As quantum mechanics enters its second century, quantum computing has been hot stuff for the last third of it, beginning with Feynman’s lectures on computation in 84 – 86. Articles on quantum computing appear all the time in Nature, Science and even the mainstream press.

Perhaps you tried to understand it 20 years ago by reading Nielsen and Chuang’s massive tome Quantum Computation and Quantum information. I did, and gave up. At 648 pages and nearly half a million words, it’s something only for people entering the field. Yet quantum computers are impossible to ignore.

That’s where a new book “Quantum Computing for Everyone” by Chris Bernhardt comes in. You need little more than high school trigonometry and determination to get through it. It is blazingly clear. No term is used before it is defined and there are plenty of diagrams. Of course Bernhardt simplifies things a bit. Amazingly, he’s able to avoid the complex number system. At 189 pages and under 100,000 words it is not impossible to get through.

Not being an expert, I can’t speak for its completeness, but all the stuff I’ve read about in Nature, Science is there — no cloning, entanglement, Ed Frenkin (and his gate), Grover’s algorithm, Shor’s algorithm, the RSA algorithm. As a bonus there is a clear explanation of Bell’s theorem.

You don’t need a course in quantum mechanics to get through it, but it would make things easier. Most chemists (for whom this blog is basically written) have had one. This plus a background in linear algebra would certainly make the first 70 or so pages a breeze.

Just as a book on language doesn’t get into the fonts it can be written in, the book doesn’t get into how such a computer can be physically instantiated. What it does do is tell you how the basic guts of the quantum computer work. Amazingly, they are just matrices (explained in the book) which change one basis for representing qubits (explained) into another. These are the quantum gates — ‘just operations that can be described by orthogonal matrices” p. 117. The computation comes in by sending qubits through the gates (operating on vectors by matrices).

Be prepared to work. The concepts (although clearly explained) come thick and fast.

Linear algebra is basic to quantum mechanics. Superposition of quantum states is nothing more than a linear combination of vectors. When I audited a course on QM 10 years ago to see what had changed in 50 years, I was amazed at how little linear algebra was emphasized. You could do worse that read a series of posts on my blog titled “Linear Algebra Survival Guide for Quantum Mechanics” — There are 9 — start here and follow the links — you may find it helpful — https://luysii.wordpress.com/2010/01/04/linear-algebra-survival-guide-for-quantum-mechanics-i/

From a mathematical point of view entanglement (discussed extensively in the book) is fairly simple -philosophically it’s anything but – and the following was described by a math prof as concise and clear– https://luysii.wordpress.com/2014/12/28/how-formal-tensor-mathematics-and-the-postulates-of-quantum-mechanics-give-rise-to-entanglement/

The book is a masterpiece — kudos to Bernhardt