Quantum Volume Testing: Setting the Steady Pace to Higher Performing Devices
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.
How is quantum volume measured? What tests do you run?
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.
What does quantum volume measure? Why is it important?
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.
You’ve been running quantum volume tests since 2020. What is your biggest takeaway?
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.
What are the key findings from your paper?
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.
What does it take to “pass” the quantum volume threshold?
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.
How do you think the quantum volume test can be improved?
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.
You presented these findings to IBM researchers who first proposed the benchmark. How was that experience?
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.
There is a lot of debate about quantum volume and how long it will be a useful benchmark. What are your thoughts?
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.
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.
By: Harry Buhrman, Chief Scientist
Quantum computing is often framed as a race to the most qubits, the fastest gates, and the biggest benchmarks.
But a race needs a destination. In the fault-tolerant era, that means solving a valuable problem faster or at a lower cost than the best classical approach—and the time to solution is ultimately what matters most.
In this context, gate speed metrics have received a lot of attention. While gate speed is a meaningful component of the overall quality of a quantum computer, what actually matters most is fidelity. As we all know, speed on its own matters little if we don’t arrive at the correct destination.
Fidelity has emerged as the most important foundation for success in quantum computing. Higher fidelity means fewer errors in the underlying physical operations. Combined with quantum error correction, higher fidelity can reduce the number of additional qubits and operations needed to make computations reliable. This reduction in overhead can lower costs and shorten the time to deliver a useful answer—even compared with systems that have faster gates but lower fidelity.
Fast Gates Do Not Guarantee Fast Answers
Consider a simple example. In an independent-error model, a computation with 10,000 operations, each with an error rate of 10⁻³, or 99.9% fidelity, will experience about ten faults on average that can render the computation useless.
Now make every gate ten times faster without changing its error rate. You still get ten faults. You just get them ten times sooner.
Speed matters, but the relevant measure is the total time required to obtain a trustworthy and useful result. Getting to that point requires performance in many different and connected areas such as state preparation, measurement, error correction, repeated runs, and other work needed to complete the computation.
Gate speed alone cannot establish which system performs best. A fast machine that cannot reliably finish a sufficiently large computation cannot deliver commercial value.
Why Fidelity Changes the Resource Equation
Quantum error correction protects information by encoding it across multiple physical qubits. That protection requires resources: additional qubits, measurements, operations, and classical processing. These techniques work better when the underlying physical operations are reliable enough that increasing error protection reduces the logical error rate.
This requirement is known as the fault-tolerance threshold, the point below which physical error rates are low enough that adding protection reduces logical errors. Faster gates can shorten the computation, but they cannot replace the physical fidelity needed to cross that threshold.
At Quantinuum, our latest error-correction results on Helios demonstrate this principle. Using our error-correction architecture, logical memory errors fell exponentially as we increased protection. Across the tested code sizes, the fitted error reduction was about twelvefold for each increase of two in code distance. In the largest quantum-memory experiment, the estimated failure rate was about five in a million per error-correction cycle.1 This demonstrates how high-fidelity physical operations and effective error correction work together to make quantum information more reliable as protection grows.
The next question is what that reliability enables. How large a computation can a system complete, and how quickly can it deliver the result?
A New Performance Benchmark
The Quantum Universal Operations Performance System, or QUOPS, provides a standardized way to assess both. This architecture-neutral benchmark gauges performance by measuring computational “reach” and speed.2
“Reach” measures how large a benchmark circuit a system can execute successfully. Speed measures how quickly it executes that circuit, in effective quantum operations per second. QUOPS uses wall-clock time and accounts for extra samples and discarded runs caused by noise.
Together, these measures provide a common basis for comparing what different quantum systems deliver and tracking progress toward better time to solution.
Quantinuum’s H2 and Helios systems executed substantially larger benchmark circuits than Google’s Willow and IBM’s Boston. These superconducting systems sometimes achieved higher effective operation rates, but on smaller circuits, which means that they are not computationally comparable.
Superconducting systems can use error mitigation to tackle larger computations, but at a steep cost in speed. The QUOPS study estimates that the additional repetitions can make effective processing thousands of times slower. Some computations remain beyond the system’s reliable reach, even with mitigation. In those cases, faster gates may deliver no useful answer at all within practical limits on time and cost.
Useful applications require speed on much larger circuits. For example, the study estimates that factoring RSA-2048 or calculating FeMoco’s ground-state energy within five days would require roughly 100,000 times the computational reach demonstrated by today’s physical-qubit processors. Some machines approach the estimated speed requirement, but only on small circuits. The challenge is to sustain that speed at the required scale, including the additional work needed for error correction.
Larger uncorrected circuits accumulate more errors. Protecting them requires extra qubits and time. Reliability and speed must therefore scale together, and QUOPS offers a way to track both.
Higher Fidelity Makes Larger, Reliable Computations Possible
Improving fidelity can reduce the extra qubits and operations needed for error correction, lowering the time, cost, and resources required for useful computation. The benefit comes from reaching the required reliability with less protection, leaving more resources available for the computation itself.
Helios brings together the physical performance and error-correction capabilities needed to pursue those savings. In our paper published in Nature we showed that the system achieved an average single-qubit gate fidelity of 99.9975% and average two-qubit gate fidelity of 99.921% across its operational zones, while scaling the trapped-ion architecture to 98 fully connected physical qubits.3
The latest color-code experiments build on that physical performance. Alongside the logical memory results, protected two-qubit Clifford operations also became more reliable as protection increased. This connects improvements in the underlying hardware to improvements in logical computation.
A flexible error-correction architecture creates further opportunities to improve efficiency. Our recent Helix and color-code demonstrations used the same Helios hardware to explore different balances of accuracy and physical-qubit requirements. That flexibility allows us to evaluate which codes best suit different computational tasks as systems scale.
However, we continue to push ahead and accelerate the development of machines, such as Apollo, where quantum utility comes into play at scale. Decoding in the new color-code benchmarks was performed offline, and we are now turning our attention to integrating error correction, magic-state resources and real-time control into longer, reliable computations.
While that work continues, today’s systems can already contribute to scientific research. NISQ systems have advanced algorithms and hardware, enabled certified randomness, and supported studies of quantum magnetism and superconducting pairing correlations. These results leave room for useful applications before fault tolerance, even as error correction provides the scalable path to larger, reliable computations.4
The goal is to combine these capabilities so that larger computations can run reliably within practical limits on time and resources. Fidelity provides the foundation, and optimizing the full system turns that foundation into better time to solution.
Fidelity First. Then Optimize Time to Solution.
Scaling quantum computation requires continued progress in fidelity. As physical operations move further below threshold, increasing error protection can suppress logical errors more effectively, enabling longer, more demanding computations.
Speed must improve alongside that reliability. Advances in transport, cooling, measurement, compilation, and parallel execution can reduce the time and total cost of solving useful problems. These improvements become increasingly valuable as systems gain the reliability needed to complete larger computations.
Our latest Helios results are proof points on the path to Apollo, our planned universal fault-tolerant quantum computer, expected by 2029. The goal is to translate these gains into systems that can solve industrially relevant problems faster or at lower cost than the best classical approach.
Industrial partnerships help connect that progress to problems that matter, from understanding high-temperature superconductivity to how molecules interact to accelerate drug discovery. They bring practical research questions into the development process and help identify where improving quantum capabilities could deliver useful results beyond the reach of classical computing alone.
Our motto is simple: fidelity first, with speed built on that foundation.
References & For Further Reading
[1] A. Lavasani et al., "Quantum error correction well below the color code threshold," arXiv:2610.24077 [quant-ph] (2026). doi:10.48550/arXiv.2610.24077.
[2] T. Proctor et al., "Benchmarking the computational power of quantum computers," arXiv:2609.12146 [quant-ph] (2026). doi:10.48550/arXiv.2609.12146.
[3] A. Ransford et al., "A 98-qubit trapped-ion quantum computer with all-to-all connectivity," Nature 655, 81-86 (2026). doi:10.1038/s41586-026-10676-4.
[4] M. Liu, R. Shaydulin, P. Niroula et al., "Certified randomness using a trapped-ion quantum processor," Nature 640, 343-348 (2025). doi:10.1038/s41586-025-08737-1.
S. Dasu et al., "Computing with many encoded logical qubits beyond break-even," arXiv:2602.22211 [quant-ph] (2026). doi:10.48550/arXiv.2602.22211.
E. Granet et al., "Superconducting pairing correlations on a trapped-ion quantum computer," arXiv:2511.02125 [quant-ph] (2025; revised 2026). doi:10.48550/arXiv.2511.02125.
Quantinuum and GE Vernova’s Advanced Research Center are launching a collaboration to apply quantum computing to one of the research community’s most consequential challenges: understanding the behavior behind high-temperature superconductivity. Advances in this field could, over the long term, transform the energy sector by enabling lighter generators, more compact and powerful motors, and electricity infrastructure that carries more power and better withstands faults.
The research will focus on Fermi–Hubbard modeling, a framework for studying how interacting electrons give rise to complex material properties. By combining Quantinuum’s full-stack quantum computing capabilities—including access to the company’s Helios computer—with GE Vernova’s expertise in material science and engineering simulation applied to industrial applications, the collaboration will bring an industry perspective to a promising area of quantum research.
Why superconductors matter for energy
As energy systems grow, the size, weight, and performance of electrical equipment become increasingly important constraints. High-temperature superconductors offer potential ways to address those limits through their ability to carry large electrical currents without resistance under suitable operating conditions.
Potential applications span power generation, electricity grids, and industrial electrification. Superconducting generators could reduce the weight and footprint of industrial equipment. Superconducting windings could also help make utility generators and industrial or marine propulsion motors more compact and efficient. In electricity networks, superconducting cables could carry more power through constrained spaces, while fault current limiters could help protect equipment during short circuits.
Realizing those benefits more widely depends on overcoming challenges in cooling, material performance, manufacturing, and cost. Better understanding of the physics behind high-temperature superconductivity could help inform the search for materials with more practical operating characteristics.
Why quantum computing may offer new tools for understanding high-temperature superconductivity
High-temperature superconductivity involves the collective behavior of strongly interacting electrons. Accurately modeling these systems is exceptionally difficult: the interactions that make them scientifically interesting also make important aspects of their behavior computationally challenging.
The Fermi–Hubbard model captures essential features of those interactions in a simplified mathematical framework. Although it is not a complete description of a material used in industrial applications, it provides a foundation for investigating mechanisms associated with high-temperature superconductivity.
Quantum computing offers a promising way to explore the physics. Quantinuum researchers have already measured superconducting pairing correlations—including s-wave and d-wave pairing—in Fermi–Hubbard models simulated on the Helios quantum computer. These results demonstrate the ability to prepare and probe quantum states relevant to superconductivity research, establishing a foundation for further investigation.
The collaboration with GE Vernova will build on that foundation, bringing industrial expertise to the selection and interpretation of research questions.
Connecting quantum capabilities with industrial expertise
The research will be enabled through access to Quantinuum’s full-stack capabilities, including cloud-based access to Helios, the world’s most accurate quantum computer1, and Nexus, Quantinuum’s developer platform. Nexus connects quantum hardware with the software tools researchers need to develop and run applications in a unified environment.
GE Vernova’s Advanced Research Center brings the expertise in material science, engineering, and industrial applications to the research and development activity.
“High-temperature superconductors could help us overcome important limits on the size, weight, and efficiency of electrical equipment, but understanding and improving these materials remains a significant scientific challenge,” said Jonathan Owens, PhD, Senior Scientist, Computational Materials Physics at GE Vernova. “By combining our materials simulation and industrial expertise with Quantinuum’s quantum computing capabilities, we can explore new approaches to these difficult problems while building the expertise to assess where quantum computing can make a meaningful contribution.”
The collaboration also extends GE Vernova’s exploration of quantum computing into a new area of materials research while supporting the development of its internal quantum talent. Its previous published work includes investigations of quantum algorithms for carbon-capture materials using simulated quantum processors.
Building toward industrial value
Translating insights from simplified models into practical materials requires sustained scientific and engineering work. Industrial expertise helps connect that effort to the properties, operating conditions, and manufacturing considerations that ultimately determine a material’s usefulness.
For Quantinuum, this collaboration is an opportunity to advance quantum simulation with an industrial collaborator that understands both the potential applications and the barriers to adoption. It brings together demonstrated computing capabilities, a challenging materials problem, and the expertise needed to connect scientific progress with industrial requirements.
The research collaboration aims to deepen understanding of this field and explore how quantum computing may contribute to future energy technologies.
1 Based on two-qubit gate fidelity as of December 31, 2025.
From Oracle's Quantum AI Compute beta program to upcoming Helios installation milestones and Oracle AI World, our partnership continues to gain momentum.
When Quantinuum and Oracle announced a strategic partnership earlier this year, the goal was not simply to deploy a quantum computer in the cloud. It was to create a practical path for bringing quantum computing into the enterprise environments where AI, data, and high-performance computing (HPC) already come together.
By combining Oracle Cloud Infrastructure (OCI)'s AI, data, and cloud capabilities with Helios, Quantinuum's most advanced quantum computer, we're helping lay the foundation for hybrid quantum AI computing at enterprise scale. The partnership reflects our belief that some of the most valuable future applications will emerge when quantum computing, AI and classical HPC work together to tackle problems that remain difficult to solve today.
Oracle Opens Early Access for Quantum AI Compute
That vision is now being put into practice. This month, Oracle launched the OCI Quantum AI Compute Beta Program, giving select organizations an opportunity to begin evaluating how quantum computing fits into existing workflows and computational challenges.
Through the program, approved participants will gain cloud-based access to Helios, the world's most accurate commercial quantum computer, alongside OCI's GPU and HPC infrastructure. For organizations exploring quantum computing, this creates a practical starting point: access to industry-leading hardware within an enterprise cloud environment, without the need to build specialized infrastructure of their own.
The goal is to help organizations understand where hybrid quantum AI workflows may create value across areas such as drug discovery, materials science, energy, financial modeling, and optimization.
For many organizations, the starting point is not quantum technology itself. It's a business or research problem. Where are today's approaches reaching meaningful limits? Which workloads consume disproportionate resources? And where could a new computational capability create an advantage?
Organizations interested in participating can apply through Oracle's OCI Preview Programs portal. Oracle will review applications and select participants based on eligibility, capacity and program requirements.
Quantinuum and Oracle Leadership Takes the Stage at Oracle AI World
The opportunity for hybrid quantum-AI computing will be a major topic at Oracle AI World 2026.
In a main stage session, "Powering the Next Era of Enterprise AI," Larry Stack, Chief Commercial Officer at Quantinuum, will join Mahesh Thiagarajan, Executive Vice President and Head of Oracle Cloud Infrastructure, to discuss how quantum computing, AI and classical HPC can work together to address some of the world's most computationally demanding challenges.
The discussion will focus on a core question many organizations are asking: where should they start? Rather than leading with technology, the conversation will explore how organizations can identify high-value problems, establish today's performance baseline, and evaluate where quantum computing ultimately provides an advantage.
Later in the day, Quantinuum and Oracle experts will take a deeper look at how bringing Helios into OCI provides managed access to quantum computing natively within an enterprise cloud environment to support hybrid quantum-AI workflows.
Building Momentum Toward Hybrid Quantum-AI Computing
The collaboration between Quantinuum and Oracle continues to progress from vision to execution.
With Helios advancing toward installation, Oracle's Quantum AI Compute program now open for early access, and enterprise interest growing around hybrid computing, the pieces are coming together. Organizations now have a practical way to begin exploring quantum computing through cloud-based access to Helios alongside AI, HPC, and existing enterprise workflows.
We look forward to continuing the conversation at Oracle AI World 2026 and working with customers who want to better understand where hybrid quantum-AI computing can create real-world value.
We're excited to continue that conversation at Oracle AI World 2026 and to help customers begin exploring what's possible through the OCI Quantum AI Compute Beta Program.