Topological Adiabatic Quantum Computation
Alioscia Hamma, Daniel A. Lidar · arXiv (Cornell University) · 2006
We show how to adiabatically prepare the ground state of a topologically ordered model of n qubits in a time that is upper bounded by O(\\sqrt{n}). This ground state is a quantum superposition of closed strings. The computational problem of deciding whether a string is closed or not, which classically requires O(n) steps, can then be solved in at most four commuting measurements. This constitutes an example of a quantum adiabatic speedup that relies on topological order.