  Electrical engineers and physicists are naturally very interested in noise in
circuits, amplifiers and detectors. With the advent of quantum computation and
other high frequency electronics operating at low temperatures, we have entered
a regime where quantum noise and quantum-limited detectors are important. In
this paper we describe the general concept of a two-level system as a quantum
spectrum analyzer and apply it to a simple superconducting qubit, the
Cooper-pair box. We derive and discuss the quantum noise associated with both a
resistor and a classical tunnel junction, and study the effect these noise
sources will have on a Cooper-pair box. Finally, we describe a theoretical
technique for calculating quantum noise which involves studying the noisy
system of interest coupled to a two-level system. We use this technique to
calculate and give a heuristic explanation of the quantum charge noise of a
normal metal single electron transistor.
