When it comes to completing the statistical tests and other steps necessary for calculating quantum volume, few people have as much as experience as Dr. Charlie Baldwin.
Baldwin, a lead physicist at Quantinuum, and his team have performed the tests numerous times on three different H-Series quantum computers, which have set six industry records for measured quantum volume since 2020.
Quantum volume is a benchmark developed by IBM in 2019 to measure the overall performance of a quantum computer regardless of the hardware technology. (Quantinuum builds trapped ion systems).
Baldwin’s experience with quantum volume prompted him to share what he’s learned and suggest ways to improve the benchmark in a peer-reviewed paper published this week in Quantum.
“We’ve learned a lot by running these tests and believe there are ways to make quantum volume an even stronger benchmark,” Baldwin said.
We sat down with Baldwin to discuss quantum volume, the paper, and the team’s findings.
Quantum volume is measured by running many randomly constructed circuits on a quantum computer and comparing the outputs to a classical simulation. The circuits are chosen to require random gates and random connectivity to not favor any one architecture. We follow the construction proposed by IBM to build the circuits.
In some sense, quantum volume only measures your ability to run the specific set of random quantum volume circuits. That probably doesn’t sound very useful if you have some other application in mind for a quantum computer, but quantum volume is sensitive to many aspects that we believe are key to building more powerful devices.
Quantum computers are often built from the ground up. Different parts—for example, single- and two-qubit gates—have been developed independently over decades of academic research. When these parts are put together in a large quantum circuit, there’re often other errors that creep in and can degrade the overall performance. That’s what makes full-system tests like quantum volume so important; they’re sensitive to these errors.
Increasing quantum volume requires adding more qubits while simultaneously decreasing errors. Our quantum volume results demonstrate all the amazing progress Quantinuum has made at upgrading our trapped-ion systems to include more qubits and identifying and mitigating errors so that users can expect high-fidelity performance on many other algorithms.
I think there’re a couple of things I’ve learned. First, quantum volume isn’t an easy test to run on current machines. While it doesn’t necessarily require a lot of qubits, it does have fairly demanding error requirements. That’s also clear when comparing progress in quantum volume tests across different platforms, which researchers at Los Alamos National Lab did in a recent paper.
Second, I’m always impressed by the continuous and sustained performance progress that our hardware team achieves. And that the progress is actually measurable by using the quantum volume benchmark.
The hardware team has been able to push down many different error sources in the last year while also running customer jobs. This is proven by the quantum volume measurement. For example, H1-2 launched in Fall 2021 with QV=128. But since then, the team has implemented many performance upgrades, recently achieving QV=4096 in about 8 months while also running commercial jobs.
The paper is about four small findings that when put together, we believe, give a clearer view of the quantum volume test.
First, we explored how compiling the quantum volume circuits scales with qubit number and, also proposed using arbitrary angle gates to improve performance—an optimization that many companies are currently exploring.
Second, we studied how quantum volume circuits behave without errors to better relate circuit results to ideal performance.
Third, we ran many numerical simulations to see how the quantum volume test behaved with errors and constructed a method to efficiently estimate performance in larger future systems.
Finally, and I think most importantly, we explored what it takes to meet the quantum volume threshold and what passing it implies about the ability of the quantum computer, especially compared to the requirements for quantum error correction.
Passing the threshold for quantum volume is defined by the results of a statistical test on the output of the circuits called the heavy output test. The result of the heavy output test—called the heavy output probability or HOP—must have an uncertainty bar that clears a threshold (2/3).
Originally, IBM constructed a method to estimate that uncertainty based on some assumptions about the distribution and number of samples. They acknowledged that this construction was likely too conservative, meaning it made much larger uncertainty estimates than necessary.
We were able to verify this with simulations and proposed a different method that constructed much tighter uncertainty estimates. We’ve verified the method with numerical simulations. The method allows us to run the test with many fewer circuits while still having the same confidence in the returned estimate.
Quantum volume has been criticized for a variety of reasons, but I think there’s still a lot to like about the test. Unlike some other full-system tests, quantum volume has a well-defined procedure, requires challenging circuits, and sets reasonable fidelity requirements.
However, it still has some room for improvement. As machines start to scale up, runtime will become an important dimension to probe. IBM has proposed a metric for measuring run time of quantum volume tests (CLOPS). We also agree that the duration of the computation is important but that there should also be tests that balance run time with fidelity, sometimes called ‘time-to-solution.”
Another aspect that could be improved is filling the gap between when quantum volume is no longer feasible to run—at around 30 qubits—and larger machines. There’s recent work in this area that will be interesting to compare to quantum volume tests.
It was great to talk to the experts at IBM. They have so much knowledge and experience on running and testing quantum computers. I’ve learned a lot from their previous work and publications.
The current iteration of quantum volume definitely has an expiration date. It’s limited by our ability to classically simulate the system, so being unable to run quantum volume actually is a goal for quantum computing development. Similarly, quantum volume is a good measuring stick for early development.
Building a large-scale quantum computer is an incredibly challenging task. Like any large project, you break the task up into milestones that you can reach in a reasonable amount of time.
It's like if you want to run a marathon. You wouldn’t start your training by trying to run a marathon on Day 1. You’d build up the distance you run every day at a steady pace. The quantum volume test has been setting our pace of development to steadily reach our goal of building ever higher performing devices.
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.
Our quantum algorithms team has been hard at work exploring solutions to continually optimize our system’s performance. Recently, they’ve invented a novel technique, called the Quantum Paldus Transform (QPT), that can offer significant resource savings in future applications.
The transform takes complex representations and makes them simple, by transforming into a different “basis”. This is like looking at a cube from one angle, then rotating it and seeing just a square, instead. Transformations like this save resources because the more complex your problem looks, the more expensive it is to represent and manipulate on qubits.
While it might sound like magic, transforms are a commonly used tool in science and engineering. Transforms simplify problems by reshaping them into something that is easier to deal with, or that provides a new perspective on the situation. For example, sound engineers use Fourier transforms every day to look at complex musical pieces in terms of their frequency components. Electrical engineers use Laplace transforms; people who work in image processing use the Abel transform; physicists use the Legendre transform, and so on.
In a new paper outlining the necessary tools to implement the QPT, Dr. Nathan Fitzpatrick and Mr. Jędrzej Burkat explain how the QPT will be widely applicable in quantum computing simulations, spanning areas like molecular chemistry, materials science, and semiconductor physics. The paper also describes how the algorithm can lead to significant resource savings by offering quantum programmers a more efficient way of representing problems on qubits.
The efficiency of the QPT stems from its use of one of the most profound findings in the field of physics: that symmetries drive the properties of a system.
While the average person can “appreciate” symmetry, for example in design or aesthetics, physicists understand symmetry as a much more profound element present in the fabric of reality. Symmetries are like the universe’s DNA; they lead to conservation laws, which are the most immutable truths we know.
Back in the 1920’s, when women were largely prohibited from practicing physics, one of the great mathematicians of the century, Emmy Noether, turned her attention to the field when she was tasked with helping Einstein with his work. In her attempt to solve a problem Einstein had encountered, Dr. Noether realized that all the most powerful and fundamental laws of physics, such as “energy can neither be created nor destroyed” are in fact the consequence of a deep simplicity – symmetry – hiding behind the curtains of reality. Dr. Noether’s theorem would have a profound effect on the trajectory of physics.
In addition to the many direct consequences of Noether’s theorem is a longstanding tradition amongst physicists to treat symmetry thoughtfully. Because of its role in the fabric of our universe, carefully considering the symmetries of a system often leads to invaluable insights.
Many of the systems we are interested in simulating with quantum computers are, at their heart, systems of electrons. Whether we are looking at how electrons move in a paired dance inside superconductors, or how they form orbitals and bonds in a chemical system, the motion of electrons are at the core.
Seven years after Noether published her blockbuster results, Wolfgang Pauli made waves when he published the work describing his Pauli exclusion principle, which relies heavily on symmetry to explain basic tenets of quantum theory. Pauli’s principle has enormous consequences; for starters, describing how the objects we interact with every day are solid even though atoms are mostly empty space, and outlining the rules of bonds, orbitals, and all of chemistry, among other things.
It is Pauli's symmetry, coupled with a deep respect for the impact of symmetry, that led our team at Quantinuum to the discovery published today.
In their work, they considered the act of designing quantum algorithms, and how one’s design choices may lead to efficiency or inefficiency.
When you design quantum algorithms, there are many choices you can make that affect the final result. Extensive work goes into optimizing each individual step in an algorithm, requiring a cyclical process of determining subroutine improvements, and finally, bringing it all together. The significant cost and time required is a limiting factor in optimizing many algorithms of interest.
This is again where symmetry comes into play. The authors realized that by better exploiting the deepest symmetries of the problem, they could make the entire edifice more efficient, from state preparation to readout. Over the course of a few years, a team lead Dr. Fitzpatrick and his colleague Jędrzej Burkat slowly polished their approach into a full algorithm for performing the QPT.
The QPT functions by using Pauli’s symmetry to discard unimportant details and strip the problem down to its bare essentials. Starting with a Paldus transform allows the algorithm designer to enjoy knock-on effects throughout the entire structure, making it overall more efficient to run.
“It’s amazing to think how something we discovered one hundred years ago is making quantum computing easier and more efficient,” said Dr. Nathan Fitzpatrick.
Ultimately, this innovation will lead to more efficient quantum simulation. Projects we believed to still be many years out can now be realized in the near term.
The discovery of the Quantum Paldus Transform is a powerful reminder that enduring ideas—like symmetry—continue to shape the frontiers of science. By reaching back into the fundamental principles laid down by pioneers like Noether and Pauli, and combining them with modern quantum algorithm design, Dr. Fitzpatrick and Mr. Burkat have uncovered a tool with the potential to reshape how we approach quantum computation.
As quantum technologies continue their crossover from theoretical promise to practical implementation, innovations like this will be key in unlocking their full potential.
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.
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.
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.
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.
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 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.
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?