Why a quantum computer stops at a lattice
Shor’s algorithm eats RSA in one move. The same machine gets almost nothing on a grid of points with a little noise added. One slider shows the difference.
Stage Shor
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- 1
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- 4
Tap a part of the diagram to open that stage.
What actually changed
RSA hid its secret inside a question a quantum computer turns out to be able to ask. Lattices hide it inside a question that stays exponential for both kinds of machine — while the owner of a short basis skips the question altogether.
What's inside
- 1 Factoring stops being hard — Nothing was wrong with the mathematics. The hardness was simply living in the wrong place.
- 2 Points instead of numbers — The lattice itself is public. Everybody can see the points.
- 3 The message is a point, then it is nudged — The noise is small enough to be undone and large enough to hide which point you started from.
- 4 Finding the nearest point is the whole problem — Known quantum algorithms shave the exponent on this problem. They do not remove it.
- 5 With the right basis it is one rounding — The secret is not the lattice. It is a good description of the lattice.
Explorable Explanations
- How a drug is smuggled past the blood–brain barrier The brain refuses almost every drug molecule, and it is right to. One slider follows the trick the labs are trying instead: wrap the molecule in a bubble the wall already knows how to carry.
- How a robot draws the map of a room it has never seen A lidar returns a few hundred dots per sweep and no idea where it is. One slider walks from that cloud to a floor plan with the robot standing in the right spot.
- How two people type in one line without losing a letter Two cursors, one line, nobody holding the pen in the middle. One slider takes an index-based merge apart and rebuilds it out of addresses that sit between the letters.
- Cooling a building by pointing it at space A coating that stays colder than the air around it, in full sun, drawing no power at all. One slider follows the heat from the sun to the far side of the atmosphere.
- How a robot predicts the next second A text model guesses the next word. A world model guesses the next frame — mass, speed and gravity included. One slider walks the whole loop, from the camera to the catch.
- Proving a secret without revealing it One slider walks through the stages, the other adds rounds. Watch certainty climb to almost total while the secret stays a secret.
- Getting lithium out of brine: ponds versus direct extraction Move the slider through five stages and compare two ways of taking the same metal out of the same salt water.
- How a personalised mRNA cancer vaccine works Move the slider through five stages and watch how a tumour’s own mutations become the instructions that teach the immune system to find it.
- The edge of the app Everything arriving from outside is untrusted. Break one link at a time and watch where the chain stops and what the screen shows.
- How search over your documents works Move the sliders and watch a search pipeline decide what the model is allowed to see — and what happens when it is fed the wrong passage.
- Retries and slow responses The network drops in the middle of an operation. Press the button twice and see what ends up in the database — with an idempotency key and without one.
- How a language model writes The weights are frozen and nothing is remembered. Pull the sliders and watch the model pick the next piece of text, over and over.
- How a language model learns Pull one slider and watch a pile of random numbers turn into a prediction over a thousand training steps.
- Where electricity comes from Pull one slider and follow the energy from a river all the way to a pump that lifts water back up.