Quantum does not mean "small and discrete", it only means "discrete", as in "quantisation" - fitting values into a discrete defined set. For instance in mathematics the operation of "rounding" quantises fractions into the set of integers.
Similarly in electronics, sampling signals quantises them into a discrete digital value.
You have the connotation of "small" because quantum physics coincidentally mostly deals with very small things - the smallest divisions (or quanta) of matter.
A quantum leap, however, has the connotation of large, because a leap covers a large distance. However it is quantum, so cannot be further divided within the context that it is used.
For instance the United States could have all its coordinates quantised to within the individual states. A step from the center of one state to the center of a neighbouring state is quite a large distance, but it is only a change of one quanta.
So a quantum leap is a discrete change from one state (not a US state now) to the next state, with the connotation that the states involved are big and cover a large "area".
Another good way of thinking about it is a staircase. Each step is a quanta. The bigger the steps the bigger the leap to get to the next one.
A good synonym is also "step change".