Authors
Ali T Rezakhani, Damian F Abasto, Daniel A Lidar, Paolo Zanardi
Publication date
2010/7
Journal
Physical Review A—Atomic, Molecular, and Optical Physics
Volume
82
Issue
1
Pages
012321
Publisher
American Physical Society
Description
We elucidate the geometry of quantum adiabatic evolution. By minimizing the deviation from adiabaticity, we find a Riemannian metric tensor underlying adiabatic evolution. Equipped with this tensor, we identify a unified geometric description of quantum adiabatic evolution and quantum phase transitions that generalizes previous treatments to allow for degeneracy. The same structure is relevant for applications in quantum information processing, including adiabatic and holonomic quantum computing, where geodesics over the manifold of control parameters correspond to paths which minimize errors. We illustrate this geometric structure with examples, for which we explicitly find adiabatic geodesics. By solving the geodesic equations in the vicinity of a quantum critical point, we identify universal characteristics of optimal adiabatic passage through a quantum phase transition. In particular, we show that in the …
Total citations
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Scholar articles
AT Rezakhani, DF Abasto, DA Lidar, P Zanardi - Physical Review A—Atomic, Molecular, and Optical …, 2010