By Michael Nielsen, December 2018

In natural science, Nature has given us a world and we’re just to discover its laws. In computers, we can stuff laws into it and create a world. – Alan Kay

Quantum computing originated in the 1980s with several papers that received little fanfare at the time. Even by the mid-1990s, mentioning quantum computing to a physicist usually resulted in the question: “What’s a quantum computer?” Answers would often then be greeted with: “Isn’t that engineering? What’s it got to do with physics?”

Sometimes, these questions were asked with a large dollop of chauvinism, implying that engineering is somehow – it was never quite explained how – a pursuit inferior to physics. But remove that chauvinism and there’s still an interesting underlying question: in what sense (if any) can quantum computing be considered a science? And will it lead to the understanding of important new fundamental truths about the universe?

The roots of these questions go back much further than quantum computing. They’re reflective of some broad questions described in Herbert Simon’s book The Sciences of the Artificial.

Historically, the earliest sciences studied the natural world: astronomy, physics, chemistry, and biology. Each took extant natural systems, and tried to uncover the underlying ideas. But many more recent sciences study systems made by humans. Examples include computer science, linguistics, synthetic biology, and economics. While the corresponding systems were made by humans, they have an extraordinary, rich structure, unanticipated by the humans who made them. What Simon means by the sciences of the artificial is the discovery of this structure, i.e., the discovery of deep ideas and principles such as the invisible hand, comparative advantage, public-key cryptography, and so on.

This notion of the sciences of the artificial is particularly striking in the case of computer science, which began with its theory of everything, but which has flourished as we study the emergent consequences of that theory:

[C]omputer science began in 1936 when Alan Turing developed the mathematical model of computation we now call the Turing machine. That model was extremely rudimentary, almost like a child’s toy. And yet the model is mathematically equivalent to today’s computer: Computer science actually began with its “theory of everything.” Despite that, it has seen many extraordinary discoveries since: ideas such as the cryptographic protocols that underlie internet commerce and cryptocurrencies; the never-ending layers of beautiful ideas that go into programming language design; even, more whimsically, some of the imaginative ideas seen in the very best video games.

I’ve used the term emergent here, a term going back to a famous 1972 article by Phil Anderson, entitled “More is Different”. Anderson argued for the now-commonplace (1) point that there may be many levels of behaviour in systems, with each new level giving rise to deep new ideas. Just because you know the equations governing a water molecule does not mean you will understand the principles governing the crash of ocean waves, or the way a rainbow arcs across the sky. Anderson’s own field of condensed matter physics is a fount of examples of emergence, such as superconductivity, superfluidity, and Bose-Einstein condensation. In each case, there are multiple emergent levels of behaviour, and beautiful ideas to be discovered at each level.

A different, though parallel, way of looking at the sciences of the artificial is as examples of what Simon calls design science (2). Design sciences are about the invention of new types of object with new types of behaviour. Examples of such invention range widely: arabic numerals (in mathematics); the stealth fighter (in aeronautics); the notion of a layer in software such as Illustrator (in user interface design); and homoiconicity (in programming language design). The essence in each case is that of a new type of object, with new kinds of behaviour.

A challenge in describing what is meant by a design science is that examples of genuinely new types of object and behaviour are rarely clearcut. Arabic numerals drew on earlier numeral systems which introduced ideas like a place-number system. The first stealth fighters drew on earlier generations of fighters, some of which attempted to reduce their radar cross section. And so on. Still, the stealth fighter was a fundamentally new type of object in that “invisible on radar” was a primary property. And anyone who has ever tried to muliply numbers represented in roman numerals won’t need much convincing that arabic numerals are fundamentally different.

In physics, an example of this design science approach is Kitaev’s notion of a topological quantum computer. This is one of the most radical new ideas of the past hundred years. Rather than building a computer out of component parts, the aspiration is to create a novel phase of matter that wants to compute. Fluids want to flow; solids want to maintain a stable shape; topological quantum computers want to compute. Indeed, not only do they want to compute, they want to quantum compute, and to do so in a way that protects the quantum state against the effects of noise!

Up to now, physics has for the most part not been a design science. But my guess is that’s going to change in the coming decades. There are more and more examples where design seems the right way to think: topological quantum computers; new designer phases of matter; the Alcubierre warp drive and other designer spacetimes; constructor theory and universal constructors; programmable matter and utility fog. These are not just about emergence, traditionally construed. Rather they’re about designing to a target. Indeed, not just to target, but conceiving of entirely new types of target, often even more radical than notions like a stealth fighter or a homoiconic programming language.

I said above that design sciences are about the “invention” of new types of object. When writing that sentence I equivocated between using the term “invention” and the term “discovery”. Neither is quite right. Invention is accurate in the sense that it’s a creation of the human mind. But it’s a discovery in the sense that it seems as though it’s a pre-existing property of the universe. Topological quantum computers, homoiconicity, stealth, arabic numerals, even the idea of layers: all have a depth and unitary quality that makes it hard to see them entirely as ad hoc inventions. It’s true that many details are ad hoc: the specifics of arabic numerals are obviously not universal! But if we meet aliens I won’t be surprised to find that they’ve discovered (and perhaps superseded) many of the same ideas used in the arabic numerals. Indeed, I won’t be surprised if they’ve also discovered homoiconicity, topological quantum computing, and perhaps even something like our conceptions of stealth and the idea of layers.

So, to come back to the question with which I started: in what sense is quantum computing a basic science? And in what sense is it about discovering important new fundamental truths about the universe?

I think the answer is that quantum computing will be in considerable part a design science (3). That is, it’ll be about discovering new types of object and behaviour. This is a point of view that is perhaps unusual, even idiosyncratic. It will take many decades to tell if I am correct. But I believe it’s a stimulating point of view, and likely to be correct.

What would it mean for quantum computing to be a design science? We can get some small insight by asking: how does one invent something like the arabic numerals? Or concepts like homoiconicity, or layers? The heuristics of discovery used by the designers behind these are radically different than the traditional ways physicists work. Physicists often work from the bottom up, understanding simple systems, or putting things together in “natural” ways (e.g., by cooling materials down or heating them up). Routine design work is somewhat similar, taking extant elements and combining them in standard ways. But the deepest types of imaginative design are very different, creating fundamentally new types of objects and new types of behaviour. I won’t try to enumerate the heuristics behind that kind of work here (though see my earlier essay). But it’s a very different kind of work than traditional physics.

This point of view contrasts with the conventional point of view that says quantum computing will mostly be about finding fast new algorithms. Certainly, it will in part be about finding new algorithms. But I don’t think it’s likely to just or even primarily be about algorithms, any more than classical computing has been. Indeed, I believe the design of new prototocols and new interfaces – the invention of new types of object and behaviour – has been much more important in classical computing. And so, perhaps, it may ultimately be for quantum computing.

Critical Addendum

This is a draft written as part of the process of writing a much longer essay covering a wider array of quantum topics. In that sense it’s been written as a sort of version 0 of a section of that essay, with a (hopefully much improved) version 1 to be included in the longer essay. My main critique of the current draft is that it struggles to adequately convey what it would mean for quantum computing to be a design science. The notion of designing radically new classes of object and behaviour hasn’t made it into popular culture in any really deep way, and it certainly isn’t part of the culture of physics. Perhaps what’s need to make the essay work is a longer discussion – or, at least, a more compelling discussion! – of what it would mean for quantum computing to be a design science.

The other main critique of this version 0 is that it focuses so much on design science that it doesn’t quite do the job of answering the underlying question: in what sense will quantum computing be a science, and address fundamental questions? The design science aspects may be the most unfamiliar (and so need the most explanation), but they’re only part of a broader picture, which needs to be painted more convincingly.

Notes

(1) I presume this broad point of view wasn’t novel when Anderson wrote his article. Still, Anderson crystallized the point of view, and provided some beautiful examples and useful terminology. So it seems reasonable to attribute to his article.

(2) My notion of what a design science is has changed considerably since reading Simon, influenced particularly by the work of Bret Victor and Lev Vygotsky. Rather than revert to Simon’s definition, the description that follows is my own current way of thinking.

(3) Of course, it won’t just be a design science. Quantum computing has also stimulated lines of enquiry leading to new work about black holes and quantum gravity. The desire to build quantum computers has stimulated a tremendous amount of work understanding how many different types of physical system work, and how to control them. And once quantum computers have been built, they will be exceptionally useful as tools of understanding, just as conventional computers have been. All these activities are science, and don’t fall squarely under the rubric of design science. Still, as implied in the main text, over the long run I expect quantum computing will primarily be a design science, in much the same way as conventional computing has become a design science.

Citation and licensing

In academic work, please cite this as: Michael A. Nielsen, “In what sense is quantum computing a science?”, http://cognitivemedium.com/qc-a-science, 2018.

This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License. This means you’re free to copy, share, and build on this essay, but not to sell it. If you’re interested in commercial use, please contact me.