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book reviews
books on quantum computingreviewed by T. Nelson |
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book reviews
books on quantum computingreviewed by T. Nelson |
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 might wonder what in physical terms 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? 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 2p 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 entangulated 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, it seems to me the doubters may have a valid point. We can easily visualize molecular bonds as electron clouds of two nearby atoms overlapping each other. There’s no similar way to visualize entanglement: all we have are two equations with a different sign, along with some observations.
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.
According to the Bible, Noah's ark, as designed by God himself, was 300 × 50 × 30 cubits, for a total of 450,000 cubits. (They spelled qubits differently in those days.) 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
Reviewed by T. Nelson
One of the biggest challenges for newcomers to qubits is making sense of the formulas. There’s no advanced math, but the Dirac bra-ket notation, which everyone in the field uses, makes the formulas hard to read. It also drives computer programmers up the wall with all the mismatched left and right brackets.
Here’s a typical one from Chapter 4 depicting two qubits that are ‘separable,’ which means they’re not entangled:
ρAB = 1 2 |0⟩⟨0|A⊗ |1⟩⟨1|B + 1 2 |+⟩⟨+|A ⊗ |−⟩⟨−|B
Knowing whether qubits are entangled or not is an important task. But if it looks like uninterpretable gibberish, it means two things: (1) you’re not alone and (2) you need this book.
The first two chapters are unique: they explain the math and all the notation for qubits using actual numbers (!) without skipping a single step. It is the clearest explanation I’ve ever seen and this section alone makes this layman-friendly book worth the price.
The remaining chapters are also interesting, though despite the authors’ efforts at friendlyification, the topic is still mostly abstract: there’s little discussion of how the qubits are produced and measured. The focus is exclusively on the qubits as carriers of information. This makes sense because we have little understanding of why entanglement occurs physically—especially compared to our understanding of molecules. Chemists are way ahead!
I’m not alone in this view. Reinhold Bertlmann makes a similar comment in Modern Quantum Theory (Oxford, 2023; 1012 pages):
There was a certain disconnect between established books on quantum mechanics . . . and quantum information processing, which frequently take a view heavily influenced by computer science and classical information processing.
These two books make a good pair, like left and right socks. You need one of each. Each is understandable without an advanced degree and they’re complementary to each other, especially on the topic of entanglement.
In the chapter on quantum money (what sci-fi fans might call Quatloos), it becomes clear that there can be no such thing unless we’re talking about virtual currency. Qubits are not stable and the last thing we need is currency that ceases to exist when observed. The authors know this; what they’re really doing is gently introducing the concept of a quantum channel. Elsewhere, they talk about storing important data like launch codes in qubits, which also sounds like a generally bad idea.
There’s no discussion about how quantum computing can be used against classically encrypted messages. The goal is to explain how to use qubits to create a secure communication channel.
Thus, the real question in this book is not how to do quantum cryptography but whether there is any such thing. The authors try to make a case that there is, at least for quantum key distribution using the classic BB84 protocol and the device-independent version (DIQKD), which they say is mostly the same as an entanglement protocol called E91. They do it in an understandable and friendly way, complete with many worked examples.
Of course friendliness and brevity come at a price. Bertlmann’s description of entanglement entropy is much clearer than the one in this book, which fails to mention that the formula doesn’t use just a log, but a log in base d. So I got the wrong answer using their formula until I checked in Bertlmann. On the other hand, Bertlmann’s book weighs 4.69 pounds—a potential issue for casual readers taking it to the beach.
I knocked off a star because there’s a definite need for an erratum sheet (their explanation of XOR is also garbled) and also because the authors get too familiar with their characters, imagining Alice playing guessing games and discussing her favorite flavor of ice cream. Of course ‘Alice’ and ‘Bob’ are just traditional shorthands for ‘person A’ and ‘person B’, which is cumbersome. In the real world, ‘Alice’ would probably be a wiry Russian hacker named Vladimir with a six-inch scar across his face and Bob would be a guy with no tan who lives on Cheetos. More colorful, perhaps, but in the world of qubits all colors are superposed and, perhaps, entangled.
jul 01 2026