Journal
PHYSICAL REVIEW B
Volume 90, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.90.045101
Keywords
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Funding
- NSERC
- Institute for Quantum Information and Matter, a NSF Physics Frontiers Center
- Betty Moore Foundation [PHY-0803371, PHY-1125565]
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We consider the problem of converting a product state to a ground state of a topologically ordered system through a locally generated open-system dynamic. Employing quantum-information tools, we show that such a conversion takes an amount of time proportional to the diameter of the system. Our result applies to typical two-dimensional topologically ordered systems as well as, for example, the three-dimensional and four-dimensional toric codes. It is tight for the toric code, giving a scaling with the linear system size. Our results have immediate operational implications for the preparation of topologically ordered states, a crucial ingredient for topological quantum computation: Dissipation cannot provide any significant speedup compared to unitary evolution.
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