Adiabatic Preparation of Topological Order

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.

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

References in corpus (6)

• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Bounds for the adiabatic approximation with applications to quantum computation
• Topological Order and Conformal Quantum Critical Points
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• General entanglement scaling laws from time evolution

Cited by in corpus (8)

• Robustness of a perturbed topological phase
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
• Topology induced anomalous defect production by crossing a quantum critical point
• Entanglement, fidelity and topological entropy in a quantum phase transition to topological order
• Entanglement renormalization and gauge symmetry
• Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes
• Exact results on the quench dynamics of the entanglement entropy in the toric code