Motivation

What is the motivation for quantum information theory, and specifically for quantum computation? What makes it worthwhile? For the inaugural post of the Quantum Monastery, it seems appropriate to say something introductory on this topic, and to provide some idea of the approach to quantum computation which I intend to take at the “Monastery”.

I will not touch on any mathematical first principles of quantum information theory in this post. Instead, I will describe possible motivations to pursue quantum computation, and how they might the way you approach the subject.

Motivations from above and below

What you would consider the “basic idea” of quantum computing depends on what your background is, in part because it will depend on what ideas you are already happy to take for granted. A physicist may take quantum mechanics itself for granted, in which case the novel idea is to take seriously the fact that it can be used to realise computing technology. A computer scientist, on the other hand, will likely be more interested in how quantum mechanics expands what they already know of computing, some of which might be fairly abstract. From these two different perspectives, I could tell two different stories to motivate the study of quantum computation:

• “Information is physical” — what we call information is an interpretation of distinguishable states of physical systems. The way in which that information can be stored and worked upon is then determined by the laws of nature. It follows that the most comprehensive (and accurate) theory of computation is one which is governed by our best models of physics. Quantum computation is the model of information processing which we obtain when we use quantum mechanics, in particular, to inform our ideas of information.
• “Quantum information generalises randomness” — we understand probability theory well enough to define models of computation involving randomness — both on a pragmatic level (i.e. in every-day programming) and on a mathematically formal level (e.g. in terms of Bayesian networks). Quantum information theory is the model of information processing which we obtain when we generalise our probabilistic theory to include the sort of randomness and other effects which can be produced by quantum mechanics.

The first of these stories serves to motivate quantum information theory in the context of the broader world (a top-down motivation), and emphasises that quantum computation is in a sense forced upon us if we take physics seriously. The second serves to motivate quantum information theory as an elaboration of a simpler model of computation (a bottom-up motivation), emphasising that quantum computation is an interesting extension of what we knew about before.

The two motivations above can also be tailored to the interests of specific audiences. For instance:

(Cryptography:) because information is physical, if you want to be sure that your secret data remains future-proof against all possible technological developments, then you must do so by taking physics (i.e. quantum mechanics) into account. In particular:

1. You should guard against the possibility that your cryptographic scheme could be compromised in principle using quantum mechanics;
2. If you are prepared to base the security of your cryptosystem on quantum mechanics being correct, or nearly so, then you can in principle define cryptographic schemes whose security does not rely on any computational assumptions.

(Computing technology:) because quantum information generalises randomness, we can get more powerful computers than we have today by harnessing quantum mechanical effects. This would allow us to solve problems which we didn’t previously know how to solve practically.

Naturally, these application-driven observations are among the most commonly repeated practical motivations of quantum information theory, and quantum computation in particular.

Reasons for considering motivations

What do these things have to do with the aims of this blog?

For the most part, my aim is not to spend much time motivating the “why” of quantum computation. (There are interesting “why” questions, but these lie mostly in the domain of your opinion of the value of scientific research and technological progress, which it would be a mistake for me to spend much time writing about.) My aim is to try to present the “what” and the “how” of quantum computing — with forays into quantum information theory in general and other subjects as appropriate — and to try when I can to address the subject of “how could it possibly be” when appropriate.

However, one’s motivations will inevitably affect what one considers interesting — that is the main role of “motivations” in science. When considering quantum computation, are we interested in considering “naturally occurring” physical systems which are well-known to physicists, or conceivable physical systems which generalise ideas which are well-known to computer scientists? Do we consider only those things which are closely linked to the project of building and using a quantum computer, or do we spend time thinking about things which do not seem to have immediate application — and which possibly falls entirely outside of what we expect quantum computers could do? Do we spend much time thinking about the fact quantum computing involves actual matter which is located in space and time, or would we prefer to avoid such messy details?

As I have hinted at above, there are some distinctions that I perceive between the starting point of “information is physical” and the starting point of “quantum information generalises randomness” in terms of their attitude towards quantum computation, and I think that these affect what one is willing to consider as a worthwhile question. Carefully considering both of these motivations will inform what we consider a reasonable idea to consider, and on occasion in what context an idea is reasonable to consider.

One difference between “information is physical”” and “quantum information generalises randomness” is a certain form of dogmatism:

• The argument that “information is physical” seems intended to confront the listener with the necessity of considering physics in general, and quantum mechanics in particular, when thinking about the theory of computation.
• The idea that “quantum information generalises randomness” allows for the possibility that traditional problems of computer science (which may have originally been motivated on the grounds of pure logic) can be enriched by considering what happens, when we extend them to consider systems that behave quantum mechanically.

The first of these imposes a sort of obligation to consider the physicality of systems, while the second is about expanding what sorts of ideas one considers. Ultimately, one is invited either to consider the question of possibilities, or of limits — even if those limits are, in some respects, more generous than in traditional computer science.

The approach pursued in the Monastery

The “Monastery” is meant as a place of calm reflection — but not a place of austerity. While I will not seriously entertain the possibility that quantum mechanics is somehow wrong, I hope (perhaps ironically) to maintain a mood in this blog which is not dogmatic — that we are contemplating possibilities which are underwritten by physics, not forced upon us by physics. At the same time, however — speaking particularly as someone who is interested in quantum architectures — it is important to be mindful of certain constraints which are motivated by physics. This motivates an approach to quantum computation which is not unknown, but not entirely common, either in presentations of quantum computation or in the research community.

As a place of contemplation — and in acknowledgement that we are after all talking about a model of computation which we can only realise today with great difficulty — I intend in the Monastery to emphasise what we can conceive of a little bit more than what we can practically achieve. In future posts,

• I shall try to carefully describe what the mathematical formalism of quantum computation actually is, so that we can be as sure as possible of what is actually justifiable to consider.

• Furthermore, I will try to clearly describe how we try to accommodate the constraints which we recognise in physical systems, even when we are describing those physical systems in an abstract way.

By being mindful of physical constraints, and above all of the mathematical formalism of quantum computation, we can aim to describe quantum computation in a way which is close to what we can physically realise. But: there is no problem with occasionally indulging in the luxury of relaxing one or more constraints, so long as we are mindful of the constraints which we are relaxing, and bear in mind why we want to relax them — especially if we wish to consider the impact of those constraints. And on rare occasion, we may entertain excursions beyond what quantum mechanics actually justifies, fully conscious of the fact that we have left the monastery and are exploring the surrounding rocky mountainsides.