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Urmila Mahadev spent eight years in graduate school solving one of the most basic questions in quantum computation: How do you know whether a quantum computer has done anything quantum at all?

18-year-old Ewin Tang has proven that classical computers can solve the “recommendation problem” nearly as fast as quantum computers. The result eliminates one of the best examples of quantum speedup.

What’s easy for a computer to do, and what’s almost impossible? Those questions form the core of computational complexity. We present a map of the landscape.

Computer scientists have been searching for years for a type of problem that a quantum computer can solve but that any possible future classical computer cannot. Now they’ve found one.

The mathematician Gil Kalai believes that quantum computers can’t possibly work, even in principle.

The quest for “quantum supremacy” – unambiguous proof that a quantum computer does something faster than an ordinary computer – has paradoxically led to a boom in quasi-quantum classical algorithms.

The fusion of quantum computing and machine learning has become a booming research area. Can it possibly live up to its high expectations?

Quantum computers should soon be able to beat classical computers at certain basic tasks. But before they’re truly powerful, researchers have to overcome a number of fundamental roadblocks.

A complete classification could lead to a wealth of new materials and technologies. But some exotic phases continue to resist understanding.

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