Simulating the Hadamard gate in the Fibonacci disk code for universal topological quantum computation

A figure for the disk code (artistic imagination)

The 21st century is widely believed to be a century of information processing. In particular, of quantum information processing, including quantum communication and quantum computation. It is well known that quantum states are generally fragile, in the sense that quantum coherence and entanglement needed for information processing cannot be kept for a sufficiently long time due to unavoidable noises and environmental disturbances. Fortunately, this problem may be overcome by exploring the so-called topological states of matter, whose physical properties, at least some of the main ones to be used, are robust against disorders and variations in interactions. Thus emerged the research field of topological, or fault-tolerant, quantum computation.