They'd be cracking most online-security systems, revolutionizing science and even, in effect, solving the other six of the so-called Millennium Problems, all of which were chosen in the year 2000.

Here’s how it works. In theory, quantum computers could solve problems beyond the most powerful classical computer. But such devices will need to become much larger and more reliable first.

In a world increasingly shaped by artificial intelligence, the question of how machines make decisions under uncertain ...