Superconducting quantum processors run near 10 millikelvin - about a hundredth of a degree above absolute zero, colder than anywhere in deep space.
The reason is simple: heat is motion, motion is noise, and noise destroys the qubit's state. A qubit holds a direction, and any stray energy nudges that direction. Nudge it enough and the information is gone. This is decoherence, and it is the central engineering problem of the field.
The dilution refrigerator does the cooling - that gold chandelier in every quantum computing photograph is mostly plumbing and wiring, not the computer. The actual chip is a fingernail-sized square at the very bottom.
Not every design needs this. Trapped-ion machines hold atoms in electromagnetic fields and run much warmer. Photonic approaches use light and can operate at room temperature in parts of the system. The cold is a consequence of one particular choice of hardware, not a law of quantum computing.