computational cost

A conventional computer computes by shuttling electric charges along wires. But can you compute with heat? A network of pipes carrying hot and cold water can perform simple logic operations if the pipes are connected in the right order.

A quantum computer is like an orchestra where each musician-qubit easily loses the rhythm. The slightest noise, and the melody of computation turns into cacophony. To keep the orchestra playing in harmony, you need a conductor who instantly spots wrong notes and corrects them without stopping the performance.

Clocks in the Universe are tricky things. Usually, in calculations of the birth of the world, a special scalar field plays the role of a clock — something like an invisible fluid filling all of space. It ticks, and physicists watch how the world changes relative to that ticking. But these clocks are man-made, introduced for convenience. The authors of the new work took a different path.

Technological disasters like Chernobyl rarely strike without warning. They gestate for years: organizations ignore warnings, their complexity mirroring the rise of entropy — a measure of relentless chaos that builds up unnoticed until it avalanches.

A quantum computer is like an orchestra without a conductor: each qubit is a musician, and the slightest slip throws off the entire symphony. To keep the music from turning into cacophony, quantum error-correcting codes were invented.

Gold doesn't lie on the surface: it's hidden in tons of barren rock. To extract a gram of precious metal, prospectors sift through cubic meters of dirt.

In 1953, mathematician Alexander Grothendieck proved a theorem that became a cornerstone in the theory of tensor products. It states that for ordinary function spaces, two natural norms, the projective and the injective, are equivalent up to a universal constant. In other words, two ways of measuring the 'size' of combinations of vectors give similar results.

In the 1990s, philosopher John Searle devised a thought experiment: a person sits in a room and, without knowing Chinese, follows instructions to produce correct answers in Chinese. From the outside, it seems they understand the language, but inside, it's just mechanical rule-following.

In the scorching heart of a dying star, an invisible stream is born — a neutrino gas. The particles race through matter almost without stopping, but when their density is enormous, they start to feel each other. Old calculations described this as a jostle in a crowd: each shove changes direction, but no connection arises between passersby.

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.

The quantum world plays a strange game with causality. If in everyday life salt is always added to soup before serving, here the ingredients end up in the bowl at the same time, and the chef doesn't remember the order. Physicists asked: can we measure this 'recipe'? The answer is no.

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.

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 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.

Instead of millions of rigidly fixed particles — 10,000 atoms, working as beads on a quantum abacus. Each bead can be both zero and one at the same time. But the key is: if an error creeps into the calculation, the atoms can be physically moved: as if you could rearrange the abacus on the fly so that the glitch doesn't ruin the result.

Bitcoin mining is like a lottery: miners sift through billions of numbers to find one lucky winner. A regular computer does this blindly, burning electricity. A quantum computer could sort through possibilities faster, like finding a needle in a haystack by shaking the whole stack at once. The authors of a new study calculated what such a quantum "shaker" would actually cost.

Like an iceberg, the visible part of the code is the data, while beneath the surface lies a massive foundation of auxiliary particles. They quietly monitor noise and fix errors without touching the information. This approach squeezes many protected logical qubits into a modest number of physical ones. The experiment ran on a 98-ion processor inside an electric trap.

A pot of water on the stove is just water, but inside each molecule, a continuous dance goes on. Hydrogen and oxygen atoms jitter, even at absolute zero, because that's how the quantum world works. These jitters change how much heat water stores and how it flows.

A magnetic film divided into tiny arrow-shaped cells behaves like a crowd in a square. While it's cold, all arrows point in the same direction — perfect order. Heat the film, and the arrows start darting around like pedestrians who have lost their purpose. Somewhere between these extremes, there is a moment when the system stops being uniform but hasn't yet dissolved into random noise.

Light races through a maze of mirrors and beam splitters, but at the end of its journey, it doesn't just flash on a detector: it transforms itself. In the new photonic computer, nonlinear modules have been added to the familiar linear circuits, and now light can perform any quantum operation, not just a subset.

A quantum walk is like a drunk person who turns randomly at every intersection. Except instead of streets, there are graph nodes, and instead of steps, there are quantum transitions. Scientists have discovered that such a walk has a hidden measure — Krylov complexity.

Quantum computers have gained a built-in self-repair mechanism. The new two-dimensional scheme works like living tissue: each qubit-cell interacts with neighbors by local rules, automatically suppressing random disorder — entropy. Unlike previous methods, it doesn't require constant measurements, which themselves generate errors.

A quantum computer is like an orchestra where each musician plays their own part but sometimes hits a wrong note. To keep the music from turning into cacophony, you need a conductor who corrects mistakes in time. In quantum computing, the role of the conductor is played by error-correcting codes.

When making popcorn, a microwave uses electricity only to heat the kernels. A gas stove heats the entire burner and the air around it. The same difference applies between a photonic quantum chip and a classical supercomputer when solving a problem devised by Scott Aaronson.

A conventional computer sees the world flat: numbers are just points on a line. But a color image or a 3D scene demands more — four numbers that describe both position and rotation. Such quadruples are called quaternions, and until now electronics handled them clumsily, breaking them apart and reassembling them. The new chip changes the approach.

An orchestra plays inside a giant refrigerator. The musicians are qubits, the elementary cells of a quantum computer. To play in harmony, they need silence: thermal noise drowns out the melody. That's why the heart of a quantum processor is cooled to nearly absolute zero — minus 273 degrees Celsius.

To quickly dissolve sugar, you don't need to stir carefully — just shake the glass. A similar principle works in quantum systems: noise, usually considered a disturbance, speeds up the transition to a thermal state.

Quantum computers require magical states — special helper particles for error-free operation. Previously, they were obtained through repeated purification, akin to endless distillation of alcohol: each step added энтропию (disorder), like weeds in a garden, and consumed resources.

Turning CO₂ into fuel is like finding the one perfect way to pack billions of items into a suitcase. A classical computer tries options one after another, taking decades, while a quantum computer sees all combinations at once.

The task resembles a giant maze with a single exit among billions of dead ends. A conventional computer checks each corridor step by step — taking centuries. A quantum processor launches a wave that seeps through all paths at once. The correct route echoes back, amplifying, and the answer is found in hours. That’s exactly how the “peak” circuits worked in the new experiment.

Three thousand meters above sea level, a sheer cliff face. A classical climber picks a single route and crawls up step by step, often getting stuck in a local minimum: a small niche with no upward path. A quantum climber acts differently: it can leap across a canyon and land in a neighboring energy basin where the route is better.

A laser pulse lasting one and a half nanoseconds hits a nonlinear crystal, and a stream of squeezed light is born. That is how an experiment on the Jiuzhang 4.0 quantum processor in China begins.

A quantum computer is like an orchestra: each musician plays their part, but the slightest false note ruins the symphony. The physical qubits it is built from are noisy and error-prone. To protect computations, they are combined into logical qubits using quantum error correction.

In 2019, a group of theorists asked a simple question: what would happen if you embedded a single irreversible element into an ordinary quantum computer, a gate that slightly "eats" probability? The answer was devastating. Any such gate, no matter how weak, instantly turns the machine into a device capable of solving problems in the class PostBQP = PP.

In a dark room, a resonator catches light the way a spiderweb catches dew drops. A laser pulse bursts in, and the mechanical membrane starts to vibrate in sync, leaving a trace in the very fabric of the system. That is how memory is born: not in a silicon cell, but in the dance of photons and phonons.

A superconducting quantum processor is like a microscopic metropolis locked in a cryogenic fridge: streets of superconducting lines, blocks of qubits. Each resident demands silence and cold, but expanding the city inside a single cryostat is like stacking skyscrapers in a cramped courtyard — wires heat the environment, noise builds up, coherence threatens to collapse.

Every day, the power grid faces a puzzle: which power plants should be switched on to reliably meet demand without breaking the bank? For 15 generators and 24 hours, the number of possible schedules exceeds 2.3×$$10^{108}$$, more than the number of atoms in the visible universe. No classical supercomputer can sift through all of them, so dispatchers settle for a compromise.