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Adiabatic Preparation of Topological Order

Alioscia Hamma·Daniel A. Lidar
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Abstract

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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Alioscia Hamma, Daniel A. Lidar. 2007-10-13. Adiabatic Preparation of Topological Order. https://doi.org/10.1103/physrevlett.100.030502

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