Aurelia Butler

For the first time, mathematicians have partnered with artificial intelligence to suggest and prove new mathematical theorems. The work was done in a collaboration between the University of Oxford, the University of Sydney in Australia and DeepMind, Google’s artificial intelligence sister company.
While computers have long been used to generate data for mathematicians, the task of identifying interesting patterns has relied mainly on the intuition of the mathematicians themselves. However, it’s now possible to generate more data than any mathematician can reasonably expect to study in a lifetime. Which is where machine learning comes in.
A paper, published today in Nature, describes how DeepMind was set the task of discerning patterns and connections in the fields of knot theory and representation theory. To the surprise of the mathematicians, new connections were suggested; the mathematicians were then able to examine these connections and prove the conjecture suggested by the AI. These results suggest that machine learning can complement mathematical research, guiding intuition about a problem.
Using the patterns identified by machine learning, mathematicians from the University of Oxford discovered a surprising connection between algebraic and geometric invariants of knots, establishing a completely new theorem in the field. The University of Sydney, meanwhile, used the connections made by the AI to bring them close to proving an old conjecture about Kazhdan-Lusztig polynomials, which has been unsolved for 40 years.
Professor Andras Juhasz, of the Mathematical Institute at the University of Oxford and co-author on the paper, said: ‘Pure mathematicians work by formulating conjectures and proving these, resulting in theorems. But where do the conjectures come from?
‘We have demonstrated that, when guided by mathematical intuition, machine learning provides a powerful framework that can uncover interesting and provable conjectures in areas where a large amount of data is available, or where the objects are too large to study with classical methods.’
Professor Marc Lackeby, of the Mathematical Institute at the University of Oxford and co-author, said: ‘It has been fascinating to use machine learning to discover new and unexpected connections between different areas of mathematics. I believe that the work that we have done in Oxford and in Sydney in collaboration with DeepMind demonstrates that machine learning can be a genuinely useful tool in mathematical research.’
Professor Geordie Williamson, Professor of Mathematics at the University of Sydney and director of the Sydney Mathematical Research Institute and co-author, said: ‘AI is an extraordinary tool. This work is one of the first times it has demonstrated its usefulness for pure mathematicians, like me.
‘Intuition can take us a long way, but AI can help us find connections the human mind might not always easily spot.’
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For quantum computers to surpass their classical counterparts in speed and capacity, their qubits — which are superconducting circuits that can exist in an infinite combination of binary states — need to be on the same wavelength. Achieving this, however, has come at the cost of size. Whereas the transistors used in classical computers have been shrunk down to nanometer scales, superconducting qubits these days are still measured in millimeters — one millimeter is one million nanometers.
Combine qubits together into larger and larger circuit chips, and you end up with, relatively speaking, a big physical footprint, which means quantum computers take up a lot of physical space. These are not yet devices we can carry in our backpacks or wear on our wrists.
To shrink qubits down while maintaining their performance, the field needs a new way to build the capacitors that store the energy that “powers” the qubits. In collaboration with Raytheon BBN Technologies, Wang Fong-Jen Professor James Hone’s lab at Columbia Engineering recently demonstrated a superconducting qubit capacitor built with 2D materials that’s a fraction of previous sizes.
To build qubit chips previously, engineers have had to use planar capacitors, which set the necessary charged plates side by side. Stacking those plates would save space, but the metals used in conventional parallel capacitors interfere with qubit information storage. In the current work, published on November 18 in Nano Letters, Hone’s PhD students Abhinandan Antony and Anjaly Rajendra sandwiched an insulating layer of boron nitride between two charged plates of superconducting niobium dieselenide. These layers are each just a single atom thick and held together by van der Waals forces, the weak interaction between electrons. The team then combined their capacitors with aluminum circuits to create a chip containing two qubits with an area of 109 square micrometers and just 35 nanometers thick — that’s 1,000 times smaller than chips produced under conventional approaches.
When they cooled their qubit chip down to just above absolute zero, the qubits found the same wavelength. The team also observed key characteristics that showed that the two qubits were becoming entangled and acting as a single unit, a phenomenon known as quantum coherence; that would mean the qubit’s quantum state could be manipulated and read out via electrical pulses, said Hone. The coherence time was short — a little over 1 microsecond, compared to about 10 microseconds for a conventionally built coplanar capacitor, but this is only a first step in exploring the use of 2D materials in this area, he said.
Separate work published on arXiv in August from researchers at MIT also took advantage of niobium diselenide and boron nitride to build parallel-plate capacitors for qubits. The devices studied by the MIT team showed even longer coherence times — up to 25 microseconds — indicating that there is still room to further improve performance.
From here, Hone and his team will continue refining their fabrication techniques and test other types of 2D materials to increase coherence times, which reflect how long the qubit is storing information. New device designs should be able to shrink things down even further, said Hone, by combining the elements into a single van der Waals stack or by deploying 2D materials for other parts of the circuit.
“We now know that 2D materials may hold the key to making quantum computers possible,” Hone said. “It is still very early days, but findings like these will spur researchers worldwide to consider novel applications of 2D materials. We hope to see a lot more work in this direction going forward.”
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Materials provided by Columbia University School of Engineering and Applied Science. Original written by Ellen Neff. Note: Content may be edited for style and length. More

There is a huge global effort to engineer a computer capable of harnessing the power of quantum physics to carry out computations of unprecedented complexity. While formidable technological obstacles still stand in the way of creating such a quantum computer, today’s early prototypes are still capable of remarkable feats.
For example, the creation of a new phase of matter called a “time crystal.” Just as a crystal’s structure repeats in space, a time crystal repeats in time and, importantly, does so infinitely and without any further input of energy — like a clock that runs forever without any batteries. The quest to realize this phase of matter has been a longstanding challenge in theory and experiment — one that has now finally come to fruition.
In research published Nov. 30 in Nature, a team of scientists from Stanford University, Google Quantum AI, the Max Planck Institute for Physics of Complex Systems and Oxford University detail their creation of a time crystal using Google’s Sycamore quantum computing hardware.
“The big picture is that we are taking the devices that are meant to be the quantum computers of the future and thinking of them as complex quantum systems in their own right,” said Matteo Ippoliti, a postdoctoral scholar at Stanford and co-lead author of the work. “Instead of computation, we’re putting the computer to work as a new experimental platform to realize and detect new phases of matter.”
For the team, the excitement of their achievement lies not only in creating a new phase of matter but in opening up opportunities to explore new regimes in their field of condensed matter physics, which studies the novel phenomena and properties brought about by the collective interactions of many objects in a system. (Such interactions can be far richer than the properties of the individual objects.)
“Time-crystals are a striking example of a new type of non-equilibrium quantum phase of matter,” said Vedika Khemani, assistant professor of physics at Stanford and a senior author of the paper. “While much of our understanding of condensed matter physics is based on equilibrium systems, these new quantum devices are providing us a fascinating window into new non-equilibrium regimes in many-body physics.”
What a time crystal is and isn’t More

Grouping of pathogen-recognising proteins on immune T cells may be key to identifying if someone has had an infection in the past, suggests a study published today in eLife.
While tests measuring antibodies against a pathogen are often used to detect signs of a previous infection, it is more difficult for researchers to measure the strength and targets of a person’s T-cell response to infection or vaccination, but the findings hint at a potential new approach. This patient information could one day be useful for detecting infections, guiding treatments or supporting the research and development of new therapies and vaccines.
Immune T cells help the body find and destroy harmful viruses and bacteria. Proteins on the outer surface of T cells — called receptors — allow the T cells to recognise and eliminate human cells that have been infected by specific pathogens.
“While the abundance of specific receptors could provide clues about past infection, the enormous molecular diversity of T-cell receptors makes it incredibly challenging to assess which receptors recognise which pathogens. Not only is each pathogen recognised by a distinct set of receptors, but each individual develops a personalised set of receptors for each pathogen,” explains first author Koshlan Mayer-Blackwell, Senior Data Scientist at Fred Hutchinson Cancer Research Center, Seattle, Washington, US. “We developed a new computational approach that allows us to find similarities among pathogen-specific T-cell receptors across individuals. Ultimately, we hope this will help develop signatures of past infection despite the enormous diversity of T-cell receptors.”
The team tested their approach using data from the immuneRACE study of T-cell receptors in patients with COVID-19. Using their new software for rapidly comparing large sets of receptors, they were able to generate 1,831 T-cell receptor groupings based on similarities in the receptors’ amino acid sequences that suggest they have similar functions.
In an independent group of COVID-19 patients, the team found that the common molecular patterns associated with receptor groupings were more robustly detected than individual receptor sequences that were previously hypothesised to recognise parts of the SARS-CoV-2 virus, demonstrating a major improvement on existing approaches.
“Our study introduces and validates a flexible approach to identify sets of similar T-cell receptors, which we hope will be broadly useful for scientists studying T-cell immunity,” Mayer-Blackwell says. “Grouping receptors together in this way makes it possible to compare responses to infection or vaccination across a diverse population.”
To help other researchers use this approach to develop T-cell biomarkers with their own data, the team has created free customisable software called tcrdist3.
“Our software provides flexible tools that will enable scientists to analyse and integrate the rapidly growing libraries of T-cell receptor sequencing data that are needed to identify the features of pathogen-specific T-cell receptors,” concludes senior author Andrew Fiore-Gartland, Co-Director of the Vaccines and Immunology Statistical Center at the Fred Hutchinson Cancer Research Center. “We hope it will open new opportunities not only to identify patients’ immunological memories of past infections and vaccinations but also to predict their future immune responses.”
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The quantum world and our everyday world are very different places. In a publication that appeared as the “Editor’s Suggestion” in Physical Review A this week, UvA physicists Jasper van Wezel and Lotte Mertens and their colleagues investigate how the act of measuring a quantum particle transforms it into an everyday object.
Quantum mechanics is the theory that describes the tiniest objects in the world around us, ranging from the constituents of single atoms to small dust particles. This microscopic realm behaves remarkably differently from our everyday experience — despite the fact that all objects in our human-scale world are made of quantum particles themselves. This leads to intriguing physical questions: why are the quantum world and the macroscopic world so different, where is the dividing line between them, and what exactly happens there?
Measurement problem
One particular area where the distinction between quantum and classical becomes essential is when we use an everyday object to measure a quantum system. The division between the quantum and everyday worlds then amounts to asking how ‘big’ the measurement device should be to be able to show quantum properties using a display in our everyday world. Finding out the details of measurement, such as how many quantum particles it takes to create a measurement device, is called the quantum measurement problem.
As experiments probing the world of quantum mechanics become ever more advanced and involve ever larger quantum objects, the invisible line where pure quantum behaviour crosses over into classical measurement outcomes is rapidly being approached. In an article that was highlighted as “Editor’s Suggestion” in Physical Review A this week, UvA physicists Jasper van Wezel and Lotte Mertens and their colleagues take stock of current models that attempt to solve the measurement problem, and particularly those that do so by proposing slight modifications to the one equation that rules all quantum behaviour: Schrödinger’s equation.
Born’s rule
The researchers show that such amendments can in principle lead to consistent proposals for solving the measurement problem. However, it turns out to be difficult to create models that satisfy Born’s rule, which tells us how to use Schrödinger’s equation for predicting measurement outcomes. The researchers show that only models with sufficient mathematical complexity (in technical terms: models that are non-linear and non-unitary) can give rise to Born’s rule and therefore have a chance of solving the measurement problem and teaching us about the elusive crossover between quantum physics and the everyday world.
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Scientists used animated humanoid avatars to study how nonverbal cues influence people’s behavior. Reported in the Journal of Cognitive Neuroscience, the research offers insight into the brain mechanisms that drive social and economic decision-making.
The study revealed that participants were more willing to cooperate with animated avatars than with static figures representing their negotiation partners. It also found — somewhat surprisingly — that people were more willing to accept unfair offers from unfriendly avatars than from friendly ones.
“This work is an extension of previous studies exploring how nonverbal cues influence people’s perceptions of one another,” said Matthew Moore, who led the research at the University of Illinois Urbana-Champaign with psychology professors Florin Dolcos and Sanda Dolcos. The new research was conducted at the U. of I.’s Beckman Institute for Advanced Science and Technology, where Moore was a postdoctoral fellow.
“Nonverbal interactions represent a huge part of human communication,” Sanda Dolcos said. “We might not be aware of this, but much of the information that we take in is through these nonverbal channels.”
Previous studies often used still photos or other static representations of people engaged in social interactions to study how people form opinions or make decisions, Florin Dolcos said.
“By animating the avatars, we’re capturing interactions that are much closer to what happens in real-life situations,” he said. More

A promising route towards larger quantum computers is to orchestrate multiple task-optimised smaller systems. To dynamically connect and entangle any two systems, photonic interference emerges as a powerful method, due to its compatibility with on-chip devices and long-distance propagation in quantum networks.
One of the main obstacles towards the commercialization of quantum photonics remains the nanoscale fabrication and integration of scalable quantum systems due to their notorious sensitivity to the smallest disturbances in the close environment. This has made it an extraordinary challenge to develop systems that can be used for quantum computing while simultaneously offering an efficient optical interface.
A recent result published in Nature Materials shows how the integration obstacle can be overcome. The work is based on a multi-national collaboration with researchers from Universities of Stuttgart (Physics 3), California — Davis, Linköping and Kyoto, as well as the Fraunhofer Institute at Erlangen, the Helmholtz Centre at Dresden and the Leibniz-Institute at Leipzig.
The researchers followed a two-step approach. First, their quantum system of choice is the so-called silicon vacancy centre in silicon carbide, which is known to possess particularly robust spin-optical properties. Second, they fabricated nanophotonic waveguides around these colour centres using gentle processing methods that keep the host material essentially free of damage.
“With our approach, we could demonstrate that the excellent spin-optical properties of our colour centres are maintained after nanophotonic integration.” says Florian Kaiser, Assistant Professor at the University of Stuttgart, the supervisor of this project. “Thanks to the robustness of our quantum devices, we gained enough headroom to perform quantum gates on multiple nuclear spin qubits. As these spins show very long coherence times, they are excellent for implementing small quantum computers.”
“In this project, we explored the peculiar triangular shape of photonic devices. While this geometry is of commercial appeal because it provides versatility needed for scalable production, little has been known about its utility for high performing quantum hardware. Our studies reveal that light emitted by the colour centre, which carries quantum information across the chip, can be efficiently propagated through a single optical mode. This is a key conclusion for viability of integration of colour centres with other photonic devices, such as nanocavities, optical fibre and single-photon detectors, needed to realize full functionalities of quantum networking and computing.” — says Marina Radulaski, Assistant Professor at the University of California — Davis.
What makes the silicon carbide platform particularly interesting are its CMOS compatibility and its heavy usage as high-power semiconductor in electric mobility. The researchers now want to benefit from these aspects to leverage the scalable production of spin-photonics chips. Additionally, they want to implement semiconductor circuitry to electrically initialise and readout the quantum states of their spin qubits. “Maximising electrical control — instead of traditional optical control via lasers — is an important step towards system simplification. The combination of efficient nanophotonics with electrical control will allow us to reliably integrate more quantum systems on one chip, which will result in significant performance gains.,” adds Florian Kaiser, “In this sense, we are only at the dawn of quantum technologies with colour centres in silicon carbide. Our successful nanophotonic integration is not only an exciting enabler for distributed quantum computing, but it can also boost the performance of compact quantum sensors.”
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