Quantum Information Group  -  PhD Projects

Topological Quantum Computation with Gaussian states

Dr. N. Korolkova (St Andrews), in collaboration with Prof. P. van Loock (Univ. Mainz, Germany)

The efficient processing and storage of quantum information has turned out to be a major hurdle in the effort to construct a quantum computer. One of the most promising solutions to this problem has been the suggestion that information can be stored in topological states as a global property of the system. This approach, known as Topological Quantum Computation (TQC), protects information from local errors caused by environmental decoherence and ensure quantum gates can be implemented with extremely good accuracy. TQC employs anyons, the quasi-particles of topological models. Anyons exhibit fractional statistics, i.e., when two anyons are braided the quantum state acquires a phase shift; unlike boson or fermion states which, when exchanged, have no effect on the state. Anyonic states first emerged in connection with the fractional quantum hall effect, which occurs in a two dimensional electron gas at low temperatures. Recently it has been shown that anyonic statistics can be produced in lattice models which are relatively easy to generate and control. Furthermore, the states produced can be used to implement universal fault tolerant quantum computation over discrete variables (qubits/qudits). Our recent contribution in this area is the generalization of these ideas to continuous variable (CV) regime, that is to Gaussian states and operations. This has allowed us to construct computational universality models for CV anyons that are, in principle, easier to implement that their qubit counterparts [D. F Milne, N. V Korolkova and P. van Loock, Universal Quantum Computation with Continuous Variable Abelian Anyons, Phys. Rev. A 85, 052325 (2012]. The goal of the current project is to continue with developing of TQC model based on Gaussian states and operations extending it into the regime of non-abelian anyons.

Category: Theoretical Hard Condensed Matter

Coherent Signal Transfer

Dr. N. Korolkova (St Andrews)

The project will develop and demonstrate a quantum toolbox for Quantum Information Technology (QIT) based on condensed matter systems and advanced photonics using novel methods of noise management and coherent control. The emphasis will be put on investigating coherent information processing in the presence of noise, with the goal to study in detail not only how to circumvent noise and cope with it, but also to develop efficient strategies to use it. These studies of noise-enhanced signal transport (including quantum state transport) will then be applied in communication channels, complex networks, sensing protocols and in the design of quantum simulators. The acquired methods will be applied to accomplish efficient quantum simulations in practical systems via exploiting controlled coherent dynamics or nature-given evolution in condensed matter systems and in photonic devices. For example, complex many-body systems and transport in photosynthesis will be simulated using 3D optical waveguides and fibre networks with tailored properties. We will then look for resource optimization in QIT and explore quantum correlations in real-world noisy networks including secure communication links and quantum signal transport in turbulent atmosphere. The project includes collaboration with theory and experimental groups at Heriot Watt University and at the Max Planck Institute for the Science of Light (Erlangen, Germany).

Category: Theoretical Hard Condensed Matter