Thus, the sole reason to prefer a quantum computer is that the subatomic world obeys different laws of probability than the ones we are used to. In everyday life, it would be silly to speak of a “minus 30 percent chance of rain tomorrow,” much less a “square root of minus 1 percent chance.” However, quantum mechanics is based on numbers called amplitudes, which are closely related to probabilities but can also be negative (in fact, they are complex numbers). ...No, quantum computers are not like fusion power. Fusion has been physically demonstrated in H-bombs, and are only impractical today because of engineering difficulties. I quoted Aaronson below saying “It’s entirely conceivable that quantum computing is impossible for some fundamental reason.”
But the biggest payoff so far may have been an improvement in the way quantum mechanics itself is taught and understood. Since its beginnings in the 1920s, quantum mechanics has been considered the prototype of an abstruse, complicated theory: something beyond the grasp of all but a few physicists. Today, though, I and others regularly explain its underlying logic to students by focusing on the simplest imaginable system to which that logic applies: the qubits that make up a quantum computer.
Like fusion power, practical quantum computers are a tantalizing possibility that the 21st century may or may not bring — depending on the jagged course not only of science and technology, but of politics and economics. By contrast, as a scientific endeavor that combines many of the deepest questions of physics and computer science, there’s no need to wait for quantum computing: It’s already here.
He brags of factoring 15 in the article, but in the podcast he tells of a recent paper on the Quantum Factorization of 143.
That "biggest payoff" is absurd. That 1920s quantum mechanics was widely understood by 1930. He may think that it helps to explain the theory in terms of qubits, but no one has ever been able to make a true qubit, and quantum mechanics is used to solve problems every day anyway. He says that the central idea is that probabilities can be negative. However I don't think that it is helpful at all to think about negative probabilities. He says that it helps understand how waves interfere, but I don't.
Update: A new paper argues that entanglement is necessary for the quantum computational speedup. Others have disagreed.