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I have a computer science background, and I'm interested in studying 'quantum algorithms' and anything that is related like 'quantum complexity'.

I would like to have all important resources that is needed to study quantum algorithms. For example, textbooks, papers, surveys.

If there are any resources for algorithms like Shor's algorithm, then please could you also share these. There are multiple of textbooks and papers, so can you specify the good one for computer science background.

This video by John Watrous is really good for an introduction to quantum algorithms.

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For complexity theory, Watrous' CSSQI 2012 lectures are the best resource I found so far. Here's the corresponding review paper. He approaches the subject in a fairly rigorous manner which is a great thing if you like clarity.

You could also follow Scott Aaronson's undergraduate lectures and his 2013 book Quantum Computing Since Democritus in parallel for a more intuitive although slightly hand-wavy approach.

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I would like to add some more sources:

Perhaps the most well-known source is the book "Quantum Computation and Quantum Information" by Nielsen & Chuang. Even though the scope of the book is broader than just quantum algorithms, it is well-structured so there is no need to dig through unrelated topics.

Another source is Ronald de Wolf's lecture notes, which you can find here. As these are updated every year, they are a bit more up-to-date than Nielsen & Chuang's book.

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I found this overview of quantum algorithms and their implementation (for majority of them) on IBM Q Experience quite useful: https://arxiv.org/abs/1804.03719.

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I would also like to mention these:

  • The Introduction to Quantum Computing: It has a few rough edges and it leans on the multiple universes interpretation of measurement in quantum mechanics, but it was well organized and provides a good overview in a short time.
  • Quantum Computer Science: An Introduction: A bit surprised that Mermin's textbook was not mentioned yet. It provides some additional ways of thinking about the algorithms. I found his group theory explanation (as background for understanding how period finding relates to factoring) in the appendix a little too concise, but that may be just me.
  • Quantum Computing: A Gentle Introduction: I found this book to be pretty comprehensive and clear enough so that if I needed an alternative explanation of something, I could find it here:
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There is a textbook that starts from scratch and teaches you all the fundamental concepts of quantum computing, including quantum algorithms. I would also recommend the tutorials as these are written in python so should accessible to Computer Scientists. There are also further tutorials on things such as Shor's.

When learning I also found there were lots of useful videos about specific topics on YouTube.

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