Neither the instructions nor the interface helped me to understand what I was doing or how to achieve it, for example I don't understand why if I click a row I can't click a column next, and vice versa. From which I can only conclude that it's just not for my sort of brain.

However I'm sure there is a diverting puzzle game in here somewhere. I wonder if you used narrative language and symbolism unrelated to linear reversible circuit synthesis (but kept whatever mechanic is important) an average player might be able to grasp it more easily?