In the spring of 2017, Urmila Mahadev found herself in what most graduate students would consider a pretty sweet position. She had just solved a major problem in quantum computation, the study of computers that derive their power from the strange laws of quantum physics. Combined with her earlier papers, Mahadev’s new result, on what is called blind computation, made it “clear she was a rising star,” said Scott Aaronson, a computer scientist at the University of Texas, Austin.

Mahadev, who was 28 at the time, was already in her seventh year of graduate school at the University of California, Berkeley — long past the stage when most students become impatient to graduate. Now, finally, she had the makings of a “very beautiful Ph.D. dissertation,” said Umesh Vazirani, her doctoral adviser at Berkeley.

But Mahadev did not graduate that year. She didn’t even consider graduating. She wasn’t finished.

For more than five years, she’d had a different research problem in her sights, one that Aaronson called “one of the most basic questions you can ask in quantum computation.” Namely: If you ask a quantum computer to perform a computation for you, how can you know whether it has really followed your instructions, or even done anything quantum at all?

This question may soon be far from academic. Before too many years have elapsed, researchers hope, quantum computers may be able to offer exponential speedups on a host of problems, from modeling the behavior around a black hole to simulating how a large protein folds up.

But once a quantum computer can perform computations a classical computer can’t, how will we know if it has done them correctly? If you distrust an ordinary computer, you can, in theory, scrutinize every step of its computations for yourself. But quantum systems are fundamentally resistant to this kind of checking. For one thing, their inner workings are incredibly complex: Writing down a description of the internal state of a computer with just a few hundred quantum bits (or “qubits”) would require a hard drive larger than the entire visible universe.

And even if you somehow had enough space to write down this description, there would be no way to get at it. The inner state of a quantum computer is generally a superposition of many different non-quantum, “classical” states (like Schrödinger’s cat, which is simultaneously dead and alive). But as soon as you measure a quantum state, it collapses into just one of these classical states. Peer inside a 300-qubit quantum computer, and essentially all you will see is 300 classical bits — zeros and ones — smiling blandly up at you.

“A quantum computer is very powerful, but it’s also very secretive,” Vazirani said.

Given these constraints, computer scientists have long wondered whether it is possible for a quantum computer to provide any ironclad guarantee that it really has done what it claimed. “Is the interaction between the quantum and the classical worlds strong enough so that a dialogue is possible?” asked Dorit Aharonov, a computer scientist at the Hebrew University of Jerusalem.

During her second year of graduate school, Mahadev became captivated by this problem, for reasons even she doesn’t fully understand. In the years that followed, she tried one approach after another. “I’ve had a lot of moments where I think I’m doing things right, and then they break, either very quickly or after a year,” she said.

But she refused to give up. Mahadev displayed a level of sustained determination that Vazirani has never seen matched. “Urmila is just absolutely extraordinary in this sense,” he said.

Now, after eight years of graduate school, Mahadev has succeeded. She has come up with an interactive protocol by which users with no quantum powers of their own can nevertheless employ cryptography to put a harness on a quantum computer and drive it wherever they want, with the certainty that the quantum computer is following their orders. Mahadev’s approach, Vazirani said, gives the user “leverage that the computer just can’t shake off.”