In 1994, a mathematician figured out how make a quantum computer do something that no ordinary classical computer could. The work revealed that, in principle, a machine based on the rules of quantum mechanics could efficiently break a large number into its prime factors — a task so difficult for a classical computer that it forms the basis for much of today’s internet security.
A surge of optimism followed. Perhaps, researchers thought, we’ll be able to invent quantum algorithms that can solve a huge range of different problems.
But progress stalled. “It’s been a bit of a bummer trajectory,” said Ryan O’Donnellof Carnegie Mellon University. “People were like, ‘This is amazing, I’m sure we’re going to get all sorts of other amazing algorithms.’ Nope.” Scientists discovered dramatic speedups only for a single, narrow class of problems from within a standard set called NP, meaning they had efficiently verifiable solutions — such as factoring.