Dynamical quantum phase transition is a critical phenomenon involving out-of-equilibrium states and broken symmetries without classical analogy. However, when finite-sized systems are analyzed, dynamical singularities of the rate function can appear, leading to a challenging physical characterization when parameters are changed. Here, we report a quantum support vector machine algorithm that uses quantum Kernels to classify dynamical singularities of the rate function for a multiqubit system. We illustrate our approach using N long-range interacting qubits subjected to an arbitrary magnetic field, which induces a quench dynamics. Inspired by physical arguments, we introduce two different quantum Kernels, one inspired by the ground state manifold and the other based on a single state tomography. Our accuracy and adaptability results show that this quantum dynamical critical problem can be efficiently solved using physically inspiring quantum Kernels. Moreover, we extend our results for the case of time-dependent fields, quantum master equation, and when we increase the number of qubits.

中文翻译：

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用于对多量子位系统中的动态奇点进行分类的量子内核


动态量子相变是一种涉及非平衡态和对称性破缺的关键现象，没有经典类比。然而，当分析有限尺寸的系统时，可能会出现速率函数的动态奇点，从而在参数变化时导致物理表征具有挑战性。在这里，我们报告了一种量子支持向量机算法，该算法使用量子内核对多量子位系统的速率函数的动态奇点进行分类。我们使用 N 个长程相互作用的量子位来说明我们的方法，该量子位受到任意磁场的影响，从而引起失超动力学。受物理论证的启发，我们引入了两种不同的量子内核，一种受基态流形启发，另一种基于单态断层扫描。我们的准确性和适应性结果表明，可以使用物理启发的量子内核有效地解决这个量子动力学关键问题。此外，我们还针对时间相关场、量子主方程以及增加量子位数量的情况扩展了我们的结果。