The labor pool in quantum computing is even smaller. By some accounts, fewer than a thousand people in the world can claim to be doing leading research in the field.

The number of international students applying to physics doctoral programs in the United States fell by an average of 12 percent this year, according to a study from the American Physical Society. Universities on the coasts have maintained their numbers, the study said, but the drop is noticeable in the middle of the country.

For decades, quantum computing was purely experimental. When it was first proposed in the early 1980s, the goal was to build a system based on the seemingly magical principles of quantum mechanics. Over the past several years, scientists have shown that they can build these machines, if only on a small scale.

With traditional computers, transistors store “bits” of information, and each bit is either a 1 or a 0. Those are the fundamental slices of data that tell a computer what to do.

When some types of matter are extremely small or extremely cold, they behave differently. That difference allows a quantum bit, or qubit, to store a combination of 1 and 0. Two qubits can hold four values at once. As the number of qubits grows, a quantum computer becomes exponentially more powerful.

Scientists who build these systems specialize in the physics of those very small or cold things, which is nothing like the physics we experience from day to day.

“There just aren’t that many people who know how to do this,” said Steven Girvin, a professor of physics at Yale University. “These machines are quasi-hand-built by Ph.D.s in physics.”