Quantum walks present novel tools for redesigning quantum algorithms, universal quantum computations, and quantum simulators. Hitherto, one- and two-dimensional quantum systems (lattices) have been simulated and studied with photonic systems. Here, we report the photonic simulation of cyclic quantum systems, such as hexagonal structures. We experimentally explore the wavefunction dynamics and probability distribution of a quantum particle located on a six-site system, along with three- and four-site systems while under different initial conditions. Various quantum walk systems employing Hadamard, C-NOT, and Pauli-$Z$ gates are experimentally simulated, where we find configurations capable of simulating particle transport and probability density localization. Our technique can potentially be integrated into small-scale structures using microfabrication, and thus would open a venue towards simulating more complicated quantum systems comprised of cyclic structures.

中文翻译：

---

循环量子游动中波包动力学的实验实现

Quantum Walks提供了新颖的工具，可用于重新设计量子算法，通用量子计算和量子模拟器。迄今为止，已经利用光子系统对一维和二维量子系统（晶格）进行了模拟和研究。在这里，我们报告了诸如六边形结构之类的循环量子系统的光子模拟。我们实验性地研究了在不同初始条件下，位于六位系统以及三位和四位系统上的量子粒子的波函数动力学和概率分布。采用Hadamard，C-NOT和Pauli-$ž$对门进行了实验模拟，我们发现了能够模拟粒子传输和概率密度局部化的配置。我们的技术可以潜在地使用微细加工技术集成到小规模的结构中，从而为模拟由循环结构组成的更复杂的量子系统打开了一个舞台。