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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 ҹɫֱ��, 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. (ҹɫֱ�� 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 .

“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 ҹɫֱ�� 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, .

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.

ҹɫֱ�� today honored researchers from the for their technical achievements and contributions to the field of quantum computing.

In a ceremony at the company’s U.S. headquarters in Broomfield, President and Chief Operating Officer Tony Uttley recognized the decades of innovative research by and the role it has played in the development of ҹɫֱ��’s H-series hardware technology, which recently set an industry record for performance.

“It’s impossible to overstate the impact of the NIST Ion Storage Group and its research,” Uttley said. “Quantum computing has advanced to where it is today in large part because of this group and its commitment to making its work available. Their research forms the basis for the trapped ion quantum computing technologies being developed by ҹɫֱ�� and others. It is truly a technology transfer success story for the U.S. government.”

NIST’s Colorado-based ion trap group was formed in the late 1970s not long after Dr. David Wineland, demonstrated that by using lasers, it was possible to cool ions to low enough temperatures that they could be manipulated and controlled while trapped in electromagnetic fields.

This discovery and the team’s subsequent research led to the development of some of the world’s most precise atomic clocks, a technology that helps enable Global Positioning Systems (GPS) satellites.

In the 1990s, the NIST group expanded its focus to quantum information processing and quantum computing. In 1995, the NIST team successfully executed the world’s first entangling two-qubit quantum gate, an operation that is key to quantum computing.

In 2000, the group demonstrated for the first time the more robust Mølmer-Sørensen gate, entangling four ion qubits. The Mølmer-Sørensen gate is at the heart of almost all ion-trap quantum computing gates today.

In 2002, the team outlining the concept of the Quantum Charged Coupled Device (QCCD) architecture for a trapped ion-based quantum computer. (ҹɫֱ�� uses this QCCD architecture in its H-Series hardware, Powered by Honeywell.)

These advancements and others led to Wineland sharing the 2012 Nobel Prize for Physics with Serge Haroche for "ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems.

The NIST team continues to advance trapped ion technologies. ҹɫֱ�� recently signed an agreement with NIST to collaborate on some trap design elements.

Uttley said ҹɫֱ��’s relationship with NIST is critical to the company’s success and its ongoing efforts to build the highest performing quantum computers in the world.

“The NIST team has a deep expertise in ion trap design, which will continue to help us on the technical side,” Uttley said. “The agency also has trained a great number of students and researchers over the years to become leading experts in the field and helped bolster the current and future quantum workforce.”

“Technology transfer is an important way that NIST achieves its mission of promoting U.S. innovation and industrial competitiveness,” said Director of NIST’s Physical Measurement Laboratory Jim Kushmerick. “We are always excited to see our research applied to develop commercial products, particularly those with great potential such as quantum computing.”

When was the last time you knowingly encountered helium, the gas that makes balloons float and children—OK, adults too—giggle and talk in high, squeaky voices after inhaling it?  Likely at a birthday party, wedding, or another celebration, right?  

Helium, however, has many applications beyond party balloons. Pure, high-quality helium is critical to several industries and technologies, including quantum computing.

“Many quantum computing technologies use helium,” said Steve Sanders, director of engineering at ҹɫֱ��, which develops trapped-ion quantum computing technologies. “We use it to keep our ion traps very cold because they operate better below 50 degrees Kelvin. The helium also has the effect of lowering the gas pressure inside our physics packages and keeping the few remaining gas atoms cold.  Fewer gas atoms mean fewer collisions with our ions.  And cold gas atoms have far less energy, so even if they collide with our ions, they don’t disturb them.”

Found among the stars, helium is one of the most abundant elements in the universe, second only to hydrogen. On earth, where it’s formed from alpha-particles of radioactive elements decaying beneath the surface, helium is a finite resource. And that’s why ҹɫֱ�� has significantly invested in staff and infrastructure to reuse as much helium as possible.

“We recognize the physical and socioeconomic impacts of both limited natural resources and climate change, so it’s crucial for us to operate as sustainably as possible,” said Tony Uttley, president and chief operating officer at ҹɫֱ��.  

Andy Miller, an engineer at ҹɫֱ��, spends his days managing and maintaining the extensive helium recovery system at the company’s Colorado campus. (ҹɫֱ�� has a smaller system at its laboratory space in Minnesota.)

“Our helium liquefaction system is a process plant that converts helium from a gas into a liquid. That liquid is then moved into the labs where it provides cooling to the quantum computing application. As it provides cooling, it becomes a gas again and then is transported into our recovery pipeline, which is installed throughout the facility, and the recovery piping leads to a big gasbag,” Miller explains.

“This gasbag is a giant balloon that fills up with gaseous helium. And as that balloon fills up with helium, it is monitored by a level sensor that measures the size of the gas bag. Once the bag inflates to a certain volume, it turns on a high-pressure compressor. The high-pressure compressor then pulls helium from the gas bag and sends the helium over to high-pressure storage. The helium is stored in high-pressure cylinders which are 20 feet in length and two feet in diameter. It's stored as a high-pressure gas until it's ready to be liquefied again and sent back to the labs to continue the cooling and recycle process.”  

This process enables the team to recover and reuse large amounts of helium.

“Helium is an absolutely 100% nonrenewable resource,” Miller emphasizes. “Once we pull helium out of the ground, it is so light that it will float up out of the atmosphere. It’s important we recover and reuse as much of it as possible.”

Cambridge Quantum (CQ), the global leader in quantum software, and a wholly owned subsidiary of ҹɫֱ��, the world’s leading integrated quantum computing company, is pleased to announce the continuation of its expansion across Europe with the opening of its new office in Munich, Germany.

The creation and rapid expansion of the new company, CQ Deutschland (CQD), underlines ҹɫֱ��’s commitment to the ambitious project of the German government in supporting and promoting quantum technologies and quantum computing. Cambridge Quantum already has a scientific team in Munich that complements its existing work in ab-initio Quantum Chemistry with a model-based perspective from Condensed Matter Physics. The goal of the Condensed Matter Group in Munich is to develop algorithms and software that will be the driver of strongly correlated systems research and the commercialization of quantum materials. Cambridge Quantum will continue to expand its collaboration with enterprise, government and academic partners in Germany on chemistry, optimization, finance, cybersecurity, and quantum machine learning and natural language processing in order to grow the industry's quantum computing ecosystem.

“The next milestone in quantum computation is delivering useful applications for the rapidly improving quantum hardware. Achieving this requires a combined effort in the fields of quantum software, quantum algorithms, and quantum hardware,” said Dr. Henrik Dreyer, Cambridge Quantum Deutschland’s Scientific Lead, “The German quantum computing ecosystem is exceptionally well positioned in these areas. We look forward to joining the community, in which our team of expert scientists can continue to develop applications for quantum computing in collaboration with industry, government and academic partners.”

This week, the System Model H1-2 doubled its performance to become the first commercial quantum computer to pass Quantum Volume 4096, a benchmark introduced by IBM in 2019 to measure the overall capability and performance of quantum computers.

It marks the sixth time in two years that ҹɫֱ��’s H-Series hardware, Powered by Honeywell, has set an industry record for measured quantum volume.

The achievement also fulfills a March 2020 promise made by Honeywell Quantum Solutions, which combined with Cambridge Quantum in late 2021 to form ҹɫֱ��, to increase the performance of its trapped ion technologies by an order of magnitude each year for the next five years. 

“This is the second consecutive year we’ve delivered on that promise and our commitment to developing the highest performing quantum hardware available,” said Tony Uttley, president and chief operating officer at ҹɫֱ��.

Continuous upgrades

This week marks the second time in four months that the System Model H1-2, which came online late last year, has achieved a quantum volume milestone. It set a record in December 2021 when it passed Quantum Volume 2048.

Uttley attributed the doubling of performance to the consistent upgrades that are made. 

ҹɫֱ�� currently operates two commercial quantum computers, the H1-1 and H1-2, which run projects for customers and then are taken offline for upgrades. 

“This approach provides the opportunity for us to continuously add new updates and features to our systems, which enables us to improve performance,” he said. “We learn a lot about our machines by running projects and can make small upgrades or tweaks that keep our fidelities high.” 

The data

The average single-qubit gate fidelity for this milestone was 99.994(3)%, the average two-qubit gate fidelity was 99.81(3)% with fully-connected qubits, and measurement fidelity was 99.72(5)%. The ҹɫֱ�� team ran 200 circuits with 100 shots each, using standard QV optimization techniques to yield an average of 152.97 two-qubit gates per circuit.

The System Model H1-2 successfully passed the quantum volume 4096 benchmark, outputting heavy outcomes 69.04% of the time, which is above the 2/3 threshold with greater than 99.99% confidence. 

The team used a , Dr. Charlie Baldwin and Dr. Karl Mayer, to calculate the confidence interval. 

The plot above shows the individual heavy output probability for each circuit in the Quantum Volume 4096 test. The blue line is the cumulative average heavy output probability and the green regions are the cumulative two-sigma confidence interval calculated by the new method. The heavy output probability crosses the 2/3 threshold with two-sigma confidence after 100 circuits.

The plot above shows the growth of measured quantum volume by ҹɫֱ��. For each test, the heavy output probability ‘h’ is listed and the system is identified by the marker type. The dashed grey line shows our target scaling of increasing QV × 10 yearly. 

What’s next?

Uttley said the next step is to increase the number of qubits on both ҹɫֱ�� machines and to continue to improve gate fidelities.

“The System Model H1-2 used all 12 of its fully connected qubits to pass Quantum Volume 4096,” he said. “We have reached the limit of what we can do with 12 qubits. To continue to improve performance, we need to add qubits. So keep watching what happens soon.”

ҹɫֱ��'s quantum chemistry team, in collaboration with TotalEnergies, has presented a detailing a potential use of quantum computers in mitigating climate change. The team has paved the way for the use of quantum computing to model materials, as a part of the materials discovery process, for use in carbon capture and sequestration.

In this work, the research team brought together the worlds of carbon capture and quantum computing. They developed a quantum computing methodology describing the binding of molecular carbon dioxide with a material being actively researched for carbon capture, called a Metal-Organic Framework, or MOF. This family of materials is of great scientific interest because they are capable of absorbing carbon dioxide with low energy requirements.

These synthetic materials are porous, which gives them their ability to bind to carbon dioxide molecules. MOFs can be compared to "molecular LEGO", as they can take many different configurations, which result in specific pore sizes and reactivity. They can in principle be used to design materials with specific properties.

Using classical computers to model these systems often yields imprecise solutions. Using a novel quantum method, the team opens a door to potentially overcoming some of the limitations of classical approaches. Due to the natural way in which many-body interactions can be treated, as well as the sheer size of the computational space, quantum computing is a natural future alternative for modeling such systems.

Today’s quantum computers (noisy, intermediate-scale quantum machines, or NISQ machines) are constrained by the number of qubits available for computation, and the tendency for calculations to be overwhelmed by errors. Modeling complex materials like MOFs is therefore challenging. The breakthrough represented by this paper is the use of fragmentation strategies to break down the computational task, providing a robust and versatile approach that combines quantum and classical computing methods.

The work revealed the way today’s quantum computers modeling complex many-body interactions can increase our understanding of MOF-CO2 systems. It potentially accelerates our ability to use quantum computers to solve challenges that could play an important role in tackling climate change.

‍Ilyas Khan, CEO of ҹɫֱ��, commented: "The publication of this paper in partnership with TotalEnergies, one of the world's leading developers of carbon capture and storage technologies, marks an important milestone in the much anticipated area of quantum chemistry. The mixed team of TotalEnergies and ҹɫֱ�� scientists has demonstrated a way to use today's quantum computers to conduct materials science research in a space that the Intergovernmental Panel on Climate Change says will play a vital role in stabilizing atmospheric greenhouse gas concentrations. This is the sort of work quantum computers have the potential to accelerate in the future."