Geometric Optimization of Quantum Control with Minimum Cost

Fuente: arXiv
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Auteurs principaux: Tan, Chengming, Cai, Yuhao, Zhang, Jinyi, Ma, Shengli, Lv, Chenwei, Zhang, Ren
Format: Preprint
Publié: 2024
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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