Closing the gap on the third way of computation.

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In recent times we have come to realise that our concept of information is deeply connected to the scientific laws that we believe in. One reason for this connection is that a computer is in fact a form of physical experiment. This can be understood as follows. While the electrical circuits that are used to build computers behave according to well understood rules, these rules can lead to complex behaviour, and so calculating how networks of circuits will evolve can correspond to time-consuming mathematical problems. By building computers we actually turn this problem around - we build networks of circuits, observe their evolution, and then use the observations to give answers to problems that we would have found difficult using a pen and paper.However, it turns out that there are many problems that even current computers cannot solve efficiently. Among them there is one very important example: it is extremely difficult to compute the evolution of systems obeying the laws of quantum physics. The term quantum physics refers to the laws that we believe describe the fundamental workings of the universe. These laws are particularly important for describing the behaviour of small objects such as atoms and photons (photons are elementary 'particles' of light). The fact that it is difficult to calculate the evolution of objects obeying the laws of quantum physics leads to the question: can we turn this problem around? If we can observe quantum systems, are there mathematical problems that we can solve that conventional computers find difficult? The answer to this question appears to be yes - there are some very important problems that so called quantum computers find much easier to solve than the best known methods using conventional computation. In fact, quantum physics can not only enable us to build better computers, it also enables us to communicate in very different ways. It turns out that the laws of quantum physics allow us to hide information in a very special way, and hence enable us to perform forms of cryptography (secret communication) in ways that have never been previously possible. Elementary forms of quantum cryptography are already commercially available.Despite such promise, it is still very challenging to obtain quantum systems with sufficient control to allow us to build full-blown quantum information processing devices. Although at a fundamental level quantum physics is believed to be responsible for the behaviour of almost all materials, full-blown quantum systems tend to be very small and susceptible to disturbances from their surroundings. The research project intends to find out what effect this noise has on our ability to process quantum information. In particular we will aim to understand whether realistic imperfections can still allow a third form of computation - one that is better than conventional computational, albeit not as powerful as an idealised quantum computer. Such a third form of computation, if it exists, may be significantly easier to build in real life. If it does not exist, then that would mean that either existing quantum computer proposals can tolerate much higher imperfections, or that we may simulate complex quantum systems on conventional computers much better than previously thought. All these possibilities are would have high impact, but to benefit we first need to determine which one is actually the case! The research project hopes to start making systematic progress on this extremely significant but extremely challenging problem.