Hamburg 2009 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 9: Quanteninformation: Konzepte II

Q 9.5: Vortrag

Montag, 2. März 2009, 15:00–15:15, VMP 6 HS-D

Adiabatic Preparation with Nonlinear Paths — •Gernot Schaller — Institut für Theoretische Physik, Technische Universität Berlin

Many interesting physical models show a quantum phase transition when a single parameter is varied through a critical point. For finite-size counterparts, there is usually a non-vanishing excitation gap at the critical point. This opens the possibility to adiabatically prepare the ground state of one phase from the ground state of another phase. When the parameter appears as a coupling constant (or as e.g. an external field) one may view this process as a straight line interpolation between two Hamiltonians. Unfortunately, the minimum excitation gap along this straight line trajectory often scales inversely with the system size. This does not only affect the adiabatic runtime but for systems coupled to a reservoir, also thermal excitations become likely.

For some simple models it will be demonstrated that with a nonlinear interpolation path a constant lower bound on the minimum energy gap can be proven. An interesting consequence is that the two-dimensional cluster state – encoded in the ground state of a Hamiltonian – can be prepared adiabatically in constant time.

[1] G. Schaller, Phys. Rev. A 78, 032328 (2008).