internal quality factor (Q_i)

The internal quality factor, written Q_i, is a single number that tells you how good a piece of a quantum chip is at holding onto microwave energy without quietly losing it to the materials around it. Picture pushing a child on a swing and then letting go: a high-Q_i swing keeps swinging for a very long time, while a low-Q_i one drags to a stop fast because friction is bleeding away the motion. On a chip, the swing is a tiny on-chip resonator, and the friction is every imperfect surface, oxide layer, and stray defect that soaks up energy it should not. Engineers care because Q_i is the cleanest yardstick they have for how lossy their materials and fabrication process are.

Concretely, Q_i counts roughly how many oscillation cycles the resonator's energy survives before it leaks into internal loss channels rather than out the intended port. You measure it by cooling a test resonator to near absolute zero, sweeping a microwave tone across its resonance, and reading how sharp and deep the dip is: a tall, narrow resonance means low loss and high Q_i, a broad shallow one means the energy is draining fast. The total measured Q is split into Q_i, the intrinsic loss you are trying to fight, and the coupling Q that describes the deliberate connection to the outside world, so the trick is to isolate Q_i from the part you put there on purpose. Higher Q_i roughly tracks longer achievable qubit coherence, because the same surface oxides and trapped defects that drain a resonator also drain a nearby qubit.

The honest catch is that Q_i is not one fixed property of a material; it changes with temperature, with how many photons you drive into the resonator, and even from cooldown to cooldown, because much of the loss comes from individual atomic-scale defects that fluctuate. The hardest losses to beat show up at the single-photon powers that real qubits actually use, where two-level-system defects in surface oxides dominate. So a record Q_i quoted at high drive power can look far better than what the qubit beside it ever feels, and chasing Q_i is an ongoing materials-and-cleanliness fight, not a solved problem.