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Mixed state non-Abelian holonomy for subsystems

Mikael Nordling·Erik Sjöqvist
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Abstract

Non-Abelian holonomy in dynamical systems may arise in adiabatic transport of energetically degenerate sets of states. We examine such a holonomy structure for mixtures of energetically degenerate quantal states. We demonstrate that this structure has a natural interpretation in terms of the standard Wilczek-Zee holonomy associated with a certain class of Hamiltonians that couple the system to an ancilla. The mixed state holonomy is analysed for holonomic quantum computation using ion traps.

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Mikael Nordling, Erik Sjöqvist. 2004-04-29. Mixed state non-Abelian holonomy for subsystems. https://doi.org/10.1103/physreva.71.012110

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