Reddit reviews Quantum Computing for Computer Scientists

Don't get discouraged, it's possible to get to a reasonable understanding with some sustained effort. However, you need to get the following into your head as quickly as possible:

Popular level explanations of anything quantum are a waste of your time.

Go back and read that again. You will never get close to understanding the field if you rely on someone else managing to "find the right metaphors" for you. Quantum computing is a mathematical field, and if you want to understand a mathematical field, you need to do mathematics. This sounds super scary, but it's actually no problem! Math is not what you think it is, and is actually a lot of fun to learn. You just need to put some work in. This just means maybe doing an hour or so of learning every day before you go to work, or afterwards.

Let's look at a little bit of a roadmap that you can follow to get to a reasonable understanding of quantum computing / quantum information. This is pretty much the path I followed, and now I am just about to submit my PhD thesis on quantum computational complexity. So I guess it worked out OK.

1. You can get really far in quantum computing with some basic understanding of linear algebra. Go to Khan Academy and watch their fantastic introduction.
   
   If Sal asks you to do an exercise, do the exercise.
   
   
2. Now you know what a vector is, can kind of grasp what a vector space is, and have some good intuition on how matrix-vector and matrix-matrix multiplication works, then you can probably make a reasonable start on this great intro book: https://www.amazon.co.uk/Quantum-Computing-Computer-Scientists-Yanofsky/dp/0521879965
   
   Start from the start, take it slowly, and do all of the exercises. Not some of the exercises, do all of the exercises. If you don't know a term, then look it up on wikipedia. If you can't do an exercise, look up similar ideas on Google and see if you can muddle your way through. You need to get good at not being scared of mathematics, and just pushing through and getting to an answer. If there is an explanation that you don't understand, look up that concept and see if you can find somebody else's explanation that does it better. Do the first few intro chapters, then dip in to some of the other chapters to see how far you get. You want to get a pretty good coverage of the topics in the book, so you know that the topics exist and can increase your exposure to the math involved.
   
   
3. If you manage to get through a reasonable chunk of the book from point 2), then you can make a start on the bible: Quantum information and computation by Nielsen and Chuang (https://www.amazon.co.uk/Quantum-Computation-Information-10th-Anniversary/dp/1107002176/ref=pd_lpo_sbs_14_img_1?_encoding=UTF8&psc=1&refRID=S2F1RQKXKN2268JJF3M2). Start from the start, take it slowly, and do all of the exercises.
   
   Nielsen and Chuang is not easy, but it's doable if you utilise some of the techniques I mention in point 2): Google for alternative explanations of concepts that the book explains in a way that confuses you, do all of the exercises, and try to get good coverage throughout the whole book. Make sure you spend time on the early linear algebra and basic quantum chapters, because if you get good at that stuff then the world is your oyster.
   
   Edit:
   
   Just remembered two more excellent resources that really helped me along the way
   
   A) Quantum mechanics and quantum computation, a video lecture course by Umesh Vazirani (YouTube playlist here) is fantastic. Prof. Vazirani is one of the fathers of the field of quantum computing, with a bunch of great results. His lecture course is very clear, and definitely worth devoting serious attention to. Also, he has a wonderful speaking voice that is very pleasant to listen to...
   
   B) Another lecture course called "Quantum Computing for the determined", this time given by Michael Nielsen (YouTube playlist here). In my opinion Nielsen is one of the best scientific communicators alive today (see also his unrelated discourse on neural networks and machine learning, really great stuff), and this series of videos is really great. Communicating this sort of stuff well to non-practitioners is pretty much Nielsen's whole jam (he quit academia to go on and write about science communication ), so it's definitely worth looking at.

I began by just plowing through wikipedia articles and trying to get the basic concepts in broad strokes. I would suggest that you do that.

I found this book, that is totally awesome: Quantum computing for computer scientists

Quantum computing for the determined, already mentioned here, is also awesome.

There is also IBMs quantum experience web site, that contains a front-end for programming a real 5-qubit quantum computer. It is free of charge, you just need to register with an email address in order to access it. Soon (as in a few days) there will also be a 16-qubit computer to play with at that site. Playing with the real thing is very good for study morale, at least for me..

A simpler quantum algorithm: https://secure.wikimedia.org/wikipedia/en/wiki/Deutsch%27s_Algorithm though I'm not sure that'll enlighten you. if you're really interested I'd recommend Quantum Computing for Computer Scientists which is a great intro and doesn't assume much knowledge (the first chapter introduces complex numbers, the second linear algebra).

If I were you I would read this book quantum computing for computer scientists
which is geared torward undergraduates.

He has a arxiv article which he based his book on. See an introduction to quantum computing.

Someone else suggested other books. Those are more geared toward graduates and I would read these books first and then try to tackle those.

I haven't entirely read this book, but I remember that it explains Grover's algorithm well. It might be what you are looking for because it states that it's target audience is undergraduate computer science students.