Quantum information theory has evolved in fascinating ways over the past two decades or so and I’ve been privileged to directly witness its development for ten of these years. In this post, I thought I’d have a go at predicting where it will go, and what the “next big thing” for quantum information theory will be.

Around the year 2000 quantum information theory seemed to be primarily focussed on two broad themes: building a quantum computer and developing quantum algorithms for it, and building a resource theory for quantum information via, e.g., quantum entanglement theory and quantum Shannon theory. To a large extent both of these themes continue strongly today. Although, I’d suggest that quantum Shannon theory has fared much better than the theory of quantum entanglement, in particular, that of entanglement measures, which seemed really important a decade ago but not so much now.

One thing that would have been harder to predict was the influence of quantum information theory on other areas of physics. For example, QI has now had some considerable impact in condensed matter physics, particularly with regard to the development of new classical simulation algorithms for complex quantum systems. From my considerably biased perspective I think that this second-order effect has been rather important. Also, there has been excitement about the role and influence of QI on biological physics.

So now to the question: what next for quantum information? I based the following list on topics that I personally find very interesting, and also on observations I’ve made about external pressures coming from funding agencies and from the job market.

**1. Quantum computers **

I firmly believe a quantum computer will be built, although I refuse to say how long this will take. One thing that I think may happen is the emphasis on fault tolerance thresholds in choosing a quantum computer architecture will diminish slightly as experimentalists engineer systems capable of supporting quantum coherence on longer timescales. I’m sure that cluster states will be exploited in some way in the successful quantum computer architectures. I also feel sure that as we get access to such systems this will spark our creativity in designing nontrivial things to do, i.e., in developing quantum algorithms using *dissipative quantum processes*.

**2. Quantum algorithms **

Thus I feel convinced that quantum algorithms development will continue, albeit slowly. One area which hasn’t received much attention — probably because it isn’t as glamourous as an exponential speedup — but which *really* should, is the development of quantum algorithms which give *polynomial* speedups for problems in P. These kind of speedups could turn out to be extremely important: if the best classical algorithm for a problem of *major practical importance* uses, say, operations, and you found a quantum algorithm using operations this would have major *practical* implications. I do hope that such speedups will become an area of more intense research and I feel relatively confident this area could take off. Unfortunately I don’t know enough about classical algorithms to give a firm prediction for which kinds of problems will be amenable to such quantum speedups (sorry!).

As mentioned above, another class of quantum algorithms which has been so far relatively unexplored, is that of dissipative quantum algorithms. (There are some exceptions here, see, e.g., and this, this, and, somewhat immodestly, this.) Such algorithms are extremely important because they give intermediate experimental implementations something to run!

**3. Complex quantum systems **

Quantum information will continue to play a role in the study of complex quantum systems. This is an easy prediction: QI trained people are generally quite good at thinking about quantum coherence, which plays a major role in the physics of strongly interacting quantum systems. I feel relatively confident in predicting that the physics of 2D and, to some extent, 3D lattice systems, will see major QI-inspired developments.

Another area which I am very enthusiastic about is that of quantum systems with *continuous* degrees of freedom, particularly, *quantum fields*. Lattice systems are, after all, an approximation to these systems, and it is clear that existing QI-inspired techniques will have some influence here (indeed, this is just beginning with the extension of MPS and MERA to the continuous setting). Additionally, if a good enough interplay can be developed then this would allow quantum field theorists to be able contribute to quantum information-type problems. Also, holographic correspondences such as the AdS/CFT correspondence have QI aspects, so we might see QI theorists and string theorists working together more strongly here.

**4. Classical physics **

My final prediction concerns the influence of QI on *classical physics*. The thing is, QI trained people are not only good at thinking about quantum coherence, but also about *correlations* in general (see, e.g., the continuing developments in the study of Bell’s inequalities, cryptography based on no-signalling, etc.). Correlations are always hard to think about, but the thing we’ve learnt in studying QI in the context of condensed matter is that if you have a way to think about correlations in a better way then this can lead to new simulation algorithms. Here I have in mind, for example, the study of fluid dynamics, as applied to the climate (see this for a longer discussion), and other problems of classical many body physics such as traffic flow via this, community detection, and image recognition. The nice thing about these areas is that they are much more directly connected with our everyday life. Any contribution here would have a much more direct impact on important problems facing humanity.

What do you think?

I like your predictions, but I have another to add to the list. I think that quantum information ideas could have a major impact on artificial intelligence and, in particular, machine learning. This is not about building quantum brains, but about building machines that can reason about the world. Since at least some systems in the world have to be described quantum mechanically, it is natural to ask whether we can design machines to reason about them. Simulation algorithms can be viewed as a special case of this.

The first thing that I think we can contribute is to check whether existing algorithms are robust against the introduction of quantum effects. For example, Rob Spekkens and a student have shown that current causal discovery algorithms, aimed at generating plausible causal models from data, are incapable of dealing with Bell correlations — the algorithms return a local hidden variable model. Perhaps our experience of characterizing the difference between classical and nonclassical correlations can be used to fix these algorithms. Similarly, AI researchers have developed a number of alternative representations of uncertainty beyond probability because probabilities can be hard to deal with in algorithms and sometimes a more qualitative representation suffices. We can ask similar questions about whether these measures are capable of capturing the distinction between the classical and quantum worlds.

I hope that this sort of work would feed back into simulation algorithms as well. Once we have fixed the AI algorithms, we might be able to apply them to condensed matter systems.

Thankyou Matt, those are excellent suggestions! I totally agree; it is quite fascinating that existing methods might not be robust to quantum effects…

There is at least one more possibility, namely that coming decades witness substantial advances in our

mathematicalunderstanding of quantum mechanics. To chart a roadmap for these advances, we can start with a parody of Julian Schwinger’s style of quantum field theory, which was composed (affectionately) by Schwinger’s students:Similarly we have for QIT

As it turns out, several recent

Bulletin of the AMSsurvey articles explore this possibility. Rather than discuss these articles here, I have linked to them onTCS StackExchangeas an extension to an answer that Peter Shor gave to a question asked by Joe Fitzsimons: “Physics results in TCS?“QIT will give lots of knowledge in every field since it is a branch of quantum physics. QIT will be specially useful for Bio-physics and medical sciences. As pointed out by Matt it will also be useful in artificial intelligence.

What is the next big thing? I think it is micro quantum information theory??? more deeper and deeper this is how it will go on…..