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Paul Dirac

From that insight, Dirac built an entirely new formulation of the theory using what he called “q-numbers” (quantum numbers)—abstract quantities that don’t commute. He independently rediscovered aspects of Hilbert’s operator theory, though he preferred his own algebraic route because he found mathematicians’ obsession with convergence and existence theorems unappealing.

Paul Adrien Maurice Dirac (, dih-RAK ; [ 3 ] 8 August 1902 – 20 October 1984) was a British theoretical physicist who is considered to be one of the founders of quantum mechanics. [ 4 ] [ 5 ] Dirac laid the foundations for both quantum electrodynamics and quantum field theory, coining the former term. [ 6 ] [ 7 ] [ 8 ] [ 9 ] He was Lucasian Professor of Mathematics at the University of Cambridge from 1932 to 1969, and a professor of physics at Florida State University from 1970 to 1984. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger “for the discovery of new productive forms of atomic theory.” [ 10 ]

Dirac graduated from the University of Bristol with a Bachelor of Science in Electrical Engineering in 1921, and a Bachelor of Arts in Mathematics in 1923. [ 11 ] Dirac then graduated from St John’s College, Cambridge, with a Doctor of Philosophy in Physics in 1926, writing the first ever thesis on quantum mechanics. [ 12 ]

He formulated the Dirac equation, one of the most important results in physics, in 1928. [ 7 ] It connected special relativity and quantum mechanics and predicted the existence of antimatter. [ 13 ] He wrote a famous paper in 1931, [ 14 ] which further predicted the existence of antimatter. [ 15 ] [ 16 ] [ 13 ] Dirac also contributed greatly to the reconciliation of general relativity with quantum mechanics. He contributed to Fermi–Dirac statistics, which describes the behaviour of fermions, particles with half-integer spin. His 1930 monograph, The Principles of Quantum Mechanics, is one of the most influential texts on the subject. [ 17 ] He and Schrödinger tied for eighth in a Physics World poll of the greatest physicists of all time. [ 18 ] .

Evidence of scaling advantage for the quantum approximate optimization algorithm on a classically intractable problem

We study the scaling of QAOA TTS with the problem size on the low autocorrelation binary sequences (LABS) problem (15, 16), also known as the Bernasconi model in statistical physics (17, 18). The LABS problem has applications in communications engineering, where the low autocorrelation sequences are used for designing radar pulses (15, 19). To solve LABS, one has to produce a sequence of N bits that minimizes a specific quartic objective.

We choose LABS to study the scaling of QAOA TTS for the following three reasons. First, the complexity of LABS grows rapidly, with optimal solutions known only for N ≤ 66 and the best heuristics producing approximate solutions of quality decaying with N for N 200 (20, 21). This makes it a promising candidate problem, since only a few hundred qubits are required to tackle classically intractable instances. Second, the performance of classical solvers for LABS has been benchmarked (20, 21) in terms of the scaling of their TTS with problem size. Since optimal solutions are only known for N ≤ 66, the scaling of TTS for all classical solvers is obtained by fitting results for N ≤ 66. We reproduce these results and observe that that the scaling of classical solvers at N ≤ 40 matches the behavior for N up to 66 reported in the literature. This provides evidence that the scaling we observe for QAOA at N ≤ 40 will similarly extrapolate to larger N. Third, LABS has only one instance per problem size N. Combined with the hardness of LABS, this makes it possible to reliably study the scaling of QAOA at large problem sizes, where simulating tens or hundreds of random instances would be computationally infeasible.

We obtain the scaling by performing noiseless exact simulation of QAOA with fixed schedules. Our results are enabled by a custom algorithm-specific graphics processing unit (GPU) simulator (22), which we execute using up to 1,024 GPUs per simulation on the Polaris supercomputer accessed through the Argonne Leadership Computing Facility. We find that the TTS of QAOA with number of layers p = 12 grows as 1.46N, which is improved to 1.21N if combined with quantum minimum finding. This scaling is better than that of the best classical heuristic, which has a TTS that grows as 1.34N. We note that we do not propose any new quantum algorithms in this work. Instead, we study a general quantum optimization heuristic with broad applicability (namely, QAOA) and make no specific modifications to adapt it to the LABS problem.

Taking dark energy out of the equation: Mathematicians challenge the standard cosmological model of the universe

Mathematicians are challenging the idea that dark energy is responsible for the accelerating expansion of the universe. In a new paper published in Proceedings of the Royal Society A, mathematicians from the University of California, Davis, provide mathematical proof that instabilities inherent in the Einstein-Euler equations imply that the current model of the expanding universe is not viable.

The Einstein-Euler equations are a union of general relativity and fluid dynamics equations used to model astronomical phenomena such as galaxies, black holes, and cosmic expansion.

The research directly challenges the Lambda-cold dark matter model, the standard cosmological model of the Big Bang.

Quantum tunnelling

In physics, quantum tunnel ling, barrier penetration, or simply tunnel ling is a quantum mechanical phenomenon in which an object such as an electron or atom passes through a potential energy barrier that, according to classical mechanics, should not be passable due to the object not having sufficient energy to pass or surmount the barrier.

Tunnelling is a consequence of the wave nature of matter and quantum indeterminacy. The quantum wave function describes the states of a particle or other physical system and wave equations such as the Schrödinger equation describe their evolution. In a system with a short, narrow potential barrier, a small part of wavefunction can appear outside of the barrier representing a probability for tunnel ling through the barrier.

Since the probability of transmission of a wave packet through a barrier decreases exponentially with the barrier height, the barrier width, and the tunnel ling particle’s mass, tunnel ling is seen most prominently in low-mass particles such as electrons tunnel ling through atomically narrow barriers. However tunnel ling has been observed with protons and even atoms and tunnel ling has been used to explain physical effects with particles this large.

Paul Vitányi

Consider teaching a computer how to read by giving it billions of books. You don’t teach it grammar rules or logic; you simply ask it to play a game: “Look at these words, and guess what word comes next.” To win this game at a world-class level, the computer can’t just memorize phrases. It has to start figuring out how the world works. If it’s reading a mystery novel, it needs to deduce who the killer is to guess the final sentence. If it’s reading a math textbook, it has to understand addition to predict the answer to a problem. This is the core idea explored in a recent scientific paper titled “Algorithmic Compression via Pretrained Neural Networks.”*The researchers look under the hood of today’s Large Language Models (LLMs)—like the AI assistants we use every day—to explain a fascinating mystery: Why does a machine trained merely to predict the next word end up looking like it can think, reason, and solve complex problems? Think about how a ZIP file works on your computer. If you have a massive text file filled with the word “apple” repeated a million times, a compression program won’t save all million words. It will compress it into a short rule: “Repeat ‘apple’ 1,000,000 times.” It turns a massive mountain of data into a tiny, elegant recipe. (learning how to learn). Because the AI is fed a massive, diverse diet of information, it can’t just memorize everything. Instead, it is forced to find the underlying “recipes” or rules behind the data it sees. When you type a prompt into an AI, it doesn’t just look up an answer in a database. It looks at your text, infers the “generative algorithm” (the underlying pattern or logic of what you are asking), and uses that pattern to compress the problem and generate the correct response. In essence, it deduces the hidden rules of the game on the fly. * Discover Complex Logic: When given a sequence of chess moves, the AI doesn’t just guess random moves; it actually reconstructs the abstract rules and evaluations of a chessboard in its digital “mind.” While this framework helps explain why AI is getting so smart, it also opens up big new questions. We know these models are compressing data and finding rules, but we still don’t fully understand the absolute limits of this approach. How close can a practical AI get to that theoretical “perfect” intelligence? What happens when the AI runs out of human data to learn from?

Vitányi was appointed professor of computer science at the University of Amsterdam, and researcher at the National Research Institute for Mathematics and Computer Science in the Netherlands (CWI, initially Mathematical Centre [MC]) where he is currently a CWI Fellow. He was guest professor at the University of Copenhagen in 1978; research associate at the Massachusetts Institute of Technology in 1985/1986; Gaikoku-Jin Kenkyuin (councilor professor) at INCOCSAT at the Tokyo Institute of Technology in 1998; visiting professor at Boston University in 2004, at Monash University in 1996 and at the National ICT of Australia NICTA at University of New South Wales in 2004/2005; visiting professor at and adjunct professor of computer science at the University of Waterloo from 2005.

Scientists discover strange “narwhal” waves that trap light beyond known limits

Physicists at Peking University have uncovered a new way to confine light far beyond conventional limits — without relying on metals and their inherent energy dissipation. By formulating the singular dispersion equation, the team discovered narwhal-shaped wavefunctions that trap light at deep-subwavelength volumes in purely dielectric materials. The advance, dubbed singulonics, could pave the way for ultra-efficient photonic chips, new quantum technologies, and imaging tools with unprecedented resolution.

Smartphones may soon be able to track hidden objects using LiDAR

Modern smartphones are packed with incredible technology, from high-resolution cameras and advanced graphics chips to AI processors. In premium models, this hardware includes LiDAR (light detection and ranging), which helps power augmented reality features and improve depth sensing.

And that capability could soon be in for a seriously impressive upgrade. Researchers at the Massachusetts Institute of Technology (MIT) have developed an algorithm that lets a phone’s LiDAR sensor detect objects hidden around corners. Details are in a paper published in the journal Nature.

Typically, this type of non-line-of-sight (NLOS) capability is found in labs and relies on bulky, expensive research-grade hardware. But the team’s breakthrough makes it possible for consumer LiDAR sensors to peek behind obstacles.

AI-powered stretchable computing patch can run algorithms directly on the body

A new skin-like computing patch developed at the University of Chicago Pritzker School of Molecular Engineering (UChicago PME) can analyze health data using artificial intelligence in an unprecedented way. Unlike today’s wearable devices, it carries out its AI computations directly on the body, in mere milliseconds, without relying on a wireless connection.

While your current smartwatch may be able to track your heart rate or movements, it doesn’t analyze what it finds. The analysis happens elsewhere, after it shuttles data to an external server. In some situations—detecting ventricular fibrillation in the heart, for instance—that few-seconds lag to communicate with the server is too long.

The new device, designed and tested in collaboration with researchers at Argonne National Laboratory, was made possible by the development of manufacturing processes that allow organic electrochemical transistors to be printed onto flexible surfaces.

AI atlas reveals hidden whole-body-damage caused by obesity

Obesity affects far more than metabolism and fat storage. It alters immune activity, nerve structure, and tissue organization across multiple organ systems, increasing the risk of diseases including type 2 diabetes, cardiovascular disease, stroke, neuropathy and cancer. Yet despite these systemic effects, researchers have lacked tools capable of studying disease-associated changes across the entire body in intact organisms and at high resolution.

A team led by Prof. Ali Ertürk, Director of the Institute for Biological Intelligence (iBIO) at Helmholtz Munich and Professor at the LMU, has now developed MouseMapper, a suite of foundation-model-based deep-learning algorithms designed to analyze whole-body biological imaging data. The framework automatically segments 31 organs and tissue types while quantitatively mapping nerves and immune cells throughout the body, enabling comprehensive multi-system analysis in intact mice.

“MouseMapper is built on a foundation model, which means it generalizes far beyond the data it was originally trained on,” says Ying Chen, co-first author of the study published in Nature.

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