Quantum Computing: An overview of some useful books.

Where do I get started?

There are many ways to learn quantum computing, but where do you get started? First you will need to choose whether you prefer books, videos or online materials. I don’t have a preference, but often a good book is a good starting place. In this article I am going to focus on some books that I have found useful. The selection criteria for inclusion in this list are that I have a copy of the book (mostly physical copies) and that I have something to say about them - meaning that I have found them useful in some way.

If you do a search for books on learning quantum computing, you will find that most sources will suggest Quantum Computing and Quantum Information by Michael Nielsen and Isaac Chuang; Mike and Ike, as it is popularly known, introduces all the major ideas and techniques and is well written and rigorous, but it is only an introductory text for a small group of people - those who have extensive prior preparation in computer science, mathematics, and physics. Don’t get me wrong, you should get a copy (I’m actually on my third copy, the first two were paperbacks) - but it is not a good introduction if you are not well-versed in all three disciplines. It is a great reference book for anyone actively working in the field, and is often considered to be the canonical text in the field. There are many other books that are useful, but none are ideal. Below, I summarize some of the books that I have found to be useful in a list alphabetized by the first author. Note that I refer to Qiskit and Circ in several places below, these are software tools that enable you to actually perform quantum computations on quantum computers or simulators.

Quantum Computing Since Democritus, Scott Aaronson, Cambridge University Press. (2013)

Based on lectures delivered at the University of Waterloo, this book is really an overview of the nature of reality using computational complexity as an organizational tool. One of its interesting features is that the author argues that quantum mechanics should be taught as a generalization of probability. Most topics that are fundamental to quantum computing are covered and readers will gain a good understanding of what quantum computing is and what can be done with it. The book focuses more on the philosophy of quantum computing than its practice. Thus, the book is worth reading, but it isn’t the best place to get started - it won’t help you to learn how to do quantum computing, but it could stimulate your interest in learning more.

Introduction to Quantum Computing with Qiskit, Macauley Coggins, Scarborough Quantum Computing Ltd. (2021)

The stated aim of this book is to “introduce Quantum Computing while also giving a good primer on programming Quantum Devices using Qiskit.” Aimed at those with no prior background in quantum computing. It meets its goals, providing an excellent overview. Perhaps a good place to start, or for a quick review, but you will find yourself wanting, or needing, more details.

Quantum Computing: An Applied Approach, 2nd Edition, Jack D. Hidary, Springer. (2021)

Covers the basic theory, introduces programming using Circ and Qiskit, then reviews the necessary mathematics. I used this as the basis on a 1-hour class. I didn’t like it as a course text as much as I thought I would - the sequence of topic makes for much jumping around. Often available on at a good price at the usual online bookstores. A good book to have on your shelf as a reference book.

Quantum Computing for the Quantum Curious, Ciaran Hughes, Joshua Issacson, Anastasia Perry, Ranbel F. Sun, and Jessica Turner, Springer Open Access. (2021)

A well written introduction that is accessible by students who have completed a typical high school class in physics. Some knowledge of probability, trigonometry, and simple linear algebra would help. Easily accessible for students who have completed AP Phyics and AP Calculus. You can download a PDF or an ePUB® (at no cost) directly from Springer. On the Springer website, it is easy find out how to publish an open access book, finding the open access books is harder. You can search for Springer open access books here. You can find all the Springer open access books here sorted from newest to oldest. (These links work as of publication, but they will change over time.)

Quantum Computing & Information, a Scaffolding Approach, 2nd Edition, Peter Y. Lee, Huiwen Ji, and Ran Cheng, Polaris QCI Publishing. (2025)

This is a well written book and it is suitable for undergraduates from physics or computer science. The book begins with the basics of quantum systems, followed by how to manipulate systems with gates, it then goes on to entanglement, and finishes by covering quantum algorithms, error correction, and quantum information theory.

Mathematical Foundations of Quantum Computing, a Scaffolding Approach, Peter Y. Lee, James M. Yu, and Ran Cheng, Polaris QCI Publishing. (2025)

Another book in the Scaffolding series. If you are going to buy one book on the mathematics of quantum computing, this is the one to get. It begins with some basics including sums, products, trigonometry, sets and functions. Then it goes through vectors spaces and linear spaces, matrix methods and probability. It concludes with some useful references to other books and some useful published papers. This book would be a good supplement to any of the books on quantum computing in this review.

Quantum Computer Science, An Introduction, N. David Mermin, Cambridge University Press. (2007)

From my signature on the flyleaf of my copy, this was the first book on Quantum Computing that I bought, on 10/10/2018. Casual readers of this book may get the idea that there has been an evolution in nomenclature over time - Chapter 1 has the title Cbits and Qbits, and Qbits are used throughout the book; there has been no such evolution the term qubit first appeared in print in 1995 in a paper on quantum coding by Benjamin Schumacher (Phys Rev A 51, 2738-2747 (1995) - the acknowledgements section of that paper recount the origin of the word. As he notes in the American Journal of Physics (From Cbits to Qbits: Teaching Computer Scientists Quantum Mechanics, AJP 71, 23-30 (2003), the choice was purposeful, Mermin was following the rule that in English, q is followed by u and then by another vowel, so as with Q-tip, he prefers Qbit or sometimes qbit. Mermin’s paper is well worth reading - for most computer scientists, it contains all the quantum mechanics that they will ever need to know. The book is good, but there are better books if you are primarily interested in the computing aspects of quantum computers. If you are interested in building quantum devices, you will need to learn more quantum mechanics than is contained in Mermin’s book. I consider this to be a useful book, it was my entry into the subject, but there are better choices available today. As with all of Dr. Mermin’s books and papers, the quality of writing in this work is exceptional.

Quantum Computing - A Gentle Introduction, Eleanor Rieffel and Wolfgang Polak, MIT Press. (2011)

Another book with complete coverage of the background and structure of quantum computing. No coverage of quantum computers or their programming. Assumes no prior knowledge of quantum physics and contains more text than most of the others. Note that I didn’t say that it has less mathematics, it doesn’t, it just has longer explanations (and small print if that is a consideration). Highly recommend as supplementary reading.

Dancing with Qubits, 2nd Ed., Robert S. Sutor, Packt. (2024)

Another comprehensive introduction that is self contained. I use this often as a reference. It includes an extensive list of references. An excellent resource for self-instruction.

Introduction to Classical and Quantum Computing, Thomas Wong, Rooted Grove. (2022)

One of the best introductions out there, largely self-contained. Introduces programming on real quantum computers, unfortunately it focuses on IBM’s Quantum Composer and OpenQASM editor rather than the now more widely-used Qiskit. I would recommend this as a starting point for most students with the proviso that they also use Qiskit for the examples by supplementing with another book or IBM’s online tutorials. This book has the added advantage that it is also available at no cost as a pdf here (scroll down the page). Some of the calculations are also done in SageMath and Mathematica® .

Essential Mathematics for Quantum Computing, Leonard S. Woody III, Packt. (2022)

The authors says it all on the title page: “A beginners guide to just the math you need without needless complexities.” Physics majors will be familiar with most of the mathematics covered in this text by the time they take a course in quantum mechanics or quantum computing. Much of it will be new to students coming to quantum computing from a computer or information science background. You must learn linear algebra and you must learn about bras and kets, this is a good place to learn all the linear algebra that you missed. It does not contain probability theory or set notation - knowledge of both of these fields is useful in quantum computing. The Mathematical Foundations of Quantum Computing, by Lee et al. reviewed above is a much better choice as it does contain almost all the mathematics that is needed for quantum computing.

Quantum Computing for Computer Scientists, Noson S. Yanofsky and Mirco A. Mannucci, Cambridge University Press. (2008)

Starts with all the background mathematics and quantum mechanics needed, then it devotes seven chapters to developing the ideas of quantum computing. It doesn’t introduce actual programming other than a few Matlab® exercises. This is the perfect book for learning the underlying theory - if you want to be able to read Nielsen and Chuang, working through this book first will make Mike and Ike accessible.

Hands-On Quantum Machine Learning With Python, Volume 1: Getting Started, Franck Zickert, PyQML. (2021) Hands-On Quantum Machine Learning With Python, Volume 2: Combinatorial Optimization, Franck Zickert, PyQML (2023)

Interesting books with a different approach. Using IBM’s Qiskit is built in across the curriculum in these books. This is both a great strength and a problem. It’s a problem because IBM has updated Qiskit and most of the code in these volumes will no longer run without some modification. Dr. Zickert is in the process of rewriting while he also develops additional volumes. As this will continue to be an issue, it is probably worth subscribing to his Quantum Machine Learning website - I do, it has a good Qiskit 2 tutorial and you get chapters from the new editions of the books as they become available; you also get to download the first editions which are still very useful.

So, if you are interested in learning about quantum computing or learning how to get started in quantum computing, the books above provide starting points for most levels of prior knowledge. I’ll follow this up with articles on more specialized books and introductions to videos and some online resources.