線性光學網路(LON) 在量子光學及量子計算上提供了高維度的量子系統，Clement 干涉儀更是提供了 以光學元件來實現可調變矩陣的方法，在我們的研究中，我們在自由空間上以中心波長1550nm 的自 發參量下轉換產生的光子對利用玻片來實現偏振編碼下的邏輯閘，並以偏振編碼完成Kraus cutting 的 2-qubit Shor 演算法，來探討實作上的可能性，並將概念套用到4 × 4 可編程光晶片，分別以單個MZI 和 整個晶片完成量測，並得到高Fidelity 的結果來證實晶片在θ 參數的調整下是相當穩定的。 接著我們挑選另一個需要對相位有所要求的實驗以測試ϕ 的參數，我們在自由空間上建立2-mode、 2 個系統的貝爾態糾纏驗證實驗，我們以同樣中心波長1550nm 的自發參量下轉換產生的光子對利用 50 : 50 分光比例的分光鏡完成局域性的分光，接著分別利用兩組局域性測量來完成糾纏驗證的實驗，計 算驗證算符的期望值，並成功驗證出了糾纏態。 i;Linear Optical Networks (LON) provide high-dimensional quantum systems for quantum optics and quantum computing. The Clements interferometer, in particular, provides a method to implement reconfigurable matrices using optical components. In our study, we implement polarization-encoded logic gates in a free-space setup using waveplates, utilizing photon pairs generated by spontaneous parametric down-conversion (SPDC) at a central wavelength of 1550 nm. We also implemented the 2-qubit Shor’s algorithm using Kraus cutting with polarization encoding to investigate its experimental feasibility. We applied this concept to a 4×4 programmable photonic chip, performing measurements on a single MZI and the entire chip. Finally,we obtained high-fidelity results, verifying that the chip is highly stable under the adjustment of the θ parameter. Next, we selected another phase-sensitive experiment to characterize the ϕ parameter. We constructed a freespace experiment for Bell state entanglement verification in a two-mode, bipartite system. We utilized a 50:50 beam splitter to achieve local beam splitting, using photon pairs generated by spontaneous parametric down-conversion (SPDC) at a central wavelength of 1550 nm. Then,we utilized two sets of local measurements to complete the entanglement verification experiment. Finally, We calculated the expectation value of the verification operator and successfully verified the entangled state.
