Scientists have long dreamed of developing quantum computers, machines that rely on arcane laws of physics to perform tasks far beyond the capability of today’s strongest supercomputers. In theory such a machine could create mathematical models too complex for standard computers, vastly extending the range and accuracy of weather forecasts and financial market predictions, among other things. They could simulate physical processes such as photosynthesis, opening new frontiers in green energy. Quantum computing could also jolt artificial intelligence to a vastly higher level of sophistication: If IBM’s Watson can already win at Jeopardy! and make some medical diagnoses, imagine what an enormously smarter version could do.

But to realize those visions, scientists first have to figure out how to actually build a quantum computer that can perform more than the simplest operations. They are now getting closer than ever, with IBM in May announcing its most complex quantum system so far and Google saying it is on track this year to unveil a processor with so-called “quantum supremacy”—capabilities no conventional computer can match.

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