I recommend this book I studied it in Undergrad and I never took a quantum theory course. https://www.amazon.com/Quantum-Computing-Computer-Scientists...

Quantum Computing for Computer Scientists

Note, you have to be willing to put the time in, especially if your linear algebra is rusty or (like me) you have only a passing familiarity with complex numbers.

With that in mind, it's almost entirely self-contained and you can immediately start to make connections with classical computing if you're familiar with automata.

I've been interested in learning about quantum computing for a few years now and this book finally got me going.

https://www.amazon.com/Quantum-Computing-Computer-Scientists...

[update]

As an aside it's a really great excuse to try out one of the many computer algebra systems out there. I gave Mathematica a trial for fun since I'd already used SageMath in the past.