book review

Quantum Computing Unveiled
A Concise Course with Topological Extensions
by Yidun Wan
Cambridge, 2026, 351 pages

Reviewed by T. Nelson

Quantum computers could start a revolution in computer science. They have many applications for simulating natural processes like subatomic particles and atmospheric physics. There’s obviously also interest in using them for cryptanalysis and AI. But how do they work?

This book answers that question from a computer science point of view, following the path of the legendary text by Nielsen and Chuang, which is still the best book on the subject. But N & C is now 26 years old and it’s also the most verbose at 676 pages long.

Wan’s textbook is newer, amazingly upbeat, and more concise. An important strength is a clear description of 1-qubit quantum gates, like the Hadamard or H-gate, which converts the fiducial state of a qubit to a superposed state; and 2-qubit gates, which are needed for the circuitry. The most important of these is the CNOT or control­led-NOT gate, which generates entangle­ment.

The most important algorithms are the quantum Fourier transform, quantum sorting, and Shor’s famous algorithm for factoring large integers, such as those used in crypto­graphy.

Wan gives a quick course on quantum mechanics and then describes how to create quantum circuits. In the last section he describes topological qubits, where the information is stored by ‘braiding’ things instead of the usual single-atom ground / excited state transitions.

I say ‘things’ on purpose. A conspicuous omission is any discussion of what these things are physically. If you’re hoping for insight on why a quantum computer actually works, this is not the book for you. Even with Shor’s algorithm (which all Comp. Sci. students and crypto­graph­ers already know), Yan just prints the flowchart with little explanation. The main step is “Compute GCD” (greatest common denomina­tor). How do you get a qubit to do that? Yan doesn’t say.

As for topological qubits, Yan gives the impres­sion that no one actually knows whether they produce entangle­ment (which is essential for quantum speed-up) or even how to manipulate the bits (which is obviously needed). Topological qubits are supposed to be more stable than ordinary ones—if they can be made to work.

At first the reader thinks the subject is too hard to understand. But what’s actually happening is that Yan is skipping over most of the details. You have to draw on your knowledge of computer science and quantum physics to figure out what must be happening.

Take the quantum Fourier transform (QFT) algorithm. Is it really faster than existing tech like an acousto-optic device? The book could have been improved by mentioning the fact that analog devices that convert a waveform to a spectrum in real time have been in use in electronic warfare for decades.

Readers will also be wondering what superpos­ition and entangle­ment actually do. This, says Wan, is outside the scope of the book and he refers us to the literature on the subject. The closest we get to an explanation is this:

When the QFT is applied to a quantum register, it intricately entangles the qubits, transforming computational bases into frequency bases. . . .

This coherence leads to constructive interference for the "right" answers and destructive interference for the "wrong" ones. [p. 147]

How?

For that, you need to read the physics litera­ture, like Jozsa and Linden’s article^[1] on the role of entangle­ment in quantum computa­tional speed-up. These authors say there’s a relationship between entanglement and the ability to perform a task with exponentially reduced resources. This allows multiple representations of numbers to be superposed.

How can a qubit do this? My guess is that it lies in the commonality of ordinary and topological qubits. The collection of n qubits is where the actual big number is stored as a specific pattern. If you have p qubits, you can store 2^p bits. If that’s not enough, then according to Jozsa and Linden the state is ‘p-blocked’. For a quantum computer to actually work, they say, all the qubits have to be entangled with all the other qubits, not just their neighbors. At the moment, this is a big problem with topological ones, which Wan says at best only entangle with their neighbors.

As far as what entanglement actually is physic­ally, so far all I’ve found are phenom­en­olog­ical descriptions. Maybe that’s all there are.

It’s a good demonstration that reading a textbook is only a starting point. It gets you oriented with the jargon so you can read the academic papers.

I have to admit that according to the Bible, Noah's ark, as designed by God himself, was 300 × 50 × 30 cubits, for a total of 450,000 cubits. Sounds like a powerful quantum computer. Even more impressive is that it was made of wood. Maybe they knew something we don’t.

[1] Jozsa R, Linden N (2003). On the role of entanglement in quantum computational speed-up. Proceedings: Mathematical, Physical and Engineering Sciences Vol. 459, No. 2036 (Aug. 8, 2003), pp. 2011–2032

jun 27 2026