Decoherence in a dynamical quantum phase transition

Abstract

Motivated by the similarity between adiabatic quantum algorithms and quantum phase transitions, we study the impact of decoherence on the sweep through a second-order quantum phase transition for the prototypical example of the Ising chain in a transverse field and compare it to the adiabatic version of Grovers search algorithm, which displays a first order quantum phase transition. For site-independent and site-dependent coupling strengths as well as different operator couplings, the results show that (in contrast to first-order transitions) the impact of decoherence caused by a weak coupling to a rather general environment increases with system size (i.e., number of spins/qubits). This might limit the scalability of the corresponding adiabatic quantum algorithm.

14 pages, 9 figures

References in corpus (8)

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• Quench dynamics across quantum critical points
• Sweeping from the superfluid to Mott phase in the Bose-Hubbard model
• Preservation of Positivity by Dynamical Coarse-Graining
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Cited by in corpus (7)

• Analog Nature of Quantum Adiabatic Unstructured Search
• Criticality in transport through the quantum Ising chain
• Nonadiabatic dynamics of the excited states for the Lipkin-Meshkov-Glick model
• Feynman's Clock for open quantum systems
• Polaron-transformed dissipative Lipkin-Meshkov-Glick Model
• Transport through a quantum critical system: A thermodynamically consistent approach
• Duality in spin systems via the $SU(4)$ algebra