Adiabatic Dynamics of Entanglement

• URL: http://arxiv.org/abs/2407.18301v2
• Date: Tue, 03 Jun 2025 22:29:27 GMT
• Title: Adiabatic Dynamics of Entanglement
• Authors: Einar Gabbassov, Achim Kempf,
• Abstract summary: During adiabatic evolution, changes of entanglement can be traced to avoided energy level crossings.<n>The efficiency of this weaving of entanglement depends on the narrowness of the avoided level crossings.<n>The amount of entanglement involved in an adiabatic quantum computation can be related to the ruggedness of its energy landscape.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that, during adiabatic evolution, any changes of entanglement can be traced to a succession of avoided energy level crossings at which eigenvalues swap their eigenvectors. These swaps of eigenvectors weave the entanglement in multipartite systems. The efficiency of this weaving of entanglement depends on the narrowness of the avoided level crossings and it is, therefore, constraining the speed of adiabatic evolution. Applied to adiabatic quantum computation, these results directly relate the adiabatic quantum computation speed to its utilization of the resource of entanglement. Further, the amount of entanglement involved in an adiabatic quantum computation can be related to the ruggedness of its energy landscape. We therefore obtain new tools for exploring the origins of quantum advantage in adiabatic quantum computation.

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