1. One way to build a qubit (e.g. a quantum bit, used for quantum computing) is to isolate a single spin-1/2 particle. In this question, you will think about how you might build and manipulate this qubit. You have at your disposal the qubit itself, and a powerful magnet that can apply static magnetic fields in the Z direction, and also time-dependent AC fields of the form B(t) = B (cos(wt)Z + sin(wt)) . (1) Finally, you have a powerful refrigerator, that can cool your system down so that it is in its lowest energy state, (a) Your first task is to prepare your qubit in the state | 1) (usually called |0} in the quantum computing literature). Describe a way that you can do this, using your refrigerator and your magnet. (b) Your next task is to develop a method to \"flip your bit\