Adiabatic Computation -a Toy Model
نویسنده
چکیده
We discuss a toy model for adiabatic quantum computation which displays some phenomenological properties expected in more realistic implementations. This model has two free parameters: the adiabatic evolution parameter s and the α parameter which emulates many-variables constrains in the classical computational problem. The proposed model presents, in the s − α plane, a line of first order quantum phase transition that ends at a second order point. The relation between computation complexity and the occurrence of quantum phase transitions is discussed. We analyze the behavior of the ground and first excited states near the quantum phase transition, the gap and the entanglement content of the ground state.
منابع مشابه
Iii Quantum Phase Transitions in Collective Spin Models. Applications to Adiabatic Quantum Computation Quantum Phase Transitions Quantum Information Collective Spin Systems Lipkin-meshkov-glick Model Coherent Spin States Majorana Representation Semi-classical Limit Adiabatic Quantum Computation Remerciements -acknowledgements
Part I: Quantum Collective Spin Systems We use a coherent spin state formalism in order to study collective spin models, which have many applications in physics. In particular, the Lipkin-Meshkov-Glick (LMG) has been analyzed in the thermodynamic limit. The method developed during this work can, in principle, be used for more general Hamiltonians written as a function of the su(2) algebra gener...
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