Adiabatic Preparation of Topological Order

Details Adiabatic Preparation of Topological Order Adiabatic Preparation of Topological Order

2006-07-21

arxiv.org/abs/quant-ph/0607145v4

Phys. Rev. Lett. 100, 030502 (2008)

Physics

Quantum Physics

4 pages, one figure. v4: includes new error estimates for the adiabatic evolution

Scientific paper

10.1103/PhysRevLett.100.030502

Topological order characterizes those phases of matter that defy a description in terms of symmetry and cannot be distinguished in terms local order parameters. This type of order plays a key role in the theory of the fractional quantum Hall effect, as well as in topological quantum information processing. Here we show that a system of n spins forming a lattice on a Riemann surface can undergo a second order quantum phase transition between a spin-polarized phase and a string-net condensed phase. This is an example of a phase transition between magnetic and topological order. We furthermore show how to prepare the topologically ordered phase through adiabatic evolution in a time that is upper bounded by O(\sqrt{n}). This provides a physically plausible method for constructing a topological quantum memory. We discuss applications to topological and adiabatic quantum computing.

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