Combining Viewpoints in Quantum Theory

Mathematics, computer science, and physics enjoy a beautiful but curious symbiotic relationship. Pure mathematical reasoning can uncannily have consequences for the physical world. Vice versa, physical intuition and experiment can uncover mathematical truths that seemed entirely abstract and divorced from reality. Computer science, on the one hand, can be regarded as a tool to simulate physical systems or aid mathematical exploration. On the other hand, it is also a special case of both physics and mathematics. Computers are, after all, physical objects, and are therefore governed by the laws of physics. Nevertheless, the classic questions driving computer science can be answered independently from the physical way computers are built. For example, abstract reasoning alone can decide whether a computer can in principle be programmed to solve a given problem, and if so, how efficiently.

Ever since my first acquantaince I have been amazed by this unreasonable effectiveness of pure thought in physical sciences. This has drawn me to quantum computer science, which lies at the interface of mathematics, computer science, and physics. Quantum computers are essentially small quantum-mechanical systems that we can control, used to make nature solve certain problems much more efficiently than any classical computer could. Understanding quantum computing in enough detail to allow its large-scale deployment will clearly transform our society.

There are several obstructions to high-level quantum programming. The most fundamental ones run straight to the heart of the counterintuitiveness of quantum mechanics. The problem is that the regime of quantum mechanics diminishes the power of logical thought and intuition that is usually so effective. For example, if I were to offer you a biscuit and a choice of tea or coffee, you would expect to receive either tea and a biscuit, or coffee and a biscuit. But under quantum-mechanical laws, this most basic logical truth no longer holds. This is caused by the fact that one can only extract data from a quantum system from one classical viewpoint at a time. To learn more about the system, we need to combine measurements from multiple classical viewpoints. Similarly, quantum computers are so much more powerful than classical ones precisely because of the ability of a quantum programmer to work in, and switch between, different classical viewpoints.

However, the switching between classical viewpoints has escaped systematic study for some reason, most probably because quantum systems are usually studied in isolation. Fortunately, the ties between computer science, physics, and mathematics run even deeper than sketched above. Theoretical computer science excels in handling entire communities of systems, including compound ones, that all live in parallel. Thus, transfer of computer science techniques in fact influences physics and mathematics, where such notions have not received much attention. I will place quantum systems and classical viewpoints on an equal footing in a single category, investigate the dynamical relationships between them, and eventually endeavour to restore the effectiveness of abstract thought in this realm. This will advance our theoretical understanding of nature. At the same time, it will have practical benefits by making the design of quantum protocols and algorithms more accessible to non-specialist programmers; I aim to have my biscuit and eat it too.

The main goal of the Fellowship is to study the switching between multiple classical viewpoints on a single quantum system. I firmly believe this is a very promising way forward in understanding quantum computer science in particular and science in general. However, making this perspective catch on will be a slow revolution of convincing others of this way of thinking. I will now list beneficiaries of the Fellowship, in order of descending expected gain. For the reason above, I will not be discriminate and include groups that may seem far-fetched.

First, of course, academic researchers in the disciplines directly involved - category theory, operator algebra, foundations of quantum mechanics, and logic - will appreciate the technical advances that reduce studying difficult objects to studying relationships between well-understood objects.

Second, the explicit multidisciplinary nature of the basic premise of the Fellowship will
ensure academic impact beyond these immediate narrow disciplines. In the longer term, transfer of techniques will benefit wider academic circles in which different viewpoints on a common underlying situation play a role, such as economists interested in game theory, or researchers in artificial intelligence interested in automated negotiation systems.

Third, in particular, this includes researchers in concurrent computation, and distributed database theory. By definition, both fields involve multiple agents acting on a single piece of knowledge. Both of these areas are very applicable in today's digital world of big data and the cloud. Theoretical results from the Fellowship will therefore also interest many industrial beneficiaries in due time.

Fourth, more immediately, students of quantum computer science will benefit from the Fellowship as it eases explanation of the counterintuitive nature of the subject.

Fifth, related to the previous group, the general public has a lasting fascination with fundamental questions about nature and clamours for tangible explanations. Since becoming a father I have come to appreciate the benefits - and the difficulty - of cutting
explanations down clearly to their very simple essence. This attitude changes one's own thinking for the better, and even inspires ideas. Similarly, with both students and the general public, communication is not a one-way street.

Sixth, more remotely, the Fellowship contributes towards testing trustworthiness and reliability of quantum computer science. Because this emerging area will have such a societal influence, if only through e.g. secure communication, this will benefit policy makers, judges, journalists, and others who currently find it hard to gauge this new technology.

For the seventh and final group, I have to add a caveat. Foundational research such as the current proposal can hardly be said to have direct commercial potential. However, in the longer term of 10 to 50 years, I do believe there will be an industry around quantum computer science. Inklinks already exist, such as ID Quantique (in Geneva, Switzerland), IBM's Quantum Information Group (in Yorktown, US), Microsoft Station Q (in Santa Barbara, US), and D-Wave Systems (in Burnaby, Canada) among others. Unfortunately, Hewlett-Packard had to close their quantum lab in Bristol, leaving the UK at a disadvantage. The Fellowship contributes to the future development of this emerging industry not only by developing new techniques, but also by preparing current generations of students to become suitable personnel later.