements to the two-qubit gate fidelity while maintaining high single-qubit fidelity, high SPAM fidelity, and low cross-talk.
The average single-qubit gate fidelity for these milestones was 99.9955(8)%, the average two-qubit gate fidelity was 99.795(7)% with fully connected qubits, and state preparation and measurement fidelity was 99.69(4)%.
For both tests, the Quantinuum team ran 100 circuits with 200 shots each, using standard QV optimization techniques to yield an average of 219.02 arbitrary angle two-qubit gates per circuit on the 214 test, and 244.26 arbitrary angle two-qubit gates per circuit on the 215 test.
The Quantinuum H1-1 successfully passed the quantum volume 16,384 benchmark, outputting heavy outcomes 69.88% of the time, and passed the 32,768 benchmark, outputting heavy outcomes 69.075% of the time. The heavy output frequency is a simple measure of how well the measured outputs from the quantum computer match the results from an ideal simulation. Both results are above the two-thirds passing threshold with high confidence. More details on the Quantum Volume test can be found here.
Heavy output frequency for H1-1 at 215 (QV 32,768)
Heavy output frequency for H1-1 at 214 (QV 16,384)
Quantum Volume data and analysis code can be accessed on Quantinuum’s GitHub repository for quantum volume data. Contemporary benchmarking data can be accessed at Quantinuum’s GitHub repository for hardware specifications.
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 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.
If we are to create ‘next-gen’ AI that takes full advantage of the power of quantum computers, we need to start with quantum native transformers. Today we announce yet again that Quantinuum continues to lead by demonstrating concrete progress — advancing from theoretical models to real quantum deployment.
The future of AI won't be built on yesterday’s tech. If we're serious about creating next-generation AI that unlocks the full promise of quantum computing, then we must build quantum-native models—designed for quantum, from the ground up.
Around this time last year, we introduced Quixer, a state-of-the-art quantum-native transformer. Today, we’re thrilled to announce a major milestone: one year on, Quixer is now running natively on quantum hardware.
Why this matters: Quantum AI, born native
This marks a turning point for the industry: realizing quantum-native AI opens a world of possibilities.
Classical transformers revolutionized AI. They power everything from ChatGPT to real-time translation, computer vision, drug discovery, and algorithmic trading. Now, Quixer sets the stage for a similar leap — but for quantum-native computation. Because quantum computers differ fundamentally from classical computers, we expect a whole new host of valuable applications to emerge.
Achieving that future requires models that are efficient, scalable, and actually run on today’s quantum hardware.
That’s what we’ve built.
What makes Quixer different?
Until Quixer, quantum transformers were the result of a brute force “copy-paste” approach: taking the math from a classical model and putting it onto a quantum circuit. However, this approach does not account for the considerable differences between quantum and classical architectures, leading to substantial resource requirements.
Quixer is different: it’s not a translation – it's an innovation.
With Quixer, our team introduced an explicitly quantum transformer, built from the ground up using quantum algorithmic primitives. Because Quixer is tailored for quantum circuits, it's more resource efficient than most competing approaches.
As quantum computing advances toward fault tolerance, Quixer is built to scale with it.
What’s next for Quixer?
We’ve already deployed Quixer on real-world data: genomic sequence analysis, a high-impact classification task in biotech. We're happy to report that its performance is already approaching that of classical models, even in this first implementation.
This is just the beginning.
Looking ahead, we’ll explore using Quixer anywhere classical transformers have proven to be useful; such as language modeling, image classification, quantum chemistry, and beyond. More excitingly, we expect use cases to emerge that are quantum-specific, impossible on classical hardware.
This milestone isn’t just about one model. It’s a signal that the quantum AI era has begun, and that Quantinuum is leading the charge with real results, not empty hype.
Stay tuned. The revolution is only getting started.