中国科学院半导体研究所机构知识库

二十世纪集成电路的发展，极大地推动了社会的进步。二十一世纪，由集成电路启发而来的集成光子学，在科学领域掀起了一阵研究热潮。将各种功能的光学器件集成在一块光学芯片上，节省了空间、能耗的同时增加了系统的稳定性。而随机行走作为理论计算科学的里程碑之一，在数学、物理等领域有着广泛的应用。由经典随机行走类比而来的量子随机行走，成为量子计算和量子模拟领域的生力军，弥补了基于量子傅里叶变换的量子计算在非阿贝尔问题中的不足。由于经典电磁场与量子态的光子具有一定的等价性，所以单光子的量子行走可以用经典相干光来模拟，单光子的概率分布用经典相干光强度分布来表示。

本论文致力于研究SOI微结构上的单光子量子行走行为，一方面对量子行走的行为进行光学模拟，另一方面探讨量子行走光学模拟凝聚态物理中的高阶耦合现象的可能性，最后为量子行走芯片在搜索算法以及传感方面的潜在应用进行了理论和部分实验分析，也对集成大规模可编程的量子行走线路做了基础性的研究工作。本文的主要研究内容和创新点主要包括以下几个方面：

1. 提出了   基于自准直光子晶体的硅基纳米柱定向耦合分束器阵列结构，用于经典相干光对四步离散时间量子行走的数值模拟。模拟结果与理论值进行相似度的分析，其相似度最高达到97.26%。容差性高、尺寸小，相比SOI纳米线定向耦合分束器阵列四步离散时间量子行走的线路，尺寸减小了1个数量级以上。为大规模高密度集成的量子行走线路提供了参考方案。

2.   首次提出利用基于光子晶体自准直的SOI纳米柱波导阵列，模拟三阶耦合海森堡方程。将经典光在阵列中的传输结果与考虑不同耦合阶数的连续时间量子行走结果进行相似度分析，发现考虑到三阶耦合作用的理论值与光学模拟的相似度达到最高，最高值为99.2%。高阶耦合作用使得量子行走的弹道运输发生了局域，我们观察到了适度的动态无序能够在一定程度上解除静态无序带来的局域，从而起到传输增强作用。纳米柱波导阵列的光学模拟还可以通过入射波长和环境折射率进行调制。

3.   基于连续时间量子行走的搜索算法在粘合二叉树上的验证。以纳米柱波导阵列为模拟平台，理论分析了缺陷系数对搜索速度的影响，通过到达时间和到达概率两个参数进行表征。当缺陷系数小于1时，随着缺陷系数的增大到达概率增大；当缺陷系数大于1时，随着缺陷系数的增大，到达时间变小。实验上我们先用容易制备的纳米线SOI波导阵列为平台验证了二叉树上量子行走搜索算法的加速特性。

4.   我们设计了新型的基于连续时间量子行走的传感方法，首次将量子行走的应用拓展到传感领域。我们以硅基狭缝波导阵列为平台，用经典光在其中的传输模拟量子行走现象。由于量子行走容易受环境微扰的影响，理论计算的折射率传感灵敏度为1E-11RIU。同时，作为可编程大规模量子集成线路的基础工作，我们研究了SOI纳米线波导结构的热调制马赫-曾德干涉仪（MZI），在实验上测试到了分束比随调制信号的周期性变化。

The development of integrated electronic circuits （IC） improves the progress of society in 20^th century, while integrated optics inspired by IC attracts lots of people’s interests in scientific area in 21^th century. The integration of multi-function optical devices onto a monochrome chip with low space and low cost improves the stability of system. Random walks, which act as one of the cornerstones of theoretical computer science, have been widely applied onto math and fundamental physics area. Quantum walks （QWs）, the coherent analogue of classical random walks, have been one of the main productivity of quantum computation and simulation and provided new algorithmic tools to solve similarity problems on non-Abelian groups. Due to the analogy of classical electronic field and quantum state of photons in certain circumstances, single photon QWs can be simulated by classical light, and the probability of single photon can be represented by the intensity distribution of classical coherent light.

In this thesis, we mainly do research on SOI micro-&-nano-structure based single photon QWs behavior. On one hand, we simulate QWs by classical light; on the other hand, we research the simulation of high-order coupling in condensed state with the method of optical simulation of QWs. At last we study the potential application of QWs for searching and sensing areas in theory and experiment. We do fundamental work on integrated large scale programmable QWs circuits. The main results are as follows:

1.           We propose near-self-collimated silicon based nanorod directional coupler array for the simulation of four-steps discrete time QWs. The similarity between theory and simulated results reaches 97.26%. Photonic crystal self-collimated silicon based nanorod structure has compact size and high tolerance. The size of self-collimated nanorod structure for simulating 4-steps discrete time QWs is smaller than SOI nano-wired based structure at least one order, which provides a reference for designing large scale highly integrated QWs circuits.

2.           We propose photonic crystal near-self-collimated silicon based nanorod waveguide array for the simulation of third-order coupling Heisenberg equation for the first time. We compare the similarity between the simulated light distribution at the end of waveguide array and the theoretical results of the distribution of QWs when considering different order of coupling and realized that similarity reaches highest value when taken third-order coupling into consideration, which reaches 99.2%. What’s more localization appears compared with ballistic transport of QWs due to high-order coupling. We also find that moderated dynamic disorder can break the localization caused by static disorder, called disorder-assisted quantum transport. The optical simulation of nanorod waveguide array can be moderated by injection wavelength and the refractive index of environment.

3.           We study the continuous time QWs based search on glued-binary-tree. Nanorod waveguide array provides the platform for the simulation and we analyze the effect of defect strength on the searching speed, which is evaluated by reaching time and reaching probability. When defect strength is smaller than 1, reaching probability increases with the defect strength. While defect strength is larger than 1, reaching time decreases with the increase of defect strength. We experimentally use nanowire waveguide array to verify the acceleration of QWs based binary-tree searching.

4.           We design a new sensing method based on continuous time QWs, which extends the application of QWs to sensing area for the first time. QWs are simulated by light propagation in silicon based slot waveguide array. Due to QWs behavior is sensitive to the disturbance of environment, the sensitivity of the refractive index sensing is 1E-11RIU theoretically. At the same time, we study SOI nanowire waveguide based thermal modulated MZI as the fundamental research of programmable large scale integrated QWs circuits and experimentally discover that the beam-splitting ratio can be modulated by modulation signal periodically.