Quantum computing: it sounds more complicated than quantum mechanics, but it isn’t. Mathematician Chris Bernhardt, author of Quantum Computing for Everyone, explains why you need to know about it and which books will help you understand what it's all about.

You’ve very kindly made us a quantum computing book reading list, starting with an easy title with no math at all and going on to the reference book you need if you’re going to work in the field. Can you start by telling us what quantum computing is, and why we need to read these books and find out about it?

Standard computing involves manipulating bits. With quantum computing, you’re manipulating ‘qubits.’ You can do everything you can do with bits, but you’ve also got two additional operations with qubits: you can put them in a superposition of states and you can entangle them. At first, it’s not clear that these two operations are useful, but it turns out that they are. Quantum computing is really a more basic form of computing: you can do more things with quantum computers than you can do with classical computers.

Another reason to be interested in quantum computing is that it’s expected that sometime this year (probably) Google is going to announce ‘the era of quantum supremacy.’ What this means is that they’ll have invented a problem no classical computer can solve, and they’ll have solved it on a quantum computer. It’s going to be a highly contrived problem, but it’ll prove the concept that actual quantum computers can do things that classical computers cannot.

“Google is going to announce ‘the era of quantum supremacy.’ ”

There’s also the hope that soon we’ll be in a position where quantum computers are actually solving useful problems, most likely to do with chemistry. Chemistry, at its most fundamental level, is a quantum phenomenon; it involves quantum mechanics. So it makes sense to simulate it using a quantum computer. Here again, people want to use quantum computers because that seems to be the natural way of tackling things.

Another really interesting thing is that IBM has recently put a quantum computer on the cloud. It’s a very small quantum computer, with only five qubits, but anyone can play with it. You can play with it for free and it’s got a nice graphical interface. So, we’re getting to the stage where quantum computing is going to be in the news and it’s going to be available.

In the news, quantum computing seems to come up a lot in relation to encryption and cyber security, doesn’t it?

When people first started talking about quantum computers, it wasn’t clear what they would be able to do and whether they’d be able to do anything useful. The first major foundational paper was published in the mid-1980s by David Deutsch, whose work is described in all the quantum computing books I’ve recommended. He showed that theoretically there was, again, a highly contrived problem that a quantum computer could solve more quickly than a classical computer.

Then, there was a pause for about ten years before a mathematician called Peter Shor showed that there were actually real-world problems that quantum computers could solve. In particular, the way that we standardly encrypt—using what’s called the RSA encryption technique—could easily be broken by a quantum computer. So, suddenly, our internet banking and internet security would become insecure. That pushed things in two directions: one was to devise new encryption methods that could withstand attacks from quantum computers. The other was to spur the development of quantum computers as people saw they could actually solve practical problems.

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One use of quantum computers is breaking encryption. Another is to use the idea of entanglement to set up really secure encryption that cannot be intercepted by third parties. If a third party tries to intercept an entangled encryption process, then things become disentangled, and you can actually detect their presence.

Part of the reason you’ve chosen these quantum computing books for us is because you feel most people have no idea what quantum computing is about—and you’d like to change that. You mentioned that the difficulty comes from the fact that in our daily lives we have no experience of quantum phenomena and so we have to use math.

That’s true. There are these two things: superposition of states and entanglement, which we’re not familiar with in our everyday experience. Since we have no natural intuition about them, they need to be described mathematically. But I should add that the mathematics is quite simple. There’s this feeling that to understand quantum computing you need to understand quantum mechanics, but that’s not the case.

The mathematics for quantum computing uses a couple of ideas from quantum mechanics, but at the most elemental level. They are the really basic ideas, presented very, very simply. So, in the future, I–and a lot of other people—feel that you should study quantum computing before you study quantum mechanics. You see these ideas in a simple form first and then, later on, you can come to the partial differential equations and the really complicated mathematics.

Your book, Quantum Computing for Everyone, has math, but is still very accessible. Is that the idea, that people shouldn’t be frightened of quantum computing and we should all be engaged with it?

That’s what I feel—that quantum computing should be accessible to most people. There are just some really beautiful results—and because we’re not familiar with these two operations they seem totally counterintuitive.

Take error correction, for instance. It’s very difficult to stop your quantum computer from interacting with the rest of the universe. Errors are going to creep into these calculations. A qubit should have a certain state, but an error has crept in, and it is now in a different state. On the one hand, you’ve got to detect the error and you’ve got to correct it. On the other hand, you can never take a measurement of the qubit, because if you take a measurement you’ll change it into something else. At first sight it seems to be an impossible problem. But when you see how it’s done, it’s absolutely fascinating . . .

Let’s talk about the quantum computing books you’ve recommended, which you’ve ranked in order of difficulty. The first one on the list is Computing with Quantum Cats, which is by the British science writer John Gibben. He’s written a number of popular science books, including In Search of Schrodinger’s Cat. So this is a quantum computing book with no math at all. Tell us a bit more about it and why we should read it.

This is a history of the theory of computation. It introduces all the most important people and you see the development of the ideas. So, first of all, Alan Turing came up with what computation is. Then John von Neumann wanted to design hydrogen bombs and needed a computer to do that. So he took some of Turing’s ideas to design a computer. Then we come to Richard Feynman with quantum physics and David Deutsch and John Stewart Bell. There are little biographies of each of them.

You really get a feeling for their personalities in the book.

Yes. What you don’t get is a good feeling for what quantum computing is, because I don’t think you can get that without doing some mathematics. But if you’re completely math-phobic and you want to read a quantum computing book, this is a very good one for the underlying history and an introduction to the founders of the subject.

Computing with Quantum Cats was written a few years ago now, but he predicts that, “within a decade the computer will be turned upside down by quantum computing.” Do you agree with that?

It’s difficult to say what the applications are going to be. I certainly think that chemistry could become very, very different in the next decade. Probably the most major change is going to be that kids in school are going to be learning about quantum computing and playing with little quantum computers. It’s going to have more of an impact in education, I think.

He also says teleportation will be possible. Is Star Trek becoming a reality?

Teleportation is possible and it’s been done many times. What we’re talking about is teleporting the states of qubits. A Chinese team has actually teleported a qubit from Earth to a satellite in low earth orbit. Quantum teleportation is here and it’s used for communication—but we’re nowhere near teleporting people!

Is 30 qubits the same as 10,000 desktops? Is that roughly the order of magnitude?

You should take 2 to the power of the number of qubits and that tells you how many bits you’re talking about. If you’ve got five qubits, that’s the size of one of IBM’s quantum computers: that’s 32 bits.

So is a quantum computer much more powerful?

It’s a mixture. A lot of descriptions oversimplify things and say it’s a parallel computation. It isn’t really a parallel computation, because you’ve got all these rules about what happens when you measure qubits and so on. When you learn about quantum computing the first thing you begin to wonder is whether you can actually do anything with it because the rules seem so strange. But in fact you can.

You mentioned it might be useful for chemistry. What might you achieve with a quantum computer in chemistry? Can you give an example?

There’s work being done on photosynthesis, for instance. You want to be able to convert sunlight into energy—to be stored in batteries, for example. That’s a quantum process and it’s being studied using quantum computers. It really does have potential.

Okay, so let’s talk about the next quantum computing book on your list. This is Quantum Computing from the Ground Up by Riley Tipton Perry. This also tells the history, but with a bit more of the math thrown in.

Both this book and the next book I’ve recommended, Quantum Computing for Computer Scientists, mention Quantum Computing and Quantum Information (the fifth book on my list) as the real reference book. Both these books say they are, in some sense, introductions to that book.

What I really like about the Riley book, Quantum Computing from the Ground Up, is the description of Bell’s Inequality and what that means. If we go back to the 1920s and 30s, when quantum mechanics was first being described, Einstein really disliked it. He really felt that this idea in quantum physics of things jumping when they are measured, of probabilities coming in, shouldn’t be there. He didn’t like the idea of entanglement, where you have what he described as “spooky action at a distance.” So, he felt it was fundamentally wrong and there was a dialogue going on between Einstein and Bohr about what physics was and whether quantum mechanics was the correct way of describing things.

In the 1960s John Stewart Bell came up with a really clever experiment. He realized you could distinguish between the theory that Einstein was describing and the standard, Copenhagen theory that Bohr was in favour of. He devised this test, which has subsequently been performed several times, and it’s always come out in favour of Bohr and the Copenhagen description.

“I think quantum computing is going to become part of the standard education, certainly of computer scientists and perhaps of most scientists.”

This is a really important test and not just for historical reasons. It’s also because as you begin to learn a little bit about quantum phenomena you feel—or at least I did—much like Einstein, that there must be some sort of deeper theory, that it’s got to be simpler, that it can’t really be this strange. I think most people feel that way when they come across quantum mechanics. This test shows you quantum mechanics really does have these strange properties.

And then of course once you’ve got a clever idea you want to use it in other ways. The idea behind Bell’s test is now used in many encryption techniques, to encrypt data.

It’s a shame that Einstein died before the Bell test.

It would have been really interesting to see what he made of it.

Is Quantum Computing from the Ground Up a textbook?

It’s too short to be a textbook, I think. In a couple of places, it’s very terse. What’s very good about it is that it’s got lots of very clear, worked examples that you can read through. It’s a really good book if you want to learn about quantum computing on your own.

So the third book on your list of quantum computing books is Quantum Computing for Computer Scientists. When you mentioned this book in your email, you added that the computer scientist part of the title should be ignored. Why?

I felt it was too limiting. This is an undergraduate textbook and anyone in a STEM field could take a course with it. There are one or two exercises that involve computer programs, but they’re not essential to the book.

What do you like about it?

It’s a textbook and so it presents things in a very clear way. But where it’s especially strong is in the section on algorithms. If you remember I said that David Deutsch, in the mid-1980s, came up with the first quantum algorithm that showed you could do something faster on a quantum computer than you could on a classical computer. Deutsch’s algorithm is a highly contrived algorithm, but it’s very simple and in this book it’s presented very well.

Then there were a series of other algorithms leading to Shor’s algorithm for cracking the RSA encryption techniques. Each is a little bit more difficult, but they’re still presented in a very clear way. I really like this book for its presentation of algorithms.

When you say the book is suitable for any undergraduate studying STEM, is that because you see quantum computing being applicable to all STEM subjects?

I was thinking more that STEM students would be able to understand the book. But certainly it would be useful for chemistry and biology, and maybe as time goes on quantum computing is going to be applied to more and more STEM fields.

The book also has exercises, which might be useful. Here’s a quote from the preface: “This book is almost entirely self-contained. We do not demand the reader come armed with a large toolbox of skills. Even the subject of complex numbers,

which is taught in high school, is given a fairly comprehensive review.” So, again, even though it’s got math in it, the book shouldn’t be too hard to follow.

I was actually talking to somebody about this yesterday. When people read a math book, you get the impression it’s important to read it linearly: you must understand this chapter before you can move on to the next chapter. In fact, I think you can skip bits and then come back.

I would tend to read these books in a nonlinear fashion, because all of these books present too much mathematics at one time. You should go ahead and read the rest of the book and then see what mathematics you need and where you need it. I wouldn’t even read the mathematics chapter initially. Well, maybe read it, but I wouldn’t concentrate on it and I would skip bits if you found them difficult.

Is that why in your own quantum computing book you had breaks from the math in some sections before bringing it back in? You were also always very clear about why you were including a particular piece of math.

Yes. If you notice, in practically every other book they use complex numbers. I don’t think you need them. Then they talk about this thing called the ‘Bloch sphere’ which is very clever if you’ve got the sophistication to understand it. But I don’t think you should be worrying about it, the first time you come across these ideas. In my view, the amount of math you need initially is quite low.

What kind of audience was your own quantum computing book written for?

It’s for a Scientific American-type reader who wants to know what quantum computing is about and isn’t scared of mathematics. It’s for an audience that’s willing to sit down and perhaps run through some calculations with a pad and paper.

So fourth on your list of quantum computing books is Quantum Computing since Democritus by Scott Aaronson. Tell me about this book and why it’s on your list.

This is not a beginner’s quantum computing book, but if you already have some experience with some of the ideas of quantum computing then this could be the book for you. Scott Aaronson works in complexity theory, which is about how difficult problems are. So, for example, when we encode data, we want that to be easy, but for someone to break it, we want that to be hard. The classification of the levels of difficulty is the sort of problem Aaronson works on.

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This book wanders all over the place. I wouldn’t say it’s a linear book at all. He’s got ideas about how human minds work, about what free will is, about time travel. He mixes quantum computing in with philosophy and mathematics. It’s a mixture of these things, but he’s obviously thought very deeply about them. All sorts of interesting things crop up in the book and then he’s got really interesting things to say about them. And he’s got this very jokey style. There are nerdy jokes throughout the book which either you like or you dislike. I happen to like them. It’s a very entertaining book.

In terms of difficulty the book is very varied. Parts of it are very difficult, parts of it are easy, but it’s a book that’s worth reading. He’s got all sorts of ideas that are worth thinking about. It’s a really thought-provoking book.

One of the reviews, I think in Scientific American, said it was a ‘Big Ideas’ book.

It is. He’s a little opinionated, but he’s really intelligent and gives excellent explanations of why he is right and others are wrong!

The book has painting of Democritus on the cover. I know quantum computing goes back longer than many of us realize, but does it really go all the way back to Democritus as the title suggests?

We’re out of my area of expertise, but Democritus was talking about atoms, so in some sense, I guess. He does start with Democritus, but it’s not a big part of the book.

You last book is Quantum Computation and Quantum Information, which you already referred to. This is the Bible of the quantum computing field. Tell us about it.

This book came out in 2000, so almost 20 years ago now. Anyone who is seriously getting into quantum computation uses it. It is the Bible and it’s an enormous book, some 700 pages long. It’s very well written, though mathematically it’s at a slightly higher level than the others I’ve recommended. This is really a book for someone who seriously wants to get into quantum computing and probably has the equivalent of an undergraduate degree in math or physics or engineering. It’s a book for someone who’s really not afraid of mathematics.

Would you recommend somebody read one of the other books first?

Yes, I would, mainly because this book is so big. There’s so much information in it that I think it’s more useful coming to it after you’ve read one of the other books. Then you can read about other areas, or you can go back and read about things in more depth. This is the book to turn to if you want to know more about certain areas of quantum computing.

That said, this book has an excellent first chapter. It’s is an overview of quantum computing from an elementary level which is really good.

Quantum Computation and Quantum Information is a book to return to. It’s been the standard for 20 years now. They revised it after 10 years, but the revisions were minimal. I imagine they will probably revise it again in 2020 but again, I imagine, the revisions will be minimal. It’s really withstood the test of time.

That’s fascinating because I imagined quantum computing as a fast changing field—but in fact something written 20 years ago still dominates.

Yes. All of these are fundamental ideas. This is a basic sort of book: a theoretical computer science or theory of computation book. What’s going to happen now, I think, is that we’re going to see more concentration on how you actually build quantum computers, the physics of it, the engineering of it. Then there’ll be more applications to technical areas.

Will all computer scientists have to understand quantum computing in future?

I think most of us are going to understand quantum computing on some level in the future. Computer scientists definitely will because quantum computation is a more basic level of computation. It underlies classical computing. When you first start to learn about what it means to compute things, at the same time you’ll learn about quantum computation.

I understand that in quantum computing you can’t copy things— whereas a lot of classical computing is based on copying.

You have to be careful here. In quantum computing, if you have a qubit, it can be in one of an infinite number of states. You can’t design a mechanism that will copy an arbitrary qubit. But if you give me a zero qubit or a one qubit, there’s no problem copying in quantum computing, because just as with classical computation, you’re just copying zeros and ones.

What are people in quantum computing most excited about at the moment?

Probably the major excitement of the moment concerns the progress in actually building a quantum computer. With quantum computing you do have all these errors that keep creeping in so you have to do something to try and ameliorate that. That is the big challenge.

But what I’m personally really interested in is education and spreading these ideas to a wider audience.

So how long will it be before we’d be having this Skype conversation on a quantum computer rather than a Macbook Air?

I’m not sure we’ll ever need a quantum computer to talk via Skype. It’s difficult to say what we’re going to do with a quantum computer in the future. If people like Turing and von Neumann were asked around 1950 to predict what people would do with computers in the future, I can’t imagine they’d have said, ‘We’re going be using them to chat to one another.’

“Modern computers changed society. This could happen again with quantum computers.”

Modern computers changed society. This could happen again with quantum computers. But I think quantum computers will be used in conjunction with classical computers, and there will be certain types of problem you’ll use the quantum bit for and others that you’ll use the classical for.

You say you want to educate people about quantum computing. Does this mean you’re very confident that this is the future?

Yes. I’m confident this is the future. From a theoretical viewpoint, it’s a more fundamental form of computing. Also, I really do believe that the ideas here are very easy to learn and so it does make a lot of sense to learn about quantum computing and the basic quantum ideas before you start studying things like quantum mechanics. So, I think quantum computing is going to become part of the standard education, certainly of computer scientists and perhaps of most scientists.

And earlier you mentioned school, will quantum computing be taught in high school?

I think that’s where quantum computing should first be introduced. Here in the United States there has been this push for high school students to take calculus or statistics. . But I think theory of computation should be there alongside those two, a basic subject that everyone studies along with calculus and statistics.

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