Reading about quantum computers is fascinating and fun but it brings up the question of where are the calculations happening in the qubit? Where physically is the qubit and where does a state in superposition exist physically?
From what I've read or seen on Youtube clips an example of a qubit is physically in the form of a single atom trapped. The spin (up or down being 1 or 0) of the atom represents the 1 or 0 of a binary computer. Now being a single atom its wavefunction can be in superposition of either up or down. The spin of the atom can be simultaneously both up and down until it is measured. Think the famous Schrodinger's Cat. So when using a qubit to do a calculation what's happening in the computer? In this strange superposition where is the calculation taking place? In the single isolated trapped atom you would think. But where in the atom? This is a great example of quantum weirdness in how the quantum world is different than the classical world. The classical world has no spin of the atom, spin is a quantum property of the atom. The quantum world says that the atom can be simultaneously both spin up and spin down until it is measured. A great video by PhD Comics that discusses what a quantum computer is given here. This cartoon, especially the part with the cube representing the qubit really got me wondering. Wondering about where do quantum computers do their calculations?
In a classical computer you have physical objects such as transistors which can be used to be on or off representing the 1 or 0 's in a calculation. In running a program in a classical computer you could in principle stop the program and look at the microprocessor down at the single elements in the chip and see where all the 1's and 0's are. Kind of like taking a snapshot of the calculation occurring. You could advance the calculation by say one clock step and see how the program is evolving. How all the 1's and 0's are moving around according to the program. Apparently you can't do that with a quantum computer. Once the calculation starts you can not observe what is happening. An observation would ruin the calculation. This isn't just an observation of say stopping it and taking a picture. It is an observation of any kind and need not be by a conscious being. A vibration of the qubit is an observation. This is why the qubit is in an environment as cold as possible. An observation leads to quantum decoherence of the state. Anything that can effect the state of the object is an observation or a measurement. This gets to the heart of one of the problems in quantum mechanics in what is meant by a measurement and what it does to a state of the system. But how do you know what your program is doing in the quantum computer? Where is the calculation taking place in time? Or how is it evolving in time? I have John Preskill's Quantum Computer lecture notes in book form loaded from his website here. Maybe I just need to read more of his lectures. But not the whole book.