藉由梯度磁通量子位元的概念，其幾何對稱的特性，有效地抑制系統與環境的耦合強度，而使得相干時間大大地提升。在此概念的啟發下，我們進而分析了，系統透過一個，或數個局域維度與環境耦合—局域耦合—的量子消相干效應。此局域耦合的概念，合理地對應實驗上的局域電磁場，亦或空間局域的電子線路。透過隨時變薛丁格方程，與虛時路徑積分的適當搭配，我們分別分析哈密爾敦函數的自旋與環境維度。經由適當約化，主軸可以有效地轉化為—如何解決局域維度，在非時間局域位能下的動態行為。對於單一維度的局域耦合，相對應的噪音函數光譜密度，展現出羅倫茲函數的特性，伴隨局域耦合維度的增加，光譜密度非但顯露所謂的疊加效應，更有複雜的回聲與位移之耦合效應。除此之外，針對開放的量子系統，Keldysh非平衡格林函數分析，引領出真正的量子高階修正。此篇文章，我們也提出，藉由正則轉換，處理量子位元系統，截斷成2位元系統問題的方法。同時我們也發現，實驗上，若沒有適當的備妥初始條件及量子磁通整數n，梯度磁通量子位元是沒有辦法展現出量子位元的基本特性。

Motivated by ideal gradiometer °ux qubit (GFQ), which suppresses coupling strength as
gradient form due to geometry symmetry, we study the e®ect that qubit system seriously
couples to one or a few modes of heat bath in decoherence analysis. We set up a simple
model to analyze this coupling form dominated by several modes of heat bath so-called the
local coordinates coupling. In experiment, special electrical circuit in localized space or lo-
calized random electromagnetic ‾led are more reasonable and reality to be described by local
coordinates coupling. Moreover, we analyze the problem by e®ectively complementary meth-
ods: time dependence SchrÄodinger's equation for spin part of Hamiltonian, and imaginary
path-integral method for coordinate part. During analysis, the problem could be reduced as,
how to calculate the dynamics of local coordinates part with non-local in time potential com-
ing from heat bath. For single mode of local coordinates coupling (system seriously couples
to only one mode of heat bath), we ‾nd the bath spectral density of symmetry correlation
(or so-called noise spectrum) is Lorentzian form. When the coupling modes of local coordi-
nate are increase, there would be not only multiple e®ect, but also mixing e®ect|echo and
shifting e®ect|in spectral density. More than that, the real quantum correction should be
taken care by Keldysh non-equilibrium Green's function. In addition, we propose a way|
canonical transformation to analyze the higher eigenstates correction during truncation by
taking GFQ system as an example. And we also observe that, without carefully choosing the
initial conditions and °ux integer n, the GFQ cannot behave as a qubit.

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