qubit anharmonicity

A qubit is supposed to be a two-level system: a 0 and a 1 you can flip between. But the artificial atoms on a superconducting chip actually have a whole ladder of energy levels (0, 1, 2, 3...), and you only want to use the bottom two. Anharmonicity is the gap between the steps of that ladder being uneven. If every step took the same amount of energy, a control pulse aimed at 0->1 would also nudge 1->2, and your qubit would quietly leak out of the space you can compute in.

Concretely, anharmonicity is the difference between the energy needed for the 0->1 transition and the energy needed for the 1->2 transition. You design the device so these two are at noticeably different frequencies. Then a control pulse tuned to the 0->1 frequency mostly leaves the higher levels alone, because they simply do not resonate with it. The bigger this difference, the faster and cleaner you can drive the qubit without spilling population into level 2 and beyond.

There is a real tradeoff baked in. The popular transmon design is made deliberately flat (E_J >> E_C) to make it shrug off charge noise, and that same choice makes the anharmonicity small, only around 200 MHz negative. So engineers cannot just blast short, hard pulses; they shape them carefully to dodge the nearby 1->2 transition. Designs like fluxonium chase a much larger anharmonicity to ease this, but pay for it with other complications. No single answer has won.