Geometric Optimization of Quantum Control with Minimum Cost
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910965592752128 |
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| author | Tan, Chengming Cai, Yuhao Zhang, Jinyi Ma, Shengli Lv, Chenwei Zhang, Ren |
| author_facet | Tan, Chengming Cai, Yuhao Zhang, Jinyi Ma, Shengli Lv, Chenwei Zhang, Ren |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14540 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric Optimization of Quantum Control with Minimum Cost Tan, Chengming Cai, Yuhao Zhang, Jinyi Ma, Shengli Lv, Chenwei Zhang, Ren Quantum Physics Quantum Gases 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. |
| title | Geometric Optimization of Quantum Control with Minimum Cost |
| topic | Quantum Physics Quantum Gases |
| url | https://arxiv.org/abs/2409.14540 |