classical limit

A quantum particle moves in a circle, passing through several stations. At each station, something happens to it — for example, its properties change slightly. After completing a full circle, the particle returns, but its state is no longer exactly what it was at the start.

A quantum computer is like a fragile snowflake resting on a warm palm. The slightest breath of heat or a gentle vibration, and it turns into a droplet. To keep the snowflake alive, you constantly adjust it, restoring its original shape. That's quantum error correction.

The Josephson junction is a bridge made of superconductor, separated by an ultra-thin insulating layer. Current flows through it even without voltage. But when the current becomes too large, the bridge starts to oscillate, and even steps, Shapiro steps, appear on the voltage graph. Between these steps hide invisible gaps where the system behaves strangely.

An electrical grid stuffed with power electronics resembles a huge orchestra without a conductor. Each converter, each line adds its own note, and sometimes the instruments start playing out of tune.

General relativity, which describes the structure of the universe, does not forbid closed timelike curves. But Stephen Hawking put forward the 'chronology protection' conjecture: quantum effects should destroy such curves, making time travel to the past impossible.

Quantum devices are no longer lab curiosities. They are assembled, tuned, and repaired like ordinary hardware — except inside them, it's not just current but intricate tangles of particles that can exist in multiple states at once. Engineers draw schematics, programmers write code, physicists calculate effects.

Searching for the global minimum in the Sherrington–Kirkpatrick spin glass model resembles climbing a glacier, where every crevasse is a treacherous local optimum, and the true bottom lies buried beneath a chaos of ice blocks. A classical climber, trudging along the gradient, would almost certainly freeze in the nearest crevice.

In classical thermodynamics, heat engines are like a virtuoso musician on stage: the closer to perfection in performance (Carnot efficiency), the slower the tempo (power).

The Mpemba effect is a mystery where hot вода sometimes freezes faster than warm water. Usually this is attributed to how вода loses heat and энтропию (a measure of disorder). But in a glass of water, chaos prevents a precise model. Physicists built a quantum model: a particle in a well with two depressions separated by a barrier.

The classical neuron is a chamber musician, drawing only one note from each string: it takes a weighted sum of inputs, adds a bias, and passes it through a nonlinearity.

A quantum computer is like a finicky musical instrument: the slightest change in temperature, humidity, or string tuning, and the melody sounds different.

Once Richard Feynman saw in quantum systems a challenge for classical computers. Now we face the inverse problem: understanding what exactly the quantum processor has simulated. Among the states it births are veritable 'black boxes'—topological phases of matter.

A network of tiny magnets seeks the state with the lowest total energy: that's roughly what the quantum Max Cut problem looks like, one of the toughest in physics. Scientists have been hunting for its solution since the days of Werner Heisenberg.

In a phone battery, there is always energy that cannot be extracted: it seems glued to the terminals. In the quantum world, this "glued" part is called bound energy. The authors showed that if you connect a helper particle to the battery (it only observes, but doesn't give up its own), bound energy ceases to be dead weight. The key finding is a hard ceiling for this enhancement.

Training a large neural network across hundreds of compute nodes is like making soup as a team: each 'chef' tastes the dish and tells the others what to adjust.

In the world of atoms and particles, everything tends toward rest: particles lose energy, just as a swing slows down due to energy loss (friction). But many devices — from hydrogen masers to atomic clocks — live by repetitive cycles.

A billiard game would be strange if the balls had no mass. They wouldn't collide but would pass through each other, ignoring obstacles. That's roughly what it looks like to imagine light as a stream of classical particles — tiny elastic bodies flying in straight lines. A new proof puts an end to that picture.

For almost a century, cosmologists have been grappling with the mystery: what makes the Universe expand ever faster? The standard answer — dark energy — creates a monstrous discrepancy between the theoretical vacuum density and observations. But there's another path, one that turns causality on its head.

A long chain of atoms, each a tiny magnet. They talk to each other and to a common field, like musicians in an orchestra who hear both the conductor and their neighbors. When the external field changes, the orchestra either plays out of sync or all instruments come in together: that's a quantum phase transition.

Conventional neural networks learn from thousands of examples, burning hours and gigawatts. Physicists have found a quantum workaround. As early as Max Planck showed the discreteness of energy, today this allows generation without training.

A swing can rock strongly or barely move. Usually, if left alone, it stays in its chosen mode. But in the microworld, things are different: a tiny membrane, oscillating under the action of a laser beam, can spontaneously jump from one amplitude to another.

In the ocean of bank transactions, fraud is rarer than neutron stars in space, just 0.1% of all operations. A conventional detector gets used to the clean flow and loses vigilance. Enter Q-SYNTH, a hybrid system with a quantum generator. It creates plausible fake transactions itself, drawing on scraps of real data.

Two simultaneous interpreters sit in the same booth. The first translates from English into Russian but swallows half the words. The second goes from Russian into French, and also loses half. If you put them together, you'd expect a mess: the losses would add up, and only a quarter of the meaning would reach the listener. But what if they start correcting each other?

Dip your finger into water once, and from that single sensation, try to guess its temperature. In the quantum world, such one-shot measurements happen all the time, except you have to guess invisible parameters: say, the squeezing strength of a laser beam.

The shape of a riverbed precisely follows the equation describing the growth of a universe with negative curvature. In the lab, water flowing over sand spontaneously carves a cross-section that matches the solution for the Anti-de Sitter model. A river tends toward a shape that maximizes bottom friction.

A driver turns the steering wheel to make the car turn. The quantum world also has its own "steering wheels"—external parameters that are slowly varied to shuttle particles from one place to another.

In the kitchen, the sequence of actions is strictly dictated by the recipe: first chop, then fry, and nothing else. In quantum physics, the role of the recipe is played by causality — one event causes another, and they cannot be swapped. But in recent years, theorists have devised clever scenarios where the order of events seems to 'hang' in uncertainty.

The Universe's expansion is accelerating, and maybe gravity doesn't work the way we think. Physicists come up with alternative theories, but to test them, they need to calculate how ripples after the Big Bang grew into galaxies. Such calculations involve long equations with hundreds of terms, where it's easy to get lost.

Three craftsmen work in the same workshop. The first tries to figure out whether tiny hourglasses are built into nature's own machinery. The second attaches a laser pointer to a microscope to see details invisible to the naked eye. The third, conversely, takes living threads and carefully weaves them into fragile quantum circuits.

Quantum computers promise to solve problems that regular computers can't. But where is the line? The authors of a new study stumbled upon a surprising case: electrons paired up behave like a well-behaved orchestra. Even if you add a bit of "magic"—a special quantum resource: their behavior remains predictable.

Imagine a line of dominoes: when the first one falls, it pushes its neighbor, and a wave rushes down the chain. The boundary between fallen and standing dominoes is a perfect image of a magnetic wall. In microscopic magnetic films, these walls separate zones with different magnetizations.

A coin in your hand always lands either heads or tails: that's how the familiar world works. But a cloud of 370 ultracold atoms can behave differently: it can freeze into a state akin to a coin that is both heads and tails at the same time. A new study shows how to test this experimentally. The idea rests on comparing two scenarios.

A quantum computer is like an orchestra where every musician must come in at exactly the right moment. Previously, to play a complex piece, you had to constantly move the instruments around — slow and noisy. The new scheme, called "parity architecture," keeps everyone in place, and the conductor simply changes the notes.

The best AI assistant for scientists scored worse on this exam than a C student on a pop quiz. Just 21% correct answers, and that's the ceiling for the four strongest models. The problems for the new test were written not by programmers but by graduate students: people who deal with real science every day. The test is called COMPOSITE-STEM.

A classical computer sorts data like a person meticulously sifting through grains of sand of different colors. A quantum processor takes its cue from nature: just as a droplet of water splits sunlight into a rainbow, revealing all hues at once, this new algorithm instantly grasps the essence of vast information arrays.

The biggest puzzle in physics is how to reconcile spacetime curvature with quantum mechanics. At the Planck length, billions of billions times smaller than an atom, the rules break down. This frontier was discovered by Max Planck.

A modern hospital sensor is like a sensitive microphone in a noisy hall. It picks up a weak signal from the heart or brain, but along with it comes the hum of machines, footsteps, the breathing of neighbors. Separating the desired sound from the interference is a science in itself.

Imagine reality as an undeveloped photograph: until the moment of measurement, it exists only as a cloud of probabilities — a superposition of all possible states. Only the act of observation, like developing film, forces a particle to acquire definite properties.

In a lab, you measure a very weak signal — say, a tiny change in a magnetic field. The instrument trembles from passing cars, from the experimenter's breathing, from wires heating up. This technical noise can't be fully eliminated, and it sets a limit on precision. An ordinary sensor works like a scale that sways with any draft.

In ping-pong, two paddles connected by an invisible thread feel each other's movements, guessing the ball's trajectory. Researchers gave a computer a similar thread — quantum entanglement. Into an ordinary trial-and-error learning program, they embedded a quantum circuit of eight qubits — particles that can spin like a coin on its edge.