使用通用遗传算法设计的具有位置依赖相互作用的 Heisenberg 自旋链的量子态传输性能
Quantum state transfer performance of Heisenberg spin chains with site-dependent interactions designed using a generic genetic algorithm
AI总结：
本文使用遗传算法设计 Heisenberg 自旋链以优化量子态传输，通过修改代价函数获得平滑变化的交换系数，发现平滑 Hamiltonian 传输能力不优于粗糙版本且两者对静态无序鲁棒性相似，并确定了其特征值谱所属的随机矩阵系综。
摘要：
在自旋链中为任意量子态设计良好的传输通道意味着优化代价函数，通常是传输的平均保真度。传输保真度衡量传输后的状态与传输协议开始时制备的状态的相似程度。对所有可能的初始状态求平均后，该品质因数量化了协议的质量。已有研究提出优化给定的 Hamiltonian 以完成特定任务，量子态传输即其中之一。具体而言，我们考虑使用遗传算法设计 Heisenberg 自旋链。这种非常高效的算法使我们能够研究具有良好至优异传输能力的 Hamiltonian 的不同性质。使用随机搜索方法的一个明显缺点是，它会导致交换系数强度在各个位置之间发生急剧变化。通过修改代价函数，我们获得了交换系数沿链长平滑变化的 Hamiltonian。我们的结果表明，平滑的 Hamiltonian 具有与粗糙 Hamiltonian 相同或更低的传输能力，并且两者对静态无序均表现出相似的鲁棒性。通过研究具有不同传输能力的 Hamiltonian 的特征值的统计性质，我们确定了这些谱所属的随机矩阵系综。
英文摘要：
Designing a good transfer channel for arbitrary quantum states in spin chains implies optimizing a cost function, usually the averaged fidelity of transmission. The fidelity of transmission measures how much the transferred state resembles the state prepared at the beginning of the transfer protocol. When averaged over all the possible initial states, the figure of merit quantifies the quality of the protocol. There are proposals for optimizing a given Hamiltonian to accomplish a particular task. The transfer of quantum states is one of them. In particular, we consider the design of Heisenberg spin chains using a genetic algorithm. This very efficient algorithm allows us to study different properties of Hamiltonians with good to excellent transfer ability. One apparent drawback of using a random search method is that it results in exchange coefficient strengths that change abruptly from site to site. Modifying the cost function, we obtain Hamiltonians with exchange coefficients varying smoothly along the chain length. Our results show that the smoothed Hamiltonians have the same, or less, transfer ability than the rough ones, and both kinds show similar robustness against static disorder. By studying the statistical properties of the eigenvalues of Hamiltonians with varying transfer abilities, we determine the ensemble of random matrices to which the spectra belong.
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