论文标题
通过Magnus扩展和非交通性多项式优化的量子最佳控制
Quantum Optimal Control via Magnus Expansion and Non-Commutative Polynomial Optimization
论文作者
论文摘要
量子最佳控制具有许多重要的应用，从磁性想象中的脉冲塑形到对化学反应和量子计算的激光控制。我们的目标是解决迄今为止量子最佳控制应用成功的两个主要挑战：量子系统中固有的非交换性以及涉及三个量子水平以上的量子最佳控制问题的非共同性。 Methodologically, we address the non-commutativity of the control Hamiltonian at different times by the use of Magnus expansion. To tackle the non-convexity, we employ non-commutative polynomial optimisation and non-commutative geometry. As a result, we present the first globally convergent methods for quantum optimal control.
Quantum optimal control has numerous important applications ranging from pulse shaping in magnetic-resonance imagining to laser control of chemical reactions and quantum computing. Our objective is to address two major challenges that have limited the success of applications of quantum optimal control so far: non-commutativity inherent in quantum systems and non-convexity of quantum optimal control problems involving more than three quantum levels. Methodologically, we address the non-commutativity of the control Hamiltonian at different times by the use of Magnus expansion. To tackle the non-convexity, we employ non-commutative polynomial optimisation and non-commutative geometry. As a result, we present the first globally convergent methods for quantum optimal control.
