Towards quantum control of topological phases in mesoscopic superconductors

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.

Research into graphene is receiving a massive amount of attention and financial backing from governments and industries around the world. The mounting pressure to deliver results will drive the production and commercialisation of high quality material over the coming years, especially in europe where a burgeoning graphene community will soon embrace collaborative infrastructures such as the Graphene Flagship. At the same time the race is on to find new materials and concepts capable of hosting the building blocks for products in the emerging sector of quantum computing. My proposal forges a bridge between these two areas and its timeliness means there is a strong chance of making a high impact on both research communities. Although currently only a niche capability, there is a strategic need for the UK to sustain a world-leading status in this area because widespread access to quantum computers would have a far-reaching impact on national security and the ability of society to use resources more sustainably. The emergence of cloud computing, for instance, has led to an ever-growing number of large data centers whose hardware facilities and cooling systems consume huge amounts of energy. A quantum computer would improve the efficiency of such data centers by calculating the optimal way to distribute computational tasks, a calculation that is not currently possible. 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 many-body ground states such as high-temperature superconductivity. Since internet security is based on the near impossibility of factoring large numbers, the ability to factor in polynomial time using a quantum computer would also be of monumental importance and the UK must maintain and grow its presence in this area. This project also has economic impact in areas where graphene is used to process high frequency signals. With an ever increasing demand for high bandwidth mobile communication, driven largely through the popularity of smart phones, there is an increasing need for high frequency materials that can help increase the bandwidth of these devices. There is also a growing demand for a skilled scientists and engineers who understand how high frequency measurements are made and how high frequency systems work. Another community which will feel the impact of my work will be those working in quantum-enhanced metrology. It is the function of modern quantum metrology to define, maintain, and develop universal realizations of electrical units and provide practical standards which represent them. The long standing goal of electrical metrology is to link the units of current, voltage, and resistance to fundamental and invariant constants of nature. While this has been achieved for voltage and resistance, there is a pressing need to put the ampere on the same exact footing by relating it to the fundamental charge of the electron, and the race is on to find the best way to do it. The proposed single-electron devices in this research could provide the answer. The unusual nature of its electronic excitations also makes graphene an excellent material for testing the universality and material-independence of such quantum representations. Together this would enable the metrological triangle to be closed and standard units to be redefined in terms of fundamental constants of nature. The observation of non-Abelian anyons is also an outstanding problem in condensed matter physics, so realising the ideas in my fellowship will have an impact on how the UK stands in terms of fundamental physics research.