I'm intently curious what sort of common-sense explanation you'd ascribe to how one programs an ordinary classical computer. Would you describe a computer programmer as one who orchestrates a delicate movement of charge through an intricate arrangement of n–p–n bipolar transistors?

Quantum computers really can be instructed to do an abstract operation on an abstract quantity, just like I can on an ordinary computer. You tell quantum computers to add and multiply, just as you do in your favorite programming language. In the programming language Quil, which a couple quantum computers of different base technologies use, one can literally write down a matrix of numbers in a program to define a new mathematical function, and later use that function to manipulate the contents of the computer's RAM[1]. On top of this, you can have loops, boolean conditions, and all that jazz a programmer expects. You don't even need a physicist to do this; a completely physics-ignorant programmer could do this.

All this business about energy levels, evolution, etc. are distractions, just as the electrodynamics of a transistor are distractions from what it means to program a computer.

[1] I'm abusing the word "RAM" here, where I truly mean the state of your quantum register(s).