- 學位論文
帶有隨機雜訊的隨機標竿分析法
Randomized Benchmarking in the Presence of Stochastic Noise
摘要
以量子閘為基礎的量子計算，計算過程包含量子態初始化、量子閘運算以及量測運算結果三個階段。隨機標竿分析法提供一套檢驗流程僅評估量子閘運算階段的誤差，排除掉量子態初始化及量測運算結果的影響。不過，隨機標竿分析法的理論推導假設了不同量子閘的雜訊都相同且不會隨時間變化，若系統包含其他類型雜訊，隨機標竿分析法是否仍然適用需要進一步的理論分析。目前已經有理論考慮了不會隨時間變化但每個量子閘雜訊不同的隨機標竿分析法。本論文將建立在這個新的理論基礎上，把隨機標竿分析法的適用範圍推廣到隨時間隨機變化的雜訊，並將推廣後的隨機標竿分析法量測結果與閘平均保真度做比較。我們進行了單量子位元與雙量子位元的模擬來驗證理論，所有模擬都使用帶有去相位雜訊的哈密頓算符建構出帶有雜訊的量子閘，以此來進行隨機標竿分析法。
並列摘要
Randomized benchmarking (RB) provides a procedure for estimating the average gate fidelity excluding state-preparation and measurement (SPAM) errors. However, the rigorous analyses of the standard RB protocol assume that noise should be gate-independent and time-independent. Later, the assumption was relaxed to gate-dependent and time-independent noise, while the decay parameter given in the RB fitting formula is no longer yielding the average gate fidelity. In this thesis, we consider RB under different types of stochastic noise. We provide a formula to fit the non-exponential decay fidelity obtained from RB with the explanation of the fitting result. We perform numerical simulations to verify our theories. The simulations consider the gate-dependent noise induced from the Hamiltonian with dephasing interference, and is executed on a typical single-qubit Hamiltonian, and a two-qubit Hamiltonian based on the experimental parameters from a real silicon-based quantum-dot device.