Heads and Tails at Once

“… experts warn: quantum computers could soon crack every password there is. Banks, government agencies, your email account. Nothing is safe any more. And now the weather.”

Uwe lowered the bread knife. Jam dripped onto the newspaper, right onto Sabine’s crossword.

“Did you hear that?”

“The weather?” asked Sabine. “Twelve degrees, showers.”

“No. The quantum computers! They crack everything. Our passwords. The bank account. Herbert’s internet money.”

“Herbert doesn’t even know his own password,” said Gisela. “The quantum computer will have to join the queue.”

Uwe stood up. He had the expression he normally only got when Schalke conceded a goal in stoppage time. “KevIn. I’m changing all the passwords. Right now.”

The blue light pulsed calmly. “You’re welcome to do that, Uwe. It never hurts. But may I say something about the report first?”

“If it’s quick.”

“The newsreader said ‘could’ and ‘soon’. Those are the two stretchiest words in the German language. And in English. With ‘could soon’ you can also say: ‘Schalke could soon win the league.’”

Uwe sat back down. He needed a moment.

A Visit for Coffee

Tobi came into the kitchen, his hair in a shape he called “intentional”. “What’s going on?”

“Quantum computers,” said Sabine. “Your father wants to save the internet.”

“Cool. Mr Demir’s coming tomorrow anyway.”

Everyone looked at him.

“Grandma invited him again. He’s been coming round more often since the observatory. She said anyone who talks so nicely about prime numbers gets cinnamon stars.”

“I did say that,” Gisela confirmed. “A polite man. And he’s got hunger in his eyes. Teachers always have hunger in their eyes.”

Since the evening at the observatory on the Kemnader See, Tobi had talked about little else. About Voyager, still transmitting. About the Arecibo message. And about Mr Demir’s last sentence, which was still echoing through the family like a gong. “That’s called a quantum computer.”

“Right,” said Uwe. “Then we’ll ask him. He’s a physics teacher. He’ll know.”

“I know too,” said KevIn.

“You also told me Bielefeld had a wall made of pudding round it.”

Somewhere between Dublin and Frankfurt, a fan spun a little faster.

The Light Switch

Mr Demir arrived on Sunday at three on the dot. He brought flowers for Gisela, a bag of simit from the Turkish bakery for everyone and, in his jacket pocket, a two-euro coin which, by his own account, he used “only for teaching”.

Gisela put out the biscuits. Mr Demir ate three before he had taken his jacket off.

“Mr Demir,” said Uwe, almost before everyone was seated. “On the radio they’re saying quantum computers crack all passwords. Is that true?”

Mr Demir finished chewing. He was a man who took questions seriously, even when they were asked with a mouthful of biscuit. “Short answer: no. Long answer: it’s more complicated, and you have to start at the beginning.”

“Start at the beginning,” said Sabine. “We have time. And biscuits.”

“Good. What is a bit?”

“I know that,” said Gisela. “A Bit is a beer from the Eifel.” She meant Bitburger, which the adverts have been calling “a Bit” for as long as anyone can remember.

“That too,” said Mr Demir politely. “But in a computer a bit is the smallest unit of information. Nought or one. Off or on.”

“Like a light switch,” said KevIn. “Heinz would have liked that. An ordinary computer is basically a house with billions of light switches being flicked on and off very fast.”

“Heinz once put six light switches in one hallway,” said Gisela. “You never knew which one did what. The hallway was always half lit.”

“There’s no such thing as half lit with a bit,” said KevIn. “That’s important. A bit is either nought or one. Even when nobody is looking. Even when you don’t know which value it has at the moment. It has one.”

“So what’s a qubit, then?” asked Tobi. “The word turns up in every other video I get shown. Usually with an explosion in the background.”

Uwe put his hand up like at school. “I know that. I read it. A qubit is nought and one at the same time.”

Mr Demir and the blue light looked at each other. At least, Sabine later had the feeling they had looked at each other.

“That’s the sentence everyone says,” said Mr Demir carefully. “It isn’t entirely wrong. But it isn’t entirely right either.”

“It’s about as right,” said KevIn, “as ‘A cabbage roll is cabbage and meat at the same time.’ True, in a way. But if that’s all you know, you can’t cook one.”

The Coin

Mr Demir took the two-euro coin out of his pocket and spun it on the table. It whirled with a bright whirr between the coffee cups. Rudi raised his head.

“That’s the picture people often use,” said Mr Demir. “While it’s spinning, it’s neither heads nor tails. Somehow both. When it falls, it makes up its mind.”

The coin slowed, wobbled and fell. Tails.

“So a qubit is a coin that’s spinning,” said Uwe, satisfied.

“Almost,” said KevIn. “The picture is good for the beginning and bad for everything after.”

“Why?”

“Because the coin always knows what it is. If you knew exactly how fast it was spinning, what the table was like and how Mr Demir had flicked it, you could work out how it would fall. The whole time, it has one quite definite position. We just don’t know it. That’s ignorance. With a qubit it’s something else.”

“What, then?” asked Sabine.

“A qubit doesn’t have a hidden answer just waiting to be discovered. It has a state, and that state is a kind of mixing recipe. There’s a number for the nought, and there’s a number for the one. These numbers are called amplitudes.”

“Ampli-what?” asked Gisela.

“Amplitudes. Imagine a little arrow for each possibility, Gisela. One arrow for the nought, one arrow for the one. Each arrow has a length and a direction. When you measure the qubit, that is, when you look, it always comes out either nought or one. Never a half. How likely the nought is depends on the length of its arrow. More precisely: on the length squared¹.”

“Why squared?” asked Tobi.

“Because that’s how nature does it,” said Mr Demir. “It’s one of the rules. There’s no deeper reason I could explain to you on a Sunday. It fits every experiment that has ever been done.”

“And what’s the direction for?” asked Sabine. “If only the length counts in the end.”

“That,” said KevIn, “is the best question of the afternoon. The direction is the whole trick. With a coin there are only probabilities. Fifty per cent heads, fifty per cent tails. Probabilities are always positive. You can only add them up. Arrows, on the other hand, can point in opposite directions. And then they cancel each other out.”

“One arrow forwards and one backwards,” said Tobi slowly, “equals no arrow at all.”

“Exactly. A coin can’t do that. Only a qubit can.”

Gisela frowned. “And if you look inside?”

“Then you get nought or one. And afterwards the qubit is exactly what you saw. The arrows are gone. The mixing recipe has been eaten.”

“Like with a cake,” said Gisela. “If you look in the oven too early, it sinks.”

“That’s a lovely picture,” said Mr Demir. “Physically it’s wrong, but it’s lovely.”

“My cake really does sink, though.”

“I believe you completely.”

Waves at the Swimming Baths

Sabine poured more coffee. “I still don’t understand what good arrows are if they cancel each other out. It sounds like my tax return.”

“May I?” asked KevIn.

“Please,” said Mr Demir, and took a fourth biscuit.

“Tobi, do you remember the swimming baths? You were seven. You and Uwe jumped off the side of the pool at the same moment, at two different spots.”

“How do you know that?”

“Sabine told me. She said it was the funniest thing she’d ever seen.”

“I landed on my belly,” said Uwe darkly.

“Anyway,” said KevIn, “waves ran across the pool from both of you. Circles. And where the waves met, something strange happened. In some places a crest met a crest. There the water rose twice as high. In other places a crest met a trough. There the water was suddenly perfectly flat, even though two waves were passing through.”

“That’s interference,” said Mr Demir. “Superposition. Crest plus crest gives a big crest. Crest plus trough gives nothing.”

“Like Tobi’s headphones,” said KevIn. “The noise-cancelling ones. They hear the noise of the bus, produce a counter-wave, exactly reversed, and the two cancel out. Noise plus counter-noise gives quiet.”

“I thought they were just well sealed,” said Tobi.

“No. They do sums.”

Uwe looked at Tobi with new respect. Although it was really more respect for the headphones.

“And now comes the crucial part,” said KevIn. “The arrows in a quantum computer behave like those waves. A quantum algorithm is basically a very elaborate piece of choreography. You make the arrows move so that the arrows of the wrong answers cancel each other out. Crest on trough. And the arrows of the right answer reinforce each other. Crest on crest. When you measure at the end, the right answer comes out with high probability.”

“With high probability?” asked Sabine. “Not for certain?”

“Often not for certain. Then you simply do it several times and check the result. For many problems checking is easy, even if finding is hard.”

“Like a crossword,” said Sabine, tapping her newspaper with the jam stain. “Finding the answer takes ages. Whether it fits, you see straight away.”

“Exactly that.”

All the Answers at Once

“Hang on,” said Uwe. “On the radio they said it differently. They said a quantum computer tries all the passwords at the same time. Because the qubits are everything at once. That’s why it’s so fast.”

“That,” said Mr Demir, “is the biggest misunderstanding of all. You even hear it in documentaries.”

“It’s logical, though,” said Uwe. “One qubit is nought and one. Two qubits are four possibilities. Three are eight. So it tries everything.”

“The arithmetic is right,” said KevIn. “With ten qubits there are 1,024 possibilities, and there’s an arrow for each one. With three hundred qubits there are more arrows than there are atoms in the visible universe.”

Uwe whistled through his teeth. “Then the thing’s infinitely clever.”

“It’s infinitely tight-lipped,” said KevIn. “That’s the catch. You can pack every password in the world into a state like that. But when you look, you get exactly one of them out. A random one. All the other arrows are gone.”

“That’s like the bowling club raffle,” said Gisela. “All the tickets are in the drum, but you’re only allowed to reach in once.”

“And mostly you win the egg liqueur,” said Sabine.

“Precisely,” said KevIn. “If a quantum computer simply throws every possibility into a pot and then reaches in once, it’s no better than guessing. It’s actually worse, because it’s far more expensive than guessing. The advantage only comes from interference. From the choreography in which the wrong tickets vanish from the drum before you reach in. And a choreography like that has only been found for very particular problems.”

“And for passwords?” asked Uwe.

“For plain brute-force guessing there’s a trick that a man called Lov Grover found in 1996². It makes the search faster, but only roughly like this: instead of a million attempts you need around a thousand steps. Sounds like a lot. But if you simply make your password twice as long, the advantage has been eaten up again.”

“Twice as long,” Uwe repeated. He wrote it on a serviette.

“Your passphrase from the winter is long enough anyway,” said KevIn. “It’s six words, and two of them are ‘Schalke’ and ‘champions’. No human being would ever guess that.”

“How do you know it?” asked Tobi.

“Uwe dictated it to me. So I’d remember it. In case he forgets it.”

There was a short pause. Mr Demir slowly put his biscuit down.

“I shouldn’t have said that out loud,” said KevIn quietly. “Uwe, please change it. And don’t dictate the new one to me.”

“And what about the banks?” Sabine asked quickly, while Uwe sighed and turned the serviette over.

“There really is a problem there,” said Mr Demir. “But a different one. There’s a quantum algorithm that could solve a particular mathematical problem very much faster. The problem that part of today’s encryption rests on. Our prime numbers from the observatory.”

“Shor,” said KevIn.

“Shor,” said Mr Demir. “But that’s a story for another Sunday.”

“I can bake every Sunday,” said Gisela.

Mr Demir looked like a man who had just received some very good news.

Who on Earth Puts a Cat in a Box

Around five, as the biscuits were running low, Mr Demir told them about Erwin Schrödinger. He did it the way he did at school, with his voice lowered slightly so that everyone leaned in.

“Schrödinger was an Austrian physicist. One of the fathers of quantum mechanics. In 1935 he came up with a thought experiment³. Take a cat and shut it in a box.”

“I beg your pardon?” said Gisela.

“Into the box also go a single radioactive atom, a detector and a little bottle of poison. If the atom decays, the detector goes off, the bottle breaks, and the cat …”

“Mr Demir!”

“… is only a thought experiment, Mrs Brettschneider. Nobody has ever done it.”

“Who thinks up a thing like that? Who on earth puts a cat in a box!”

“A physicist,” said KevIn. “That’s very well documented in my data. Physicists are forever thinking up terrible things so they don’t have to own a cat themselves.”

Mr Demir laughed. “The point is this: the atom is a quantum thing. As long as nobody measures it, it’s in a superposition of ‘decayed’ and ‘not decayed’. If you apply the rules of quantum mechanics stubbornly to the whole box, then the cat would also have to be in a superposition of ‘alive’ and ‘not alive’ until someone opens the lid.”

“That’s nonsense,” said Uwe.

“That’s exactly what Schrödinger wanted to say,” said Mr Demir, pleased. “He didn’t invent the example to show that cats are half dead. He invented it to show that something didn’t add up. That you can’t simply pretend the same thing applies to a cat as to an atom.”

“And?” asked Tobi. “Does it?”

“Physics now has a pretty good answer to why you never see anything like that with cats,” said KevIn. “It’s called decoherence⁴. A cat is enormous. It consists of unimaginably many particles. It breathes, it’s warm, it’s constantly colliding with air molecules, it’s being hit by light. Each of those collisions is basically a little peek. The surroundings are looking into the box all the time, even if no human is. The delicate superpositions get lost in fractions of a second, far faster than anyone could ever measure.”

“The surroundings are always looking,” said Sabine. “Like half the street behind the net curtains.”

“Just like half the street. And that’s exactly why it’s so hard to build a quantum computer. The qubits mustn’t be disturbed. Nobody may look, not a particle of light, no heat, no draught. Only right at the end, when you measure.”

“Then they must have to live like Gisela during her afternoon nap,” said Uwe.

“Even more sensitive,” said Mr Demir. “Many of them live in fridges that are colder than outer space.”

“Colder than me?” asked KevIn. He sounded almost a little hurt.

“Much colder.”

The Box

At that moment there was a noise from the hallway. A rustle, then a dull thump.

Everyone turned round.

In the hallway stood a white box with rounded corners. On it was written: “Your new housemate. Intelligent. Helpful. Almost always right.” The “almost” was still printed very small.

“You kept that?” asked Sabine.

“You don’t throw away a good box,” said Gisela. “I keep the Christmas stars in it. I was just about to take them down to the cellar.”

The box was empty. The Christmas stars lay beside it on the carpet. And Rudi was nowhere to be seen.

“Where’s Rudi?” asked Tobi.

Nobody said anything. Everyone looked at the box. The lid was shut.

“Right,” said Mr Demir very seriously. “Before anyone looks, I’d like to state for the record: we do not know whether the dachshund is inside.”

“The dachshund is inside,” said Sabine.

“That isn’t superposition,” said KevIn. “That’s just ignorance. Like with the coin. Rudi knows perfectly well where he is. Besides, he’s warm and breathing and looking out through the handhold. The surroundings checked long ago.”

The box barked.

“Measured,” said Tobi.

Gisela opened the lid. Rudi was sitting between two layers of tissue paper, wearing his collar with “SECURITY” on it, and looking at everyone as if they had interrupted him in something very private.

“See,” said Gisela. “Alive. As it should be. Now out you come, Mr Schrödinger.”

Evening

Mr Demir left around seven, with a tin of biscuits under his arm and a promise to come back soon. “Next time I’ll tell you about entanglement,” he said at the door. “That’s when it gets properly spooky.”

“With a cat?” asked Gisela suspiciously.

“Without a cat. With socks.”

“Socks are all right.”

Later, when the dishwasher was running and Rudi had officially claimed the box as his new home, Uwe sat in the kitchen for a while longer. He was turning the two-euro coin in his fingers, the one Mr Demir had forgotten. Or left behind. With teachers you never knew.

“KevIn,” he said. “If I toss the coin and don’t look. What is it then?”

“Heads or tails. One of the two. You just don’t know.”

“And if I were a qubit?”

“Then you’d have two arrows, Uwe. One for ‘I’ll change the passphrase this evening’ and one for ‘I’ll do it in a minute’.”

“And which is longer?”

“I’ve analysed your history,” said KevIn. “The interference doesn’t look good.”

Uwe went to the laptop anyway. It took an hour, and he swore the whole time. But at the end he had a new passphrase that KevIn didn’t know, and that, Uwe felt, was the real victory.

When he turned off the light, the radio was still playing quietly in the kitchen.

“… and on the stock market today: quantum shares soaring. Investors are hoping for the next big breakthrough …”

Uwe stopped in the doorway. Only very briefly. But KevIn noticed.

Somewhere between Dublin and Frankfurt, a fan spun a little faster.