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I want to try my hand at designing quantum algorithms to solve certain problems. I feel like I understand (for example) how Grover's algorithm and Shor's algorithm work, and I'm excited to apply the various "computing tricks" that aren't available in classical computing. Unfortunately, my knowledge of such tricks is limited to their application in the few famous algorithms, and I'm not at all sure how to legitimately apply them in general.

Are there any resources available that will quickly bring me up to speed?

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the classic reference for a computer scientist wanting to get up to speed on quantum algorithms is:

Quantum Computer Science by David Mermin.

In the 1990's it was realized that quantum physics has some spectacular applications in computer science. This book is a concise introduction to quantum computation, developing the basic elements of this new branch of computational theory without assuming any background in physics. It begins with an introduction to the quantum theory from a computer-science perspective. It illustrates the quantum-computational approach with several elementary examples of quantum speed-up, before moving to the major applications: Shor's factoring algorithm, Grover's search algorithm, and quantum error correction. The book is intended primarily for computer scientists who know nothing about quantum theory, but will also be of interest to physicists who want to learn the theory of quantum computation, and philosophers of science interested in quantum foundational issues.

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Since you understand Grover's algorithm and Shor's algorithm, you're a lot closer to being up to speed than you might guess. Specifically, the field of quantum algorithms is fairly narrow, much more so than classical algorithms, so getting caught up is not as daunting. Aside from generalities like using quantum computers to simulate quantum systems, there are only three or four main types of quantum algorithms (at a broad level like "quantum Fourier sampling").

The right place to start is books like Mermin or Nielsen and Chuang, as in the other answers, but after that you'll have to move to papers. Stephen Jordan has compiled a pretty comprehensive list of about two hundred quantum algorithms papers in the Quantum Algorithms Zoo, organized by problem. Browsing through this list is a good way to get an overview of what's out there and choose some papers relevant to your interests.

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P.S. Jordan also links to several survey papers in the navigation bar on the right. – Henry Cohn May 3 '13 at 13:00

I thought the standard book was Nielsen and Chuang, "Quantum Computation and Quantum Information", but maybe it's out of date by now.

PS, you might be better off asking on .

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It's still in use in the classroom. Together with Kitaev's textbook. – Alan May 3 '13 at 12:29

I think this book is good for beginning:

"An introduction to quantum computing algorithms" by Pittenger A.O.

Also, the course by Prof. $Vazirani$ on $edx$ "(" is good way for learning the necessary material in this way.

Since, there are two main algorithms and other algorithms uses these basic algorithms, you can understand deeply these two quantum algorithms and modify your problem again to find an approach. These two basic and important algorithms are Grover's algorithm (for searching problem) and Shor's algorithm (for factorization). Also, Simons algorithm is good for studying. But, in general, you must learn Fourier sampling and superposition and the quantum gates and their works.

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