Geometric Optimization of Quantum Control with Minimum Cost

• URL: http://arxiv.org/abs/2409.14540v2
• Date: Sun, 25 May 2025 06:26:19 GMT
• Title: Geometric Optimization of Quantum Control with Minimum Cost
• Authors: Chengming Tan, Yuhao Cai, Jinyi Zhang, Shengli Ma, Chenwei Lv, Ren Zhang,
• Abstract summary: We investigate the optimization of quantum control from a differential geometric perspective.<n>In our approach, optimal control minimizes the cost associated with evolving a quantum state.<n>This framework provides a geometric method for optimizing shortcuts to adiabatic driving.
• Score: 1.8142288667655777
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the optimization of quantum control from a differential geometric perspective. In our approach, optimal control minimizes the cost associated with evolving a quantum state, with the cost quantified by the length of the trajectory on a relevant Riemannian manifold. We demonstrate the optimization protocol in systems with SU(2) and SU(1,1) dynamical symmetries, which encompass a broad range of physical systems. In these systems, the time evolution can be represented by trajectories on a three-dimensional manifold. Given the initial and final states, the minimum-cost quantum control corresponds to a geodesic on the manifold. When the trajectory between the initial and final states is specified, the minimum-cost control corresponds to a geodesic within a submanifold embedded in the three-dimensional space. This framework provides a geometric method for optimizing shortcuts to adiabatic driving.

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