Debunking algorithmic qubits
Executive Summary: Quantinuum’s H-Series computers have the highest performance in the industry, verified by multiple widely adopted benchmarks including quantum volume We demonstrate that an alternative benchmark called algorithmic qubits is deeply flawed, hiding computer performance behind a plurality voting trick and gate compilations that are not widely useful.
Recently a new benchmark called algorithmic qubits (AQ) has started to be confused with quantum volume measurements. Quantum volume (QV) was specifically designed to be hard to “game,” however the algorithmic qubits test turns out to be very susceptible to tricks that can make a quantum computer look much better than it actually is. While it is not clear what can be done to fix the algorithmic qubits test, it is already clear that it is much easier to pass than QV and is a poor substitute for measuring performance. It is also important to note that algorithmic qubits are not the same as logical qubits, which are necessary for full fault-tolerant quantum computing.
To make this point clear, we simulated what algorithmic qubits data would look like for two machines, one clearly much higher performing than the other. We applied two tricks that are typically used when sharing algorithmic qubits results: gate compilation and error mitigation with plurality voting. From the data above, you can see how these tricks are misleading without further information. For example, if you compare data from the higher fidelity machine without any compilation or plurality voting (bottom left) to data from the inferior machine with both tricks (top right) you may incorrectly believe the inferior machine is performing better. Unfortunately, this inaccurate and misleading comparison has been made in the past. It is important to note that algorithmic qubits uses a subset of algorithms from a QED-C paper that introduced a suite of application oriented tests and created a repository to test available quantum computers. Importantly, that work explicitly forbids the compilation and error mitigation techniques that are causing the issue here.
As a demonstration of the perils of AQ as a benchmark, we look at data obtained on both Quantinuum’s H2-1 system as well as publicly available data from IonQ’s Forte system.
We reproduce data without any error mitigation from IonQ’s publicly released data in association with a preprint posted to the arXiv, and compare it to data taken on our H2-1 device. Without error mitigation, IonQ Forte achieves an AQ score of 9, whereas Quantinuum H2-1 achieves AQ of 26. Here you can clearly see improved circuit fidelities on the H2-1 device, as one would expect from the higher reported 2Q gate fidelities (average 99.816(5)% for Quantinuum’s H2-1 vs 99.35% for IonQ’s Forte). However, after you apply error mitigation, in this case plurality voting, to both sets of data the picture changes substantially, hiding each underlying computer’s true capabilities.
Here the H2-1 algorithmic performance still exceeds Forte (from the publicly released data), but the perceived gap has been reduced by error mitigation.
“Error mitigation, including plurality voting, may be a useful tool for some near-term quantum computing but it doesn’t work for every problem and it’s unlikely to be scalable to larger systems. In order to achieve the lofty goals of quantum computing we’ll need serious device performance upgrades. If we allow error mitigation in benchmarking it will conflate the error mitigation with the underlying device performance. This will make it hard for users to appreciate actual device improvements that translate to all applications and larger problems,” explained Dr. Charlie Baldwin, a leader in Quantinuum’s benchmarking efforts.
There are other issues with the algorithmic qubits test. The circuits used in the test can be reduced to very easy-to-run circuits with basic quantum circuit compilation that are freely available in packages like pytket. For example, the largest phase estimation and amplitude estimation tests required to pass AQ=32 are specified with 992 and 868 entangling gates respectively but applying pytket optimization reduces the circuits to 141 and 72 entangling gates. This is only possible due to choices in constructing the benchmarks and will not be universally available when using the algorithms in applications. Since AQ reports the precompiled gate counts this also may lead users to expect a machine to be able to run many more entangling gates than what is actually possible on the benchmarked hardware.
What makes a good quantum benchmark? Quantum benchmarking is extremely useful in charting the hardware progress and providing roadmaps for future development. However, quantum benchmarking is an evolving field that is still an open area of research. At Quantinuum we believe in testing the limits of our machine with a variety of different benchmarks to learn as much as possible about the errors present in our system and how they affect different circuits. We are open to working with the larger community on refining benchmarks and creating new ones as the field evolves.
To learn more about the Algorithmic Qubits benchmark and the issues with it, please watch this video where Dr. Charlie Baldwin walks us through the details, starting at 32:40.
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.
Quantinuum is pleased to announce that applications are now open for the Quantinuum SG Grand Challenge 2026, a global innovation challenge designed to bring together researchers, developers, scientists and innovators to explore practical applications of quantum computing.
Organized by Quantinuum and supported by Singapore's National Quantum Office and Aqora, the three-month program aims to foster collaboration across academia, industry and the quantum developer community while supporting the continued growth of Singapore's quantum ecosystem.
A Platform for Quantum Computing Innovation
Participants will work in teams to develop solutions across a range of challenge areas, including chemistry and molecular simulation, optimization, AI for quantum systems, quantum error correction, condensed matter and materials science, and open innovation. Throughout the program, participants will have access to mentoring, technical enablement and Quantinuum quantum computing resources.
Singapore Grand Finale
Selected finalist teams will be invited to present their work at the Grand Finale hosted in Singapore before representatives from academia, and industry. The event will celebrate innovative applications of quantum computing while providing an opportunity for participants to engage with Singapore's growing quantum community.
Join the Challenge
The Quantinuum SG Grand Challenge welcomes participants from around the world. Whether you are an experienced quantum researcher or beginning your quantum computing journey, the program offers an opportunity to collaborate, learn and contribute to the development of practical quantum applications.
Applications are now open. Spaces are limited and subject to review and approval.
- Researchers from Quantinuum, Caltech, the University of Chicago, and Harvard created a rare topologically ordered state of matter on Quantinuum's System Model H2 and used it to perform protected universal quantum gates with non-Abelian anyons.
- The work explores an alternative approach to fault tolerance by using topological properties to protect quantum information. This could reduce the need for magic state distillation, which can (in some circumstances) be resource-intensive.
- Quantinuum continues to show leadership in fault tolerance, with successful demonstrations spanning world record error rates to exotic approaches like topological computing
Quantum computing is all about putting the exotic properties of physics to work. Qubits can exist in two states at once, like the famous cat that is both alive and dead. Qubits can also be entangled, where the state of one will instantaneously affect the state of another - even when they have no way to “talk” to each other. Qubits can even be teleported, moving a quantum state from one place to another without physically moving it through space.
These features give quantum computing its power. But the ‘spooky’ nature of quantum computing doesn’t stop there: our quantum computers are potent enough to make exotic states of matter out of our qubits, and to perform calculations that would warp the mind of more traditional thinkers.
A new approach
In a recent paper published in Nature, researchers at Quantinuum teamed up with Caltech, the University of Chicago, and Harvard to create a rare ‘topologically ordered’ state of matter from our qubits.
When the qubits become ‘topologically ordered’, they become more than individual particles, now ‘related’ to each other in a specific way. This is like how hydrogen and oxygen act as individual gas particles alone, but you can put them together in a certain way so that they become water, a liquid, and an entirely different creature.
When the qubits become topologically ordered, the quantum information that they carried individually gets spread out over the whole system, which acts as a sort of protection from noise. This is like how a net makes a stronger barrier than a bunch of un-knotted ropes.
Once the researchers had topologically ordered qubits, they used the exotic particles that resulted (called non-Abelian anyons) to compute, performing error-protected gates and measurements.
To perform gates, the researchers 'braided' the anyons, which is like changing the shape of the “net”. This is something like the children’s game ‘cats cradle’. Through a sequence of changes to the “net”, the quantum computer can perform full calculations, one day helping scientists to understand the secrets hidden in the world around us.
Why go to such trouble? Well, for the love of discovery of course - but the team had an additional, specific motivation. One of the biggest challenges in building practical quantum computers is protecting them from errors while still being able to perform every operation needed for computation (this is referred to as universality).
This work takes a fresh approach to this challenge. Unlike traditional quantum error correction, the special properties of topological matter enable a universal set of fault tolerant gates without relying on expensive magic state distillation.
Why this matters
Quantum error correction is essential for large-scale quantum computing. While it protects fragile quantum information from noise by turning delicate physical qubits into robust logical qubits, it also introduces a significant constraint: not every quantum gate can be performed directly on logical qubits.
For decades, the standard solution has been to supplement error-corrected operations with magic states. These specially prepared quantum resources enable universal computation but can come at a steep cost - in many estimates of future fault-tolerant quantum computers, magic state preparation dominates both the physical qubit count and the runtime of useful algorithms.
Reducing this overhead has therefore become an important goal in quantum computing. This new approach may significantly reduce the cost by enabling the ‘topological preparation’ of magic states, eliding expensive protocols like distillation. If universal computation can be performed without large-scale magic state distillation, quantum computers could require significantly fewer physical qubits and spend much less time generating computational resources before running useful algorithms.
We will never stop exploring
While there is still considerable work ahead to understand the practical implementation and scalability of these ideas, this result expands the landscape of what's possible in quantum fault tolerance.
Of course, this impressive demonstration describes just one approach we are taking to fault tolerance at scale. We will continue to push forward with topological computing alongside more traditional approaches to quantum error correction, as well as exploring everything we can imagine in between. We are looking at a number of ways to reduce the resource cost of magic states in particular, and are making strides in multiple dimensions. With machines that are both flexible and accurate enough to do it all, who can resist?
- Quantinuum continues its progress toward fault-tolerant quantum computing, with a series of peer-reviewed breakthroughs in fault-tolerant operations.
- Our progress is not only scientific; it is commercial. By improving logical-qubit reliability and encoding efficiency, Quantinuum is reducing the resource overhead required to scale its quantum computers toward commercially useful workloads.
- These results were achieved on commercial Quantinuum hardware, reinforcing that our architecture is not just setting new standards, but building a practical foundation for customers, partners, and researchers preparing for the fault-tolerant era.
Fault-tolerant quantum computing is the threshold the industry must cross before quantum computers can solve the hardest, highest-value problems with confidence. To be commercially useful at scale, the question is not simply who can build more qubits. It is who can build reliable, efficient, scalable systems that reduce technical risk and accelerate the path to commercial usefulness.
Quantinuum is progressing on that path.
Last year, in partnership with Microsoft, we published a breakthrough in logical computing, demonstrating logical qubits that outperformed their physical counterparts by a factor of 800. We are proud to announce that this work is now being published in Nature, one of the most highly regarded scientific journals in the world.
This work highlights our leading fidelities, as shown in Table 1:
Since then, we’ve accelerated our efforts to reach large-scale fault tolerance and advanced what we believe to be the core building blocks of fault-tolerant quantum computing, from logical-qubit teleportation and multiple error-correction breakthroughs to one of the first meaningful computations using logical qubits. Importantly, these results were achieved on commercial Quantinuum hardware, demonstrating not just scientific progress, but a practical and efficient path toward scalable, customer-ready fault tolerance.
A Recap of Our Recent Technical Progress
Since the work with Microsoft, we achieved a milestone years ahead of schedule, demonstrating high-fidelity teleportation of a logical qubit, which was published in Science, one of the world’s most prestigious journals. Later, we beat our own record in this crucial fault tolerance milestone, thanks to continued improvements to our System Model H2’s fidelity.
Then, a series of results demonstrating more error-correcting milestones (and codes):
- Better than physical results in a high-rate non-local code,
- First-ever demonstration of a single-shot error correcting code (which significantly reduces resource requirements) in 4 dimensions
- Extending qubit lifetimes by 10x with a concatenated code
- Observed fault-tolerance thresholds with concatenated codes
- High fidelity magic states and a fully fault tolerant universal gate set in two different papers
Recently, we topped ourselves yet again by performing one of the first meaningful computations with logical qubits – exploring key questions in materials and magnetism, using logical qubits with better error rates than their physical counterparts. This result also includes a leading “encoding rate” squeezing 48 logical qubits out of just 98 physical qubits, emphasizing how our architecture helps to support large scale fault tolerance without enormous resource costs.
It is worth noting that all these results were achieved on our commercial hardware, not on one-off laboratory test-stands – reflecting the performance that we are able to deliver to our customers.
We also did crucial theoretical work, exploring new options for error correction that can reduce resource requirements, time to solution, and shorten the timeline to large scale fault tolerance.
Commercial Implications and the Road Ahead
We believe the commercial implication is clear: Quantinuum is reducing the uncertainty around the path to fault-tolerant quantum computing. Our architecture, hardware fidelity, full-stack control, and error-correction progress are converging into a practical roadmap for systems that can support valuable scientific and commercial workloads.
For those evaluating when quantum computing will become strategically relevant, we believe the signal is also increasingly clear: the fault-tolerant era is no longer a distant concept. It is becoming an engineering reality, and Quantinuum is leading the way.