Closing the gap on the third way of computation.

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.

ECONOMIC: The work aims to understand the possibilities of, and limitations on, developing a non classical information processor using noisy quantum systems - i.e. determining the noise levels required before quantum systems can be efficiently simulated classically. The form of the economic impact depends upon the outcomes. At one extreme team may discover that noisy quantum systems may be efficiently classically simulated with much less noise. If so, then this would contribute better classical algorithms for modelling noisy quantum technologies, thereby feeding into other programmes to exploit quantum coherence and showing that classical computer are tougher competition for quantum computers than previously known. More broadly (and depending on the details of the progress) these methods could extend to better modelling techniques for quantum materials that have their own technological applications. At the other extreme the team may discover that noisy quantum systems can still compute the answers to problems that conventional computers find difficult (not necessarily full quantum computation, but some intermediate class), and perhaps with lower overhead than typical fault tolerance schemes. In this case we will know that non classical information processing is an easier target than previously imagined. The outcomes may lie somewhere in between these two extremes. In which case we will obtain improved understanding of the information processing abilities of noisy quantum devices.

PEOPLE: The research will contribute to skills development of the two PDRAs. The topics proposed are unusual and creative, and two young RAs will benefit from both the scientific training that they will receive, as well as becoming skilled in a niche area that will be important over the next few years. The research will also contribute to people development in the wider scientific community - by disseminating results at conferences and meetings, and engaging with other researchers.

SOCIETY: The primary societal impact of the work will be policy related, by understanding how research into quantum technologies may be shaped in the future. If noisy quantum systems are more easily classically simulatable than currently known, then some avenues for building quantum information processing devices will be eliminated, thereby enabling scientists to direct their efforts accordingly. Alternatively, if it is found that noisy quantum devices are more powerful than previously imagined, then this would open up avenues for building a non-classical information processor. The project also inherits impact pathways from other applications of quantum technologies, as better classical algorithms for modelling noisy quantum systems can be applied quite broadly. The impact in this area will be achieved through dissemination of results in a manner appropriate to the research outcomes (i.e. by publicizing results to the appropriate scientific community and industrial stakeholders).

KNOWLEDGE: A key objective of the proposal is to really establish the research topic as an important field of investigation - while many papers target fault tolerance thresholds as a topic of investigation, far less work is being done on the levels of noise before efficient classical simulation kicks in. Yet the latter is just as important as the former, and some questions may be easier to answer. In addition to the direct research topics of the proposal, there are also broader connections with fundamental physics knowledge. What are the limitations of information processing using quantum systems? How easily may classical physics and classical information processors simulate quantum theories? The research has strong connections with these topics, and will exploit ideas that have been developed in relation to them (e.g. the notion of generalised entanglement).