Where does it live?

the computer is itself is in an extreme environment

It lives in the cold

    The central processing unit or CPU is the "brains" of the computer, meaning all of the computations are carried out in the CPU. The qubits in the CPU are extremely fragile, but information is stored form the rotation and orientation of these qubits. In order to get accurate readings on each of the thousands of qubits the processor is brought to a temperature of 0.015 Kelvin, which is 180 times colder than the vacuum of space.

    
  
     Since the CPU is cooled to near absolute zero, it is in a superconducting state. When something is superconductive it looses all electrical resistance, this loss of resistance causes the computer to need only about 25kW of power to operate. To put that in perspective, an average computer draws between 250 and 80 watts of power. However, you won't be browsing the internet for memes on a quantum computer.  A supercomputer will draw upwards of 500kW, which is 20 times more power than a quantum one.

How does It get so cold?

The computer uses liquid helium as a refrigerant. The helium is recycled through condensation of the gas within the cooling unit.