Projects per year
Abstract
Topological quantum computers promise a fault tolerant means to perform quantum computation. Topological quantum computers use particles with exotic exchange statistics called nonAbelian anyons, and the simplest anyon model which allows for universal quantum computation by particle exchange or braiding alone is the Fibonacci anyon model. One classically hard problem that can be solved efficiently using quantum computation is finding the value of the Jones polynomial of knots at roots of unity. We aim to provide a pedagogical, selfcontained, review of topological quantum computation with Fibonacci anyons, from the braiding statistics and matrices to the layout of such a computer and the compiling of braids to perform specific operations. Then we use a simulation of a topological quantum computer to explicitly demonstrate a quantum computation using Fibonacci anyons, evaluating the Jones polynomial of a selection of simple knots. In addition to simulating a modular circuitstyle quantum algorithm, we also show how the magnitude of the Jones polynomial at specific points could be obtained exactly using Fibonacci or Ising anyons. Such an exact algorithm seems ideally suited for a proof of concept demonstration of a topological quantum computer.
Original language  English 

Article number  045004 
Number of pages  59 
Journal  Quantum Science and Technology 
Volume  3 
Issue number  4 
DOIs  
Publication status  Published  1 Oct 2018 
Projects
 1 Finished

Determining the mass and geometric phase of a superfluid vortex
Simula, T., Galitskiy, V. & Zwierlein, M.
Australian Research Council (ARC), Monash University, Massachusetts Institute of Technology (MIT), University of Maryland, College Park
1/01/17 → 31/12/20
Project: Research