Is a quantum gate different from taking a measurement? I'm reading a book on quantum computing. It is a very non-technical book, and I do not need a very technical explanation. I keep on seeing the words quantum gate pop up, and I'm wondering whether this is the same thing as taking an observable? Or, am I confusing two concepts of physics?
 A: Physically, a quantum gate represents the operation of doing something to a quantum state in a reversible way. Reversible here means that there is no loss of information in the process and so, in principle, it is always possible to apply another (generally different) gate to come back to the initial state.
Mathematically, a quantum gate is simply a unitary operator, which applied to a state produces another state.
A measurement is very different from this because measuring a state collapses it to a specific classical output, and this process is markedly nonreversible.
A: An observable is a way of representing some measurable quantity. The observable represents the set of possible outcomes of measuring that quantity. The observables together with the state give you the probability of each of the possible measurement outcomes.
A quantum gate represents a way of changing a quantum system. If a qubit has a value of 0 and you apply a quantum not gate to it then it will have a value of 1 after the gate is applied.
So a gate is not an observable since a gate represents a way of changing the state of a system, not a measurable quantity.
A: Just to provide a very concise starting point with the key concepts.
Both gate and measurement change the quantum state to be predictable in some (linear-algebraic) basis.
Basically, a gate is a basis change, and is reversible by nature.
In a measurement a superposition collapsing happens, during which the particle is who chooses this basis (from two opposite ones), and we get this choice. This is a random event, you can't predict it, and it's not reversible in the computational sense. You can interpret (terminal) measurements as random sampling from a probability distribution.
As a simple example, imagine two polarized plate. If you hold they behind each other in the same angle, then the second filter does nothing. But when you rotate it, it will absorb more light. In this case, the first plate can be interpreted as the input, second plate as the measurement, and the rotation itself as a gate.
Multi-qubit gates interpret their components in a higher dimensional unitary space, and can mix things to an entangled state.
