Computers Math

In physics, things exist in “phases,” such as solid, liquid, gas. When something crosses from one phase to another, we talk about a “phase transition” — think about water boiling into steam, turning from liquid to gas.
In our kitchens water boils at 100oC, and its density changes dramatically, making a discontinuous jump from liquid to gas. However, if we turn up the pressure, the boiling point of water also increases, until a pressure of 221 atmospheres where it boils at 374oC. Here, something strange happens: the liquid and gas merge into a single phase. Above this “critical point,” there is no longer a phase transition at all, and so by controlling its pressure water can be steered from liquid to gas without ever crossing one.
Is there a quantum version of a water-like phase transition? “The current directions in quantum magnetism and spintronics require highly spin-anisotropic interactions to produce the physics of topological phases and protected qubits, but these interactions also favor discontinuous quantum phase transitions,” says Professor Henrik Rønnow at EPFL’s School of Basic Sciences.
Previous studies have focused on smooth, continuous phase transitions in quantum magnetic materials. Now, in a joint experimental and theoretical project led by Rønnow and Professor Frédéric Mila, also at the School of Basic Sciences, physicists at EPFL and the Paul Scherrer Institute have studied a discontinuous phase transition to observe the first ever critical point in a quantum magnet, similar to that of water. The work is now published in Nature.
The scientists used a “quantum antiferromagnet,” known in the field as SCBO (from its chemical composition: SrCu2(BO3)2). Quantum antiferromagnets are especially useful for understanding how the quantum aspects of a material’s structure affect its overall properties — for example, how the spins of its electrons interact to give its magnetic properties. SCBO is also a “frustrated” magnet, meaning that its electron spins can’t stabilize in some orderly structure, and instead they adopt some uniquely quantum fluctuating states.
In a complex experiment, the researchers controlled both the pressure and the magnetic field applied to milligram pieces of SCBO. “This allowed us to look all around the discontinuous quantum phase transition and that way we found critical-point physics in a pure spin system,” says Rønnow.
The team performed high-precision measurements of the specific heat of SCBO, which shows its readiness to “suck up energy.” For example, water absorbs only small amounts of energy at -10oC, but at 0oC and 100oC it can take up huge amounts as every molecule is driven across the transitions from ice to liquid and liquid to gas. Just like water, the pressure-temperature relationship of SCBO forms a phase diagram showing a discontinuous transition line separating two quantum magnetic phases, with the line ending at a critical point.
“Now when a magnetic field is applied, the problem becomes richer than water,” says Frédéric Mila. “Neither magnetic phase is strongly affected by a small field, so the line becomes a wall of discontinuities in a three-dimensional phase diagram — but then one of the phases becomes unstable and the field helps push it towards a third phase.”
To explain this macroscopic quantum behavior, the researchers teamed up with several colleagues, particularly Professor Philippe Corboz at the University of Amsterdam, who have been developing powerful new computer-based techniques.
“Previously it was not possible to calculate the properties of ‘frustrated’ quantum magnets in a realistic two- or three-dimensional model,” says Mila. “So SCBO provides a well-timed example where the new numerical methods meet reality to provide a quantitative explanation of a phenomenon new to quantum magnetism.”
Henrik Rønnow concludes: “Looking forward, the next generation of functional quantum materials will be switched across discontinuous phase transitions, so a proper understanding of their thermal properties will certainly include the critical point, whose classical version has been known to science for two centuries.” More

The electronic properties of solid materials are highly dependent on crystal structures and their dimensionalities (i.e., whether the crystals have predominantly 2D or 3D structures). As Professor Takayoshi Katase of Tokyo Institute of Technology notes, this fact has an important corollary: “If the crystal structure dimensionality can be switched reversibly in the same material, a drastic property change may be controllable.” This insight led Prof. Katase and his research team at Tokyo Institute of Technology, in partnership with collaborators at Osaka University and National Institute for Materials Science, to embark on research into the possibility of switching the crystal structure dimensionality of a lead-tin-selenide alloy semiconductor. Their results appear in a paper published in a recent issue of the peer-reviewed journal Science Advances.
The lead-tin-selenide alloy, (Pb1-xSnx)Se is an appropriate focus for such research because the lead ions (Pb2+) and tin ions (Sn2+) favor distinct crystal dimensionalities. Specifically, pure lead selenide (PbSe) has a 3D crystal structure, whereas pure tin selenide (SnSe) has a 2D crystal structure. SnSe has bandgap of 1.1 eV, similar to the conventional semiconductor Si. Meanwhile, PbSe has narrow bandgap of 0.3 eV and shows 1 order of magnitude higher carrier mobility than SnSe. In particular, the 3D (Pb1-xSnx)Se has gathered much attention as a topological insulator. That is, the substitution for Pb with Sn in the 3D PbSe reduces the band gap and finally produces a gap-less Dirac-like state. Therefore, if these crystal structure dimensionality can be switched by external stresses such as temperature, it would lead to a giant functional phase transition, such as large electronic conductivity change and topological state transition, enhanced by the distinct electronic structure changes.
The alloying PbSe and SnSe would manipulate the drastic transition in structure, and such (Pb1-xSnx)Se alloy should induce strong frustration around phase boundaries. However, there is no direct phase boundary between the 3D PbSe and the 2D SnSe phases under thermal equilibrium. Through their experiments, Prof. Katase and his research team successfully developed a method for growing the nonequilibrium lead-tin-selenide alloy crystals with equal amounts of Pb2+ and Sn2+ ions (i.e., (Pb0.5Sn0.5)Se) that underwent direct structural phase transitions between 2D and 3D forms based on temperature. At lower temperatures, the 2D crystal structure predominated, whereas at higher temperatures, the 3D structure predominated. The low-temperature 2D crystal structure was more resistant to electrical current than the high-temperature 3D crystal was, and as the alloy was heated, its resistivity levels took a sharp dive around the temperatures at which the dimensionality phase transition occurred. The present strategy facilitates different structure dimensionality switching and further functional property switching in semiconductors using artificial phase boundary.
In sum, the research team developed a form of the semiconductor alloy (Pb1-xSnx)Se that undergoes temperature-dependent crystal dimensionality phase transitions, and these transitions have major implications for the alloy’s electronic properties. When asked about the importance of his team’s work, Prof. Katase notes that this form of the (Pb1-xSnx)Se alloy can “serve as a platform for fundamental scientific studies as well as the development of novel function in semiconductor technologies.” This specialized alloy may, therefore, lead to exciting new semiconductor technologies with myriad benefits for humanity.
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Physicists from Swansea University are part of an international research collaboration which has identified a new technique for testing the quality of quantum correlations.
Quantum computers run their algorithms on large quantum systems of many parts, called qubits, by creating quantum correlations across all of them. It is important to verify that the actual computation procedures lead to quantum correlations of desired quality.
However, carrying out these checks is resource-intensive as the number of tests required grows exponentially with the number of qubits involved.
Researchers from the College of Science, working with colleagues from Spain and Germany, have now proposed a new technique that helps to overcome this problem by significantly reducing the number of measurements while increasing the resilience against noise.
Their method offers a solution to the problem of certifying correlations in large systems and is explained in a new paper which has just been published in PRX Quantum, a journal from American Physical Society.
Research fellow Dr Farid Shahandeh, the lead scientist of this research, said: “To achieve this we combine two processes. Firstly, consider a juicer — it extracts the essence of the fruit by squeezing it into a small space. Similarly, in many cases quantum correlations in large systems can also be concentrated in smaller parts of the system. The ‘squeezing’ is done by measurements on the rest of the system called the localization process.
“Suppose the juicer directly converts the fruit into juice boxes without any labels. We don’t know what is inside — it could be apple juice, orange juice, or just water. One way to tell would be to open the box and taste it. The quantum comparison of this is to measure a suitable quantity that tells us whether quantum correlations exist within a system or not.
“This process is called witnessing and we call the combination of the two approaches conditional witnessing.”
In their research the physicists prove their method is efficient and generically tolerates higher levels of noise in experiments. They have also compared their approach with previous techniques in a class of quantum processors that use ions to demonstrate its efficiency.
Dr Shahandeh, the recipient of a Royal Commission for the Exhibition of 1851 research fellowship, added: “This is of crucial importance in current technology where the addition of each qubit unavoidably amplifies the complexity of quantum states and experimental imperfections.”
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Artificial intelligence could be one of the keys for limiting the spread of infection in future pandemics. In a new study, researchers at the University of Gothenburg have investigated how machine learning can be used to find effective testing methods during epidemic outbreaks, thereby helping to better control the outbreaks.
In the study, the researchers developed a method to improve testing strategies during epidemic outbreaks and with relatively limited information be able to predict which individuals offer the best potential for testing.
“This can be a first step towards society gaining better control of future major outbreaks and reduce the need to shutdown society,” says Laura Natali, a doctoral student in physics at the University of Gothenburg and the lead author of the published study.
Machine learning is a type of artificial intelligence and can be described as a mathematical model where computers are trained to learn to see connections and solve problems using different data sets. The researchers used machine learning in a simulation of an epidemic outbreak, where information about the first confirmed cases was used to estimate infections in the rest of the population. Data about the infected individual’s network of contacts and other information was used: who they have been in close contact with, where and for how long.
“In the study, the outbreak can quickly be brought under control when the method is used, while random testing leads to uncontrolled spread of the outbreak with many more infected individuals. Under real world conditions, information can be added, such as demographic data, age and health-related conditions, which can improve the method’s effectiveness even more. The same method can also be used to prevent reinfections in the population if immunity after the disease is only temporary.”
She emphasises that the study is a simulation and that testing with real data is needed to improve the method even more. Therefore, it is too early to use it in the ongoing coronavirus pandemic. At the same time, she sees the research as a first step in being able to implement more targeted initiatives to reduce the spread of infections, since the machine learning-based testing strategy automatically adapts to the specific characteristics of diseases. As an example, she mentions the potential to easily predict if a specific age group should be tested or if a limited geographic area is a risk zone, such as a school, a community or a specific neighbourhood.
“When a large outbreak has begun, it is important to quickly and effectively identify infectious individuals. In random testing, there is a significant risk failing to achieve this, but with a more goal-oriented testing strategy we can find more infected individuals and thereby also gain the necessary information to decrease the spread of infection. We show that machine learning can be used to develop this type of testing strategy,” she says.
There are few previous studies that have examined how machine learning can be used in cases of pandemics, particularly with a clear focus on finding the best testing strategies.
“We show that it is possible to use relatively simple and limited information to make predictions of who would be most beneficial to test. This allows better use of available testing resources.”
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The “three-body problem,” the term coined for predicting the motion of three gravitating bodies in space, is essential for understanding a variety of astrophysical processes as well as a large class of mechanical problems, and has occupied some of the world’s best physicists, astronomers and mathematicians for over three centuries. Their attempts have led to the discovery of several important fields of science; yet its solution remained a mystery.
At the end of the 17th century, Sir Isaac Newton succeeded in explaining the motion of the planets around the sun through a law of universal gravitation. He also sought to explain the motion of the moon. Since both the earth and the sun determine the motion of the moon, Newton became interested in the problem of predicting the motion of three bodies moving in space under the influence of their mutual gravitational attraction (see attached illustration), a problem that later became known as “the three-body problem.”
However, unlike the two-body problem, Newton was unable to obtain a general mathematical solution for it. Indeed, the three-body problem proved easy to define, yet difficult to solve.
New research, led by Professor Barak Kol at Hebrew University of Jerusalem’s Racah Institute of Physics, adds a step to this scientific journey that began with Newton, touching on the limits of scientific prediction and the role of chaos in it.
The theoretical study presents a novel and exact reduction of the problem, enabled by a re-examination of the basic concepts that underlie previous theories. It allows for a precise prediction of the probability for each of the three bodies to escape the system.
Following Newton and two centuries of fruitful research in the field including by Euler, Lagrange and Jacobi, by the late 19th century the mathematician Poincare discovered that the problem exhibits extreme sensitivity to the bodies’ initial positions and velocities. This sensitivity, which later became known as chaos, has far-reaching implications — it indicates that there is no deterministic solution in closed-form to the three-body problem. More

Despite increasing concern over the intrusion of algorithms in daily life, people may be more willing to trust a computer program than their fellow humans, especially if a task becomes too challenging, according to new research from data scientists at the University of Georgia.
From choosing the next song on your playlist to choosing the right size pants, people are relying more on the advice of algorithms to help make everyday decisions and streamline their lives.
“Algorithms are able to do a huge number of tasks, and the number of tasks that they are able to do is expanding practically every day,” said Eric Bogert, a Ph.D. student in the Terry College of Business Department of Management Information Systems. “It seems like there’s a bias towards leaning more heavily on algorithms as a task gets harder and that effect is stronger than the bias towards relying on advice from other people.”
Bogert worked with management information systems professor Rick Watson and assistant professor Aaron Schecter on the paper, “Humans rely more on algorithms than social influence as a task becomes more difficult,” which was published April 13 in Nature’s Scientific Reports journal.
Their study, which involved 1,500 individuals evaluating photographs, is part of a larger body of work analyzing how and when people work with algorithms to process information and make decisions.
For this study, the team asked volunteers to count the number of people in a photograph of a crowd and supplied suggestions that were generated by a group of other people and suggestions generated by an algorithm. More

Studies show wearing masks and social distancing can contain the spread of the COVID-19 virus, but their combined effectiveness is not precisely known.
In Chaos, by AIP Publishing, researchers at New York University and Politecnico di Torino in Italy developed a network model to study the effects of these two measures on the spread of airborne diseases like COVID-19. The model shows viral outbreaks can be prevented if at least 60% of a population complies with both measures.
“Neither social distancing nor mask wearing alone are likely sufficient to halt the spread of COVID-19, unless almost the entire population adheres to the single measure,” author Maurizio Porfiri said. “But if a significant fraction of the population adheres to both measures, viral spreading can be prevented without mass vaccination.”
A network model encompasses nodes, or data points, and edges, or links between nodes. Such models are used in applications ranging from marketing to tracking bird migration. In the researchers’ model, based on a susceptible, exposed, infected, or removed (recovered or has died) framework, each node represents a person’s health status. The edges represent potential contacts between pairs of individuals.
The model accounts for activity variability, meaning a few highly active nodes are responsible for much of the network’s contacts. This mirrors the validated assumption that most people have few interactions and only a few interact with many others. Scenarios involving social distancing without mask wearing and vice versa were also tested by setting up the measures as separate variables.
The model drew on cellphone mobility data and Facebook surveys obtained from the Institute for Health Metrics and Evaluation at the University of Washington. The data showed people who wear masks are also those who tend to reduce their mobility. Based on this premise, nodes were split into individuals who regularly wear masks and socially distance and those whose behavior remains largely unchanged by an epidemic or pandemic.
Using data collected by The New York Times to gauge the model’s effectiveness, the researchers analyzed the cumulative cases per capita in all 50 states and the District of Columbia between July 14, 2020, when the Centers for Disease Control and Prevention officially recommended mask wearing, through Dec. 10.
In addition to showing the effects of combining mask wearing and social distancing, the model shows the critical need for widespread adherence to public health measures.
“U.S. states suffering the most from the largest number of infections last fall were also those where people complied less with public health guidelines, thereby falling well above the epidemic threshold predicted by our model,” Porfiri said.
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Light can be used to operate quantum information processing systems, e.g. quantum computers, quickly and efficiently. Researchers at Karlsruhe Institute of Technology (KIT) and Chimie ParisTech/CNRS have now significantly advanced the development of molecule-based materials suitable for use as light-addressable fundamental quantum units. As they report in the journal Nature Communications, they have demonstrated for the first time the possibility of addressing nuclear spin levels of a molecular complex of europium(III) rare-earth ions with light.
Whether in drug development, communication, or for climate forecasts: Processing information quickly and efficiently is crucial in many areas. It is currently done using digital computers, which work with so-called bits. The state of a bit is either 0 or 1 — there is nothing in between. This severely limits the performance of digital computers, and it is becoming increasingly difficult and time-consuming to handle complex problems related to real-world tasks. Quantum computers, on the other hand, use quantum bits to process information. A quantum bit (qubit) can be in many different states between 0 and 1 simultaneously due to a special quantum mechanical property referred to as quantum superposition. This makes it possible to process data in parallel, which increases the computing power of quantum computers exponentially compared to digital computers.
Qubit Superposition States Are Required to Persist Long Enough
“In order to develop practically applicable quantum computers, the superposition states of a qubit should persist for a sufficiently long time. Researchers speak of ‘coherence lifetime’,” explains Professor Mario Ruben, head of the Molecular Materials research group at KIT’s Institute of Nanotechnology (INT). “However, the superposition states of a qubit are fragile and are disturbed by fluctuations in the environment, which leads to decoherence, i.e. shortening of the coherence lifetime.” To preserve the superposition state long enough for computational operations, isolating a qubit from the noisy environment is conceivable. Nuclear spin levels in molecules can be used to create superposition states with long coherence lifetimes because nuclear spins are weakly coupled to the environment, protecting the superposition states of a qubit from disturbing external influences.
Molecules Are Ideally Suited As Qubit Systems
One single qubit, however, is not enough to build a quantum computer. Many qubits to be organized and addressed are required. Molecules represent ideal qubit systems as they can be arranged in sufficiently large numbers as identical scalable units and can be addressed with light to perform qubit operations. In addition, the physical properties of molecules, such as emission and/or magnetic properties, can be tailored by changing their structures using chemical design principles. In their paper now published in the journal Nature Communications, researchers led by Professor Mario Ruben at KIT’s IQMT and Strasbourg´s European Center for Quantum Sciences — CESQ and Dr. Philippe Goldner at École nationale supérieure de chimie de Paris (Chimie ParisTech/CNRS) present a nuclear-spin-containing dimeric europium(III) molecule as light-addressable qubit.
The molecule, which belongs to the rare earth metals, is designed to exhibit luminescence, i.e., a europium(III)-centered sensitized emission, when excited by ultraviolet light-absorbing ligands surrounding the center. After light absorption, the ligands transfer the light energy to the europium(III) center, thereby exciting it. Relaxation of the excited center to the ground state leads to light emission. The whole process is referred to as sensitized luminescence. Spectral hole burning — special experiments with lasers — detect the polarization of the nuclear spin levels, indicating the generation of a efficient light-nuclear spin interface. The latter enables the generation of light-addressable hyperfine qubits based on nuclear spin levels. “By demonstrating for the first time light-induced spin polarization in the europium(III) molecule, we have succeeded in taking a promising step towards the development of quantum computing architectures based on rare-earth ion-containing molecules,” explains Dr. Philippe Goldner.
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