Developing quantum computing systems with high operational fidelity, enhanced processing capabilities plus inherent (and rapid) scalability is high on the list of fundamental problems preoccupying researchers within the quantum science community. One promising R&D pathway in this regard is being pursued by the Superconducting Quantum Materials and Systems (SQMS) National Quantum Information Science Research Center at the US Department of Energy’s Fermi National Accelerator Laboratory, the pre-eminent US particle physics facility on the outskirts of Chicago, Illinois.

The SQMS approach involves placing a superconducting qubit chip (held at temperatures as low as 10–20 mK) inside a three-dimensional superconducting radiofrequency (3D SRF) cavity – a workhorse technology for particle accelerators employed in high-energy physics (HEP), nuclear physics and materials science. In this set-up, it becomes possible to preserve and manipulate quantum states by encoding them in microwave photons (modes) stored within the SRF cavity (which is also cooled to the millikelvin regime).

Put another way: by pairing superconducting circuits and SRF cavities at cryogenic temperatures, SQMS researchers create environments where microwave photons can have long lifetimes and be protected from external perturbations – conditions that, in turn, make it possible to generate quantum states, manipulate them and read them out. The endgame is clear: reproducible and scalable realization of such highly coherent superconducting qubits opens the way to more complex and scalable quantum computing operations – capabilities that, over time, will be used within Fermilab’s core research programme in particle physics and fundamental physics more generally.

Fermilab is in a unique position to turn this quantum technology vision into reality, given its decadal expertise in developing high-coherence SRF cavities. In 2020, for example, Fermilab researchers demonstrated record coherence lifetimes (of up to two seconds) for quantum states stored in an SRF cavity.

“It’s no accident that Fermilab is a pioneer of SRF cavity technology for accelerator science,” explains Sir Peter Knight, senior research investigator in physics at Imperial College London and an SQMS advisory board member. “The laboratory is home to a world-leading team of RF engineers whose niobium superconducting cavities routinely achieve very high quality factors (Q) from 10¹⁰ to above 10¹¹ – figures of merit that can lead to dramatic increases in coherence time.”

Moreover, Fermilab offers plenty of intriguing HEP use-cases where quantum computing platforms could yield significant research dividends. In theoretical studies, for example, the main opportunities relate to the evolution of quantum states, lattice-gauge theory, neutrino oscillations and quantum field theories in general. On the experimental side, quantum computing efforts are being lined up for jet and track reconstruction during high-energy particle collisions; also for the extraction of rare signals and for exploring exotic physics beyond the Standard Model.

Cavities and qubits

SQMS has already notched up some notable breakthroughs on its quantum computing roadmap, not least the demonstration of chip-based transmon qubits (a type of charge qubit circuit exhibiting decreased sensitivity to noise) showing systematic and reproducible improvements in coherence, record-breaking lifetimes of over a millisecond, and reductions in performance variation.

Key to success here is an extensive collaborative effort in materials science and the development of novel chip fabrication processes, with the resulting transmon qubit ancillas shaping up as the “nerve centre” of the 3D SRF cavity-based quantum computing platform championed by SQMS. What’s in the works is essentially a unique quantum analogue of a classical computing architecture: the transmon chip providing a central logic-capable quantum information processor and microwave photons (modes) in the 3D SRF cavity acting as the random-access quantum memory.

As for the underlying physics, the coupling between the transmon qubit and discrete photon modes in the SRF cavity allows for the exchange of coherent quantum information, as well as enabling quantum entanglement between the two. “The pay-off is scalability,” says Alexander Romanenko, a senior scientist at Fermilab who leads the SQMS quantum technology thrust. “A single logic-capable processor qubit, such as the transmon, can couple to many cavity modes acting as memory qubits.”

In principle, a single transmon chip could manipulate more than 10 qubits encoded inside a single-cell SRF cavity, substantially streamlining the number of microwave channels required for system control and manipulation as the number of qubits increases. “What’s more,” adds Romanenko, “instead of using quantum states in the transmon [coherence times just crossed into milliseconds], we can use quantum states in the SRF cavities, which have higher quality factors and longer coherence times [up to two seconds].”

In terms of next steps, continuous improvement of the ancilla transmon coherence times will be critical to ensure high-fidelity operation of the combined system – with materials breakthroughs likely to be a key rate-determining step. “One of the unique differentiators of the SQMS programme is this ‘all-in’ effort to understand and get to grips with the fundamental materials properties that lead to losses and noise in superconducting qubits,” notes Knight. “There are no short-cuts: wide-ranging experimental and theoretical investigations of materials physics – per the programme implemented by SQMS – are mandatory for scaling superconducting qubits into industrial and scientifically useful quantum computing architectures.”

Laying down a marker, SQMS researchers recently achieved a major milestone in superconducting quantum technology by developing the longest-lived multimode superconducting quantum processor unit (QPU) ever built (coherence lifetime >20 ms). Their processor is based on a two-cell SRF cavity and leverages its exceptionally high quality factor (~10¹⁰) to preserve quantum information far longer than conventional superconducting platforms (typically 1 or 2 ms for rival best-in-class implementations).

Coupled with a superconducting transmon, the two-cell SRF module enables precise manipulation of cavity quantum states (photons) using ultrafast control/readout schemes (allowing for approximately 10⁴ high-fidelity operations within the qubit lifetime). “This represents a significant achievement for SQMS,” claims Yao Lu, an associate scientist at Fermilab and co-lead for QPU connectivity and transduction in SQMS. “We have demonstrated the creation of high-fidelity [>95%] quantum states with large photon numbers [20 photons] and achieved ultra-high-fidelity single-photon entangling operations between modes [>99.9%]. It’s work that will ultimately pave the way to scalable, error-resilient quantum computing.”

Fast scaling with qudits

There’s no shortage of momentum either, with these latest breakthroughs laying the foundations for SQMS “qudit-based” quantum computing and communication architectures. A qudit is a multilevel quantum unit that can be more than two states and, in turn, hold a larger information density – i.e. instead of working with a large number of qubits to scale information processing capability, it may be more efficient to maintain a smaller number of qudits (with each holding a greater range of values for optimized computations).

Scale-up to a multiqudit QPU system is already underway at SQMS via several parallel routes (and all with a modular computing architecture in mind). In one approach, coupler elements and low-loss interconnects integrate a nine-cell multimode SRF cavity (the memory) to a two-cell SRF cavity quantum processor. Another iteration uses only two-cell modules, while yet another option exploits custom-designed multimodal cavities (10+ modes) as building blocks.

One thing is clear: with the first QPU prototypes now being tested, verified and optimized, SQMS will soon move to a phase in which many of these modules will be assembled and put together in operation. By extension, the SQMS effort also encompasses crucial developments in control systems and microwave equipment, where many devices must be synchronized optimally to encode and analyse quantum information in the QPUs.

Along a related coordinate, complex algorithms can benefit from fewer required gates and reduced circuit depth. What’s more, for many simulation problems in HEP and other fields, it’s evident that multilevel systems (qudits) – rather than qubits – provide a more natural representation of the physics in play, making simulation tasks significantly more accessible. The work of encoding several such problems into qudits – including lattice-gauge-theory calculations and others – is similarly ongoing within SQMS.

Taken together, this massive R&D undertaking – spanning quantum hardware and quantum algorithms – can only succeed with a “co-design” approach across strategy and implementation: from identifying applications of interest to the wider HEP community to full deployment of QPU prototypes. Co-design is especially suited to these efforts as it demands sustained alignment of scientific goals with technological implementation to drive innovation and societal impact.

In addition to their quantum computing promise, these cavity-based quantum systems will play a central role in serving both as the “adapters” and low-loss channels at elevated temperatures for interconnecting chip or cavity-based QPUs hosted in different refrigerators. These interconnects will provide an essential building block for the efficient scale-up of superconducting quantum processors into larger quantum data centres.

 “The SQMS collaboration is ploughing its own furrow – in a way that nobody else in the quantum sector really is,” says Knight. “Crucially, the SQMS partners can build stuff at scale by tapping into the phenomenal engineering strengths of the National Laboratory system. Designing, commissioning and implementing big machines has been part of the ‘day job’ at Fermilab for decades. In contrast, many quantum computing start-ups must scale their R&D infrastructure and engineering capability from a far-less-developed baseline.”

The last word, however, goes to Romanenko. “Watch this space,” he concludes, “because SQMS is on a roll. We don’t know which quantum computing architecture will ultimately win out, but we will ensure that our cavity-based quantum systems will play an enabling role.”

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In this week's episode of Space Minds Retired Space Force Lt. Gen. John Shaw explains what it was like building a new military branch, the risks of commercial integration and the race to protect U.S. satellites in orbit.

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By adapting mathematical techniques used in particle physics, researchers in Germany have developed an approach that could boost our understanding of the gravitational waves that are emitted when black holes collide. Led by Jan Plefka at The Humboldt University of Berlin, the team’s results could prove vital to the success of future gravitational-wave detectors.

Nearly a decade on from the first direct observations of gravitational waves, physicists are hopeful that the next generation of ground- and space-based observatories will soon allow us to study these ripples in space–time with unprecedented precision. But to ensure the success of upcoming projects like the LISA space mission, the increased sensitivity offered by these detectors will need to be accompanied with a deeper theoretical understanding of how gravitational waves are generated through the merging of two black holes.

In particular, they will need to predict more accurately the physical properties of gravitational waves produced by any given colliding pair and account for factors including their respective masses and orbital velocities. For this to happen, physicists will need to develop more precise solutions to the relativistic two-body problem. This problem is a key application of the Einstein field equations, which relate the geometry of space–time to the distribution of matter within it.

No exact solution

“Unlike its Newtonian counterpart, which is solved by Kepler’s Laws, the relativistic two-body problem cannot be solved exactly,” Plefka explains. “There is an ongoing international effort to apply quantum field theory (QFT) – the mathematical language of particle physics – to describe the classical two-body problem.”

In their study, Plefka’s team started from state-of-the-art techniques used in particle physics for modelling the scattering of colliding elementary particles, while accounting for their relativistic properties. When viewed from far away, each black hole can be approximated as a single point which, much like an elementary particle, carries a single mass, charge, and spin.

Taking advantage of this approximation, the researchers modified existing techniques in particle physics to create a framework called worldline quantum field theory (WQFT). “The advantage of WQFT is a clean separation between classical and quantum physics effects, allowing us to precisely target the classical physics effects relevant for the vast distances involved in astrophysical observables,” Plefka describes

Ordinarily, doing calculations with such an approach would involve solving millions of integrals that sum-up every single contribution to the black hole pair’s properties across all possible ways that the interaction between them could occur. To simplify the problem, Plefka’s team used a new algorithm that identified relationships between the integrals. This reduced the problem to just 250 “master integrals”, making the calculation vastly more manageable.

With these master integrals, the team could finally produce expressions for three key physical properties of black hole binaries within WQFT. These includes the changes in momentum during the gravity-mediated scattering of two black holes and the total energy radiated by both bodies over the course of the scattering.

Genuine physical process

Altogether, the team’s WQFT framework produced the most accurate solution to the Einstein field equations ever achieved to date. “In particular, the radiated energy we found contains a new class of mathematical functions known as ‘Calabi–Yau periods’,” Plefka explains. “While these functions are well-known in algebraic geometry and string theory, this marks the first time they have been shown to describe a genuine physical process.”

With its unprecedented insights into the structure of the relativistic two-body problem, the team’s approach could now be used to build more precise models of gravitational-wave formation, which could prove invaluable for the next generation of gravitational-wave detectors.

More broadly, however, Plefka predicts that the appearance of Calabi–Yau periods in their calculations could lead to an entirely new class of mathematical functions applicable to many areas beyond gravitational waves.

“We expect these periods to show up in other branches of physics, including collider physics, and the mathematical techniques we employed to calculate the relevant integrals will no doubt also apply there,” he says.

The research is described in Nature.

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CP Snow’s classic The Two Cultures lecture, published in book form in 1959, is the usual go-to reference when exploring the divide between the sciences and humanities. It is a culture war that was raging long before the term became social-media shorthand for today’s tribal battles over identity, values and truth.

While Snow eloquently lamented the lack of mutual understanding between scientific and literary elites, the 21st-century version of the two-cultures debate often plays out with a little less decorum and a lot more profanity. Hip hop duo Insane Clown Posse certainly didn’t hold back in their widely memed 2010 track “Miracles”, which included the lyric “And I don’t wanna talk to a scientist / Y’all motherfuckers lying and getting me pissed”. An extreme example to be sure, but it hammers home the point: Snow’s two-culture concerns continue to resonate strongly almost 70 years after his influential lecture and writings.

A Perfect Harmony: Music, Mathematics and Science by David Darling is the latest addition to a growing genre that seeks to bridge that cultural rift. Like Peter Pesic’s Music and the Making of Modern Science, Susan Rogers and Ogi Ogas’ This Is What It Sounds Like, and Philip Ball’s The Music Instinct, Darling’s book adds to the canon that examines the interplay between musical creativity and the analytical frameworks of science (including neuroscience) and mathematics.

I’ve also contributed, in a nanoscopically small way, to this music-meets-science corpus with an analysis of the deep and fundamental links between quantum physics and heavy metal (When The Uncertainty Principle Goes To 11), and have a long-standing interest in music composed from maths and physics principles and constants (see my Lateral Thoughts articles from September 2023 and July 2024). Darling’s book, therefore, struck a chord with me.

Darling is not only a talented science writer with an expansive back-catalogue to his name but he is also an accomplished musician (check out his album Songs Of The Cosmos ), and his enthusiasm for all things musical spills off the page. Furthermore, he is a physicist, with a PhD in astronomy from the University of Manchester. So if there’s a writer who can genuinely and credibly inhabit both sides of the arts–science cultural divide, it’s Darling.

But is A Perfect Harmony in tune with the rest of the literary ensemble, or marching to a different beat? In other words, is this a fresh new take on the music-meets-maths (meets pop sci) genre or, like too many bands I won’t mention, does it sound suspiciously like something you’ve heard many times before? Well, much like an old-school vinyl album, Darling’s work has the feel of two distinct sides. (And I’ll try to make that my final spin on groan-worthy musical metaphors. Promise.)

Not quite perfect pitch

Although the subtitle for A Perfect Harmony is “Music, Mathematics and Science”, the first half of the book is more of a history of the development and evolution of music and musical instruments in various cultures, rather than a new exploration of the underpinning mathematical and scientific principles. Engaging and entertaining though this is – and all credit to Darling for working in a reference to Van Halen in the opening lines of chapter 1 – it’s well-worn ground: Pythagorean tuning, the circle of fifths, equal temperament, Music of the Spheres (not the Coldplay album, mercifully), resonance, harmonics, etc. I found myself wishing, at times, for a take that felt a little more off the beaten track.

One case in point is Darling’s brief discussion of the theremin. If anything earns the title of “The Physicist’s Instrument”, it’s the theremin – a remarkable device that exploits the innate electrical capacitance of the human body to load a resonant circuit and thus produce an ethereal, haunting tone whose pitch can be varied, without, remarkably, any physical contact.

While I give kudos to Darling for highlighting the theremin, the brevity of the description is arguably a lost opportunity when put in the broader context of the book’s aim to explain the deeper connections between music, maths and science. This could have been a novel and fascinating take on the links between electrical and musical resonance that went well beyond the familiar territory mapped out in standard physics-of-music texts.

Using the music of the eclectic Australian band King Gizzard and the Lizard Wizard to explain microtonality is nothing short of inspired

As the book progresses, however, Darling moves into more distinctive territory, choosing a variety of inventive examples that are often fascinating and never short of thought-provoking. I particularly enjoyed his description of orbital resonance in the system of seven planets orbiting the red dwarf TRAPPIST-1, 41 light-years from Earth. The orbital periods have ratios, which, when mapped to musical intervals, correspond to a minor sixth, a major sixth, two perfect fifths, a perfect fourth and another perfect fifth. And it’s got to be said that using the music of the eclectic Australian band King Gizzard and the Lizard Wizard to explain microtonality is nothing short of inspired.

A Perfect Harmony doesn’t entirely close the cultural gap highlighted by Snow all those years ago, but it does hum along pleasantly in the space between. Though the subject matter occasionally echoes well-trodden themes, Darling’s perspective and enthusiasm lend it freshness. There’s plenty here to enjoy, especially for physicists inclined to tune into the harmonies of the universe.

• 2025 Oneworld Publications 288pp £10.99pb/£6.99e-book

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Stars are cosmic musical instruments: they vibrate with complex patterns that echo through their interiors. These vibrations, known as pressure waves, ripple through the star, similar to the earthquakes that shake our planet. The frequencies of these waves hold information about the star’s mass, age and internal structure.

In a study led by researchers at UNSW Sydney, Australia, astronomer Claudia Reyes and colleagues “listened” to the sound from stars in the M67 cluster and discovered a surprising feature: a plateau in their frequency pattern. This plateau appears during the subgiant and red giant phases of stars where they expand and evolve after exhausting the hydrogen fuel in their cores. This feature, reported in Nature, reveals how deep the outer layers of the star have pushed into the interior and offers a new diagnostic to improve mass and age estimates of stars beyond the main sequence (the core-hydrogen-burning phase).

How do stars create sound?

Beneath the surface of stars, hot gases are constantly rising, cooling and sinking back down, much like hot bubbles in boiling water. This constant churning is called convection. As these rising and sinking gas blobs collide or burst at the stellar surface, they generate pressure waves. These are essentially acoustic waves, bouncing within the stellar interior to create standing wave patterns.

Stars do not vibrate at just one frequency; they oscillate simultaneously at multiple frequencies, producing a spectrum of sounds. These acoustic oscillations cannot be heard in space directly, but are observed as tiny fluctuations in the star’s brightness over time.

M67 cluster as stellar laboratory

Star clusters offer an ideal environment in which to study stellar evolution as all stars in a cluster form from the same gas cloud at about the same time with the same chemical compositions but with different masses. The researchers investigated stars from the open cluster M67, as this cluster has a rich population of evolved stars including subgiants and red giants with a chemical composition similar to the Sun’s. They measured acoustic oscillations in 27 stars using data from NASA’s Kepler/K2 mission.

Stars oscillate across a range of tones, and in this study the researchers focused on two key features in this oscillation spectrum: large and small frequency separations. The large frequency separation, which probes stellar density, is the frequency difference between oscillations of the same angular degree (ℓ) but different radial orders (n). The small frequency separation refers to frequency differences between the modes of degrees ℓ and ℓ + 2, of consecutive orders of n.  For main sequence stars, small separations are reliable age indicators because their changes during hydrogen burning are well understood. In later stages of stellar evolution, however, their relationship to the stellar interior remained unclear.

In 27 stars, Reyes and colleagues investigated the small separation between modes of degrees 0 and 2. Plotting a graph of small versus large frequency separations for each star, called a C–D diagram, they uncovered a surprising plateau in small frequency separations.

The researchers traced this plateau to the evolution of the lower boundary of the star’s convective envelope. As the envelope expands and cools, this boundary sinks deeper into the interior. Along this boundary, the density and sound speed change rapidly due to the difference in chemical composition on either side. These steep changes cause acoustic glitches that disturb how the pressure waves move through the star and temporarily stall the evolution of the small frequency separations, observed as a plateau in the frequency pattern.

This stalling occurs at a specific stage in stellar evolution – when the convective envelope deepens enough to encompass nearly 80% of the star’s mass. To confirm this connection, the researchers varied the amount of convective boundary mixing in their stellar models. They found that the depth of the envelope directly influenced both the timing and shape of the plateau in the small separations.

A new window on galactic history

This plateau serves as a new diagnostic tool to identify a specific evolutionary stage in red giant stars and improve estimates of their mass and age.

“The discovery of the ‘plateau’ frequencies is significant because it represents one more corroboration of the accuracy of our stellar models, as it shows how the turbulent regions at the bottom of a star’s envelope affect the sound speed,” explains Reyes, who is now at the Australian National University in Canberra. “They also have great potential to help determine with ease and great accuracy the mass and age of a star, which is of great interest for galactic archaeology, the study of the history of our galaxy.”

The sounds of starquakes offer a new window to study the evolution of stars and, in turn, recreate the history of our galaxy. Clusters like M67 serve as benchmarks to study and test stellar models and understand the future evolution of stars like our Sun.

“We plan to look for stars in the field which have very well-determined masses and which are in their ‘plateau’ phase,” says Reyes. “We will use these stars to benchmark the diagnostic potential of the plateau frequencies as a tool, so it can later be applied to stars all over the galaxy.”

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