Towards quantum control of topological phases in mesoscopic superconductors

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Technologies which operate using quantum superposition and entanglement are set to revolutionise how the world stores, processes, and communicates information. A quantum computer is expected to improve the efficiency of cloud computing by calculating the optimal way to distribute computational tasks amongst classical computers. In materials science, the evolution of chemical reactions is also more efficiently simulated by a quantum computer so they are thus likely to aid developments in synthetic chemistry, where understanding the behaviour of large molecules will lead to smarter power-saving materials. Quantum simulators will also elucidate the role of quantum effects in biological processes related to energy harvesting such as photosynthesis, and inform the design of materials with exotic power-saving capabilities such as a high-temperature superconductivity. The ability for quantum computers to factor in polynomial time could also have an enormous impact on internet security, which currently relies on the near impossibility of factoring large numbers. At the heart of quantum computers are building blocks known as quantum bits, or "qubits", which physically comprise two states that can be manipulated into any quantum superposition. One of the challenges we face with building a quantum computer is preventing the environment from killing these fragile superpositions through intractable and unintentional interactions. Most qubits are based on familiar particles, such as electrons in a quantum dot, ions in an atom trap, or photons in a waveguide, and it is unclear what the ultimate limit will be in the race to optimise their performance. An alternative and elegant approach to this problem is to find a qubit that is intrinsically protected from interacting with the environment. One such qubit employs exotic particles, known as anyons, that can encode the state of a qubit non-locally. Weak interactions with the environment can never collapse its state, making it more robust as a quantum memory. The aim of this research is to pave the way towards quantum control of such qubits by developing devices and techniques for observing anyons that emerge from the collective motion of electrons in a two-dimensional gas in contact with a superconductor. Quite remarkably, particles with very similar properties are already available, though not yet detected, in a material as simple and famous as graphene. My strategy is to expose the presence of these particles by monitoring how single electrons interact with them in nanodevices. In the longer term I anticipate materials with stricter topological protection to be come available, and my aspiration is to use the techniques developed here to store, manipulate, and read out decoherence-free quantum information.