Thesis On Quantum Cryptography

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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. 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? 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.

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. But once a quantum computer can perform computations a classical computer can’t, how will we know if it has done them correctly?

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.

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. Mahadev displayed a level of sustained determination that Vazirani has never seen matched.Mahadev, who is now a postdoctoral researcher at Berkeley, presented her protocol yesterday at the annual Symposium on Foundations of Computer Science, one of theoretical computer science’s biggest conferences, held this year in Paris.Her work has been awarded the meeting’s “best paper” and “best student paper” prizes, a rare honor for a theoretical computer scientist.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?She applied to graduate school at Berkeley, explaining in her application that she was interested in all aspects of theoretical computer science — except for quantum computation.“It sounded like the most foreign thing, the thing I knew least about,” she said.Now, finally, she had the makings of a “very beautiful Ph. dissertation,” said Umesh Vazirani, her doctoral adviser at Berkeley. 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.It is possible, two different teams showed, for a quantum computer to prove its computations, not to a purely classical verifier, but to a verifier who has access to a very small quantum computer of her own.Researchers later refined this approach to show that all the verifier needs is the capacity to measure a single qubit at a time.

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