Lindblad equation

A quantum computer isn't just a bunch of qubits: it's a whole city, where each resident is one of the machine's possible states. Residents get to know each other through weak interactions between qubits: if one state can transition to another, a thread of acquaintance is drawn between them.

When a fluid flows around an obstacle, it spawns vortices and shock waves. Describing their behavior means solving a nonlinear equation in which the flow velocity depends on itself. Classical supercomputers spend days on this, while quantum computers have barely been used: their native language is linear operations, but fluids are inherently nonlinear.

In a ring accelerator, a beam of electrons circles millions of times. If the electrons are twisted like strands in a rope, their vortex motion should persist. But along the way, random jolts from imperfect magnets can disturb them. Scientists have described how vortex motion changes under such perturbations.

Two massive bodies frozen in a quantum superposition resemble a pair of dancers trying to keep a single rhythm while an orchestra blares around them. Each gravitational wave is a musician throwing them off beat.

Newton gave us a world where bodies move in a void and clocks tick the same for everyone. For three centuries, this picture worked flawlessly. But it relies on many invisible props: absolute position, the 'up-down' direction, and a single rhythm of time for the entire universe. We have never measured these directly — only through the relations between objects.

In the big world, there's a simple rule: energy density can't be negative, and its flow can't outrun light. In a café, that would look like this: a waiter can't deliver orders faster than he can run. Physicists call this restriction the energy dominance condition. But in the microworld, where quanta rule and spacetime can bend, energy starts acting up.

The quantum world is full of strange connections. Two particles can become “entangled”: the state of one instantly affects the other, even if they are kilometers apart. But how do you know if they are truly entangled? It's like a ball of yarn: at first glance, you can't tell whether it's a single tangled ball or just a mess of loose threads.

A quantum computer relies on two forces: entanglement (particles behaving as a single whole) and "magic"—a measure of how far a state is from familiar classical physics. But how these two resources relate as a many-particle system evolves in time has remained a puzzle. The authors approached the problem through time.

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.

The river of time may not be a smooth flow but a sequence of minuscule steps, like a stop-motion film shot with an unimaginably fast camera. In 1964, Yu. A. Golfand suggested that time moves not continuously but in tiny jumps, and derived an equation that predicted an inevitable increase in disorder (entropy).

In quantum mechanics, everything is fuzzy: a particle is not at a single point but smeared across space, and an event does not happen at a single moment. Yet our everyday world is full of definiteness — the coin landed heads, the light bulb turned on, a note appeared in the notebook.

The quantum world is full of transformations. Sometimes a system made of one type of particle starts behaving as if it harbors completely different ones. For example, in a chain of bosons, sociable particles that like to crowd into the same state, fermions from the Standard Model may unexpectedly appear, even though they usually keep to themselves.

A quantum system is like an island gradually eroded by the ocean. The waves, representing environmental influence, wash away the shores, stripping the island of its unique contours. The GKLS equation (Gorini–Kossakowski–Lindblad–Sudarshan) describes exactly how quickly this 'quantumness' fades. But every wave has an energy source.

The early universe expanded at an unimaginable rate — faster than light could cross it. In this boiling cauldron, any region of space resembled an open can of paint: its boundaries continuously captured new 'vapor' from outside, while some of its own contents irrevocably escaped.

If you accelerate one of four entangled particles to enormous speed, their quantum entanglement doesn't just melt away: it first weakens, then strengthens again. Physicists discovered this unexpected twist while studying the behavior of a special state called the Dicke state in a world governed by the laws of relativity.

Two entangled photons fly apart in opposite directions but continue to behave as a single whole: measuring one instantly determines the state of the other. That's quantum entanglement. But sometimes it resembles a seasoned spy — leaving no traces detectable by ordinary checks.

If you toss a handful of coins into a box with dividers, each coin lands in its own compartment and stays there forever. Roughly the same happens to atoms in a special optical lattice when excited by a laser. These atoms are called Rydberg atoms: one electron in each is promoted to a very distant orbit, making the atom sensitive to its neighbors.

A diary loses pages, yet the story migrates to the rest. Black holes act similarly: as they shrink (shown by Stephen Hawking), swallowed information shouldn't vanish; it eventually resurfaces. Theory predicts a specific rise-and-fall curve for this escape.

A quantum processor is like an orchestra where each musician (qubit) must play their part precisely in time. But in reality, the instruments go out of tune: qubits lose energy, and their interactions get distorted. To tune this orchestra, you first need to record how it sounds right now: that is, measure the noise parameters and couplings.

Ordinary messages can be intercepted without anyone noticing. Physicists have come up with a way to create a shared secret that instantly breaks if someone so much as glances at it. Instead of paper, they use single particles of light. This quantum communication exploits a rule: any measurement changes a quantum object.

A rubber band is stretched, and suddenly snaps. In the atomic world, a similar picture emerges: the string binding particles can break. In a new study, physicists took a chain of Rydberg atoms and tracked how such a string breaks. Under weak tension, the string breaks completely, and the system splits into several independent pieces, as if a rubber band shattered into segments.

A regular wall clock runs smoothly, but quantum clocks are a different story. They tick at random moments, and each tick can have a different duration. On average, if you watch such a clock for a long time, it will show the correct time. But at any given moment, its hand might jump forward by an unexpected amount.

The world of physics works like a music box: there's a speed knob. Turn it slowly, and the melody is strict — balls roll along trajectories (classical mechanics). Speed it up — the notes blend into a chord: a particle is in many places at once, all probabilities (quantum regime). The secret of switching is in the parameter κ.

The expansion of the universe is like a dance floor stretching wider. For decades, physicists assumed that more stretching would spawn more particles, like the floor spontaneously generating new dancers. But those models ignored an obvious fact: dancers sometimes link arms. When particles interact, new simulations reveal, they actually suppress creation.

Hot water sometimes freezes faster than cold — that's the classic Mpemba effect. In the quantum world, its counterpart is even more astonishing: tiny particles can reach equilibrium many times faster than expected, and what helps them is not forgetfulness, but memory.

Quantum mechanics is a linear theory. This property is so fundamental that violating it would mean losing the superposition principle and, consequently, the possibility of superluminal information transfer. But physicists have long suspected that at a deep level, where gravity meets quanta, linearity might not survive.

Two particles begin their dance in complete independence. Neither knows of the other's existence. But under the invisible music of deformed spacetime, their motions gradually synchronize: entanglement is born in the system—that very quantum connection Einstein called 'spooky action at a distance.' In the ordinary world, energies add up simply: take the energy of…

Picking up an ultraweak microwave signal is like trying to hear a whisper in a storm. Rydberg atoms, inflated to the size of bacteria, promise to become perfect antennas. But there's a fatal catch: during optical readout, up to 98% of messenger photons vanish without a trace in the detector.

A crowd in a square. At first, everyone spins to their own rhythm, but suddenly the music changes, and they all start moving in sync, as one. That's roughly how electrons behave in some metals: they either cling to magnetic impurities or break away and form a collective order.