The prospect of powerful new quantum computers comes with a puzzle. They’ll be capable of feats of computation inconceivable with today’s machines, but we haven’t yet figured out what we might do with those powers. One likely and enticing possibility: precisely designing molecules. Chemists are already dreaming of new proteins for far more effective drugs, novel electrolytes for better batteries, compounds that could turn sunlight directly into a liquid fuel, and much more efficient solar cells. We don’t have these things because molecules are ridiculously hard to model on a classical computer. Try simulating the behavior of the electrons in even a relatively simple molecule and you run into complexities far beyond the capabilities of today’s computers. But it’s a natural problem for quantum computers, which instead of digital bits representing 1 s and 0 s use “qubits” that are themselves quantum systems. Recently, IBM researchers used a quantum computer with seven ...