I am an undergraduate doing research on QC/QI. My current topic to learn is continuous-time quantum walks, but first I must learn the random quantum walk. That being said, I was wondering if someone could simply explain what a random quantum walk is. I am familiar with the classical random walk already.
A quantum walk can be thought of as the quantum version of the classical random walk.
A classical random walk is a simple dynamics in which according to the result of a coin flip a "walker" moves in one direction or the other.
A quantum walk (in its simplest, discrete-time, one-dimensional version) works the same, except that the "coin flip" operation is now a quantum operation, that is, a unitary gate. So at every step the coin is flipped and ends up in a superposition of its two states, and the walker thus moves in the two directions according to the amplitudes of the associated coin.
You can also have a look at this post for further details.