Defects in topologically ordered lattice models

Abstract

Developing quantum systems which are robust against noise are of prime importance to the realisation of quantum technologies. Without fault tolerance, we will never be able to preserve delicate quantum states for macroscopic time scales, a necessary requirement in the construction of scalable quantum computer. Topologically ordered models offer very beautiful mechanisms for preserving quantum states. In such models, quantum information is encoded globally over a degenerate topological Hilbert space which offers a natural robustness against local environmental noise. Remarkably, topological order is present in certain realistic condensed-matter systems. This provides a platform for accessing topological order in a laboratory. Moreover, considering condensed-matter systems enables us to combine topological features with other physical effects to enhance their behaviour. In this Thesis we study the physics of topologically ordered lattice models with defects. We seek practical applications of lattice defects for the realisation of a fault-tolerant quantum computer. The first result we present shows that anyonic data of point-like lattice defects, called twists, can be found by measuring the entanglement of the ground state of the host system. The data we learn relates to the capacity of a twist defect to perform quantum computational tasks. The second result in this Thesis concerns the dynamics of the qudit toric code model with line-like defects coupled to a thermal bath. We show we can entropically inspire fragile glassy dynamics in the system. Such dynamics qualitatively improve the coherence times of quantum information encoded in the ground state of the lattice. A novel way of achieving fault-tolerant quantum computation is by producing and manipulating twist defects of topologically ordered systems. In many ways, this paradigm of topological quantum computation is analogous to quantum computation using anyons. The first area of study in this Thesis extends the analogy between anyons and twists. Specifically, we show that the anyonic data of twists in Kitaev’s toric code model can be extracted