February 4, 1999

text is a cache of http://www.economist.com/displayStory.cfm?Story_ID=185440

IT COULD be a Star Trek episode, but it is actually a paper in *Physical Review Letters*. As usual, a calamity is about to befall the starship *Enterprise *and Captain Picard has grimly begun to prepare for the worst. Suddenly, Q, an irreverent, all-powerful being who has been a source of endless exasperation to the crew, appears on the bridge offering to save the ship if Picard can beat him at a simple game.

Picard is to place a coin in a box, heads up. Q then gets a turn at either flipping it, or leaving it alone. Picard, without knowing what Q has done, gets to do the same, then Q goes again. After Q’s second turn, they open the box. If the coin is heads up, Q wins. If tails are up, Picard wins.

Luckily, training for starship captains includes some rudimentary statistics, so Picard quickly realises that the odds of winning are equal for each person, as long as Q does not use his powers to cheat. Q promises, Picard agrees to play, and promptly loses every single game. Has Q broken his word? Not quite, according to David Meyer, the paper’s author, who is a physicist at the University of California, San Diego. But Q has done something that has never yet been done on Earth. He has introduced quantum mechanics into a game.

Game theory is used to understand how decisions are made in fields as diverse as economics and evolutionary biology, and even for a game as simple as coin-flipping it can yield a strategy that gives each player the best chance of winning (or, at least, of coming out even). But Picard only knows how to play classically—that is, he can either flip the coin or not. That means his best strategy is to choose randomly between the two. Q’s strategy, however, is quantum. He can use his turn to put the coin into the peculiarly quantum state of being both heads and tails at once.

At this point, Picard cannot win. If he flips the coin, it will still end up both heads and tails. If he does not flip it, the same result ensues. When Q takes his second turn, he therefore knows exactly what state the coin is in. All he needs to do is give it another quantum tweak which is exactly the opposite of his original tweak, and it obligingly goes back to being heads.

So much for science fiction. But Dr Meyer has a serious point. His thought experiment suggests that researchers in the small but potentially significant field of quantum computing should be turning their attentions to game theory.

Normal computers count in “bits” (binary digits, ie ones and zeros). These are represented physically by, for example, two different voltages of an electric current. But a quantum computer counts in “qubits”. These are superpositions of ones and zeros and are represented by, for example, the direction of spin (with respect to a magnetic field) of a particle such as an electron.

Because an electron is small enough for quantum effects to be routine, it is perfectly possible for such a spin to be pointing up and down at the same time. In theory, this uncertainty should allow a full-sized quantum computer to do lots of calculations in parallel, and thus to solve problems that would take forever—or, at least, several billion years—on a traditional machine.

Quantum-computing researchers have actually managed to build one of their fabled devices (though it had only three qubits), and have worked out the mathematics that would allow a bigger machine to solve hitherto hard problems in cryptography. But that is a rather limited field. Dr Meyer’s flight of fancy shows that such computers could also operate comfortably in the area of game theory, with all that implies for modelling complex systems—and, presumably, for games themselves. So who knows what joys await the eager player in the first quantum version of Tomb Raider?

Copyright © 1999 The Economist Newspaper and The Economist Group.

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© Mike Shor 2001-2006

© Mike Shor 2001-2006