離子阱量子位元與輸送離子的糾纏邏輯門

Two-qubit entangling gate between a stationary and a flying ion qubits

方文瀚(Wen-Han Png)

指導教授 ： 林俊達

國立臺灣大學/理學院/物理學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202102564

摘要

一個可實現且可擴充的架構在邁向實現量子電腦的過程中是至關重要的。本論文主要提出一個新穎的方案:藉由持續運動的離子實現交換儲存於兩個相隔一段距離的量子位元之量子訊息，並將其稱為 drive-through 邏輯閘。此研究成果亦可應用於量子糾纏之操作、超密編碼 （superdense coding），量子遙傳 （teleportation）及產生多體系之間的量子糾纏 （multipartite entanglement）等等。我們首先探究一個靜止的離子與運動中的離子間的時變庫倫交互作用。在兩顆離子接近彼此時，我們利用它們相互耦合的橫向運動提出兩個可控制相位翻轉邏輯閘（controlled-phase flip gate）的方案，分別為：慢速量子閘 （adiabatic gate）和快速量子閘 （fast gate）。 在慢速量子邏輯閘的框架底下，兩顆離子需個別地與高斯光束交互作用，此外，離子間的時變的庫侖交互作用必須以動態簡正模態（dynamical normal modes）表示。於快速邏輯閘的框架中，兩顆離子需共同與一束超快雷射（ultrafast laser）耦合，藉此，離子間的時變庫侖交互作用可被當成離子局部運動的微擾。我們也對固定與變動雷射重複率 (laser repetition rates) 的超快脈衝序列進行優化。 藉此，慢速邏輯閘與快速邏輯閘的保真誤差可達 10−4. 此外，我們也分析與探究雜訊 (如𝜋-脈衝的缺陷、離子平面運動的漲落及次階庫侖交互作用造成的殘餘量子糾纏) 和操控誤差的容許度 (如振幅與時間的去準確性) 對保真誤差的影響。

關鍵字

擴充的架構 ； 量子電腦 ； 捕獲離子 ； 快速量子閘

並列摘要

Towards the realization of a quantum computer, a feasible scalable architecture is imperative. In this work, we proposed a novel scheme where the stored quantum information between distant sites can be exchanged via non-stopping flying ions, hereinafter named a drive-through gate (DTG). This work offers potential applications in quantum entanglement operations such as superdense coding, teleportation, and generation of multipartite entanglement. We first study the time-dependent Coulomb interaction between one stationary ion and one moving ion. Then, we demonstrate two schemes of controlled-phase flip gate by utilizing the coupled transverse motions while the two ions are close. The first scheme is an adiabatic gate using an individually addressed Gaussian beam and the latter is a fast gate using a global ultrafast laser. In the adiabatic gate scheme, the time-dependent Coulomb interaction is treated as the dynamical normal modes. In the fast gate scheme, the time-dependent Coulomb interaction is treated as a weak perturbation to local ions’ motion. We also implemented the optimizations on the ultrafast pulse sequences with fixed and varied laser repetition rates. In both the fast and the adiabatic gate scheme, the infidelities of 10−4 are attainable. The noise sources from 𝜋-pulse imperfection, fluctuations of ions’ planar motion, and residual entanglement from the next-order Coulomb interaction are analyzed. The tolerance of controlling errors, such as amplitude and timing uncertainty, is also discussed.

並列關鍵字

scalable architecture ； quantum computer ； trapped ions ； fast gate

參考文獻

Bibliography

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