When people hear that I work on quantum computing — one of the most radical proposals for the future of computation — their first question is usually, “So when can I expect a working quantum computer on my desk?” Often they bring up breathless news reports about commercial quantum computers right around the corner. After I explain the strained relationship between those reports and reality, they ask: “Then when? In 10 years? Twenty?”

Unfortunately, this is sort of like asking Charles Babbage, who drew up the first blueprints for a general-purpose computer in the 1830s, whether his contraption would be hitting store shelves by the 1840s or the 1850s. Could Babbage have foreseen the specific technologies — the vacuum tube and transistor — that would make his vision a reality more than a century later? Today’s quantum computing researchers are in a similar bind. They have a compelling blueprint for a new type of computer, one that could, in seconds, solve certain problems that would probably take eons for today’s fastest supercomputers. But some of the required construction materials don’t yet exist.

So you might think quantum computers are something real scientists — as opposed to science-fiction buffs — won’t need to worry about for a long time. But I’d urge a different view. Quantum computing really is one of the most exciting things happening in science right now. Just not for the reasons you usually hear.

First, though, what is a quantum computer? Walk into a quantum computing lab, and you won’t see much: maybe a fist-size “trap” where ions (often cadmium or calcium) are suspended in a magnetic field, a laser for moving the ions around, a computer screen with a row of flickering white blobs representing the ions’ approximate locations. The real action, one might say, is happening in a different realm entirely: in the alien mathematics that governs what the ions are doing.