- 學位論文
除錯加密邏輯閘在超導量子位元系統中的最佳化控制
Optimal Control of Encoding Gate for Error Correction in Superconducting Qubit System
摘要
在量子電腦中，量子錯誤修正 (Quantum Error Correction) 用來保護量子資訊免於受去相干化 (Decoherence) 及其他雜訊的錯誤，因此，其已是未來大型的量子電腦中不可或缺的一環。為了實現量子錯誤修正，我們會使用具有對稱性質的量子態 (Quantum State) 將量子位元 (Qubit)) 冗餘地編碼 (Encode) 在更高維度空間中。透過投影量測 (Projective Measurement)所得的奇偶性類型 (Parity-Type) 可觀測量 (Observable) 提供了錯誤更正碼 (Error Syndrome) 的資訊，通過簡單的操作可以糾正錯誤。 在本論文裡，我們將會探討許多種加密的方法，第一種方法是將超導量子位元上的資訊加密成二分量cat codes (coherent state的疊加態)的形式，第二種方法是加密成四分量cat codes，第三種方法則是加密於binomial bosonic logical basis，接著，我們會比較此三種方法的優缺點，並且說明我們為何選擇第三種方法。 將量子位元編碼為振盪器的同調態 (Coherent State) 的疊加(Superposition)，在單腔模式 (Single Cavity Mode) 下的編碼以及保護的機制可顯著降低由於光子損失引起的錯誤。我們首先回顧一些基礎的量子超導電路 (Superconducting Quantum Circuit) 並且介紹量子計算元件 (Quantum Qubit Device) 和我們所用的物理系統。接著，我們將引入CRAB最佳化控制方法 (Optimization Method ) 來解決最佳化控制的問題。最後，我們將藉由找到最佳化的控制脈衝，以實行加密/解密邏輯閘、以及在加密空間 (encoded space)下的X gate。
並列摘要
Quantum error correction (QEC) is used in quantum computing to protect quantum information from errors due to decoherence and other noise sources and is therefore an essential component of a future large-scale quantum computer. To implement QEC, a quantum bit (qubit) is redundantly encoded in a higher-dimensional space using quantum states with symmetry properties. Projective measurements of these parity-type observables provide error syndrome information, with which errors can be corrected via simple operations. In this thesis, we study several methods for encoding. First method is encoding a superconducting qubit state information in a superposition of coherent states of an oscillator with two-component cat codes, second method is encoding in four-component cat codes, and third method is encoding in a binomial bosonic logical basis. Then we will compare the pros and cons of the methods and explain why we choose the third method (binomial bosonical logical basis). The encoding in a single cavity mode, together with a protection protocol, significantly reduces the error rate due to photon loss. We first review some basic elements of superconducting quantum circuit and introduce the qubit devices and the physical system we use. Then we will build up the encoding/decoding gate in matrix from, and explain the benefit of the cat-code we choose. We then introduce the CRAB algorithm (based on Nelder-Mead optimization method) for solving optimal control problems. Finally we implement the encoding/decoding gate and X gate operating in encoded space by finding out the optimal control pulse.