張鳳芹，　朱愛東

( 延邊大學(xué)理學(xué)院 物理系， 吉林 延吉 133002 )

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在無消相干子空間中確定性地實(shí)現(xiàn)多目標(biāo)量子比特相位翻轉(zhuǎn)門

張鳳芹，朱愛東*

( 延邊大學(xué)理學(xué)院 物理系， 吉林 延吉 133002 )

摘要：基于腔的輸入輸出過程，在無消相干子空間中利用腔中束縛的2個(gè)原子編碼成邏輯量子比特來確定性的實(shí)現(xiàn)多目標(biāo)邏輯量子比特受控相位門.該方案不僅對(duì)抵御整體退相位錯(cuò)誤是魯棒的，而且容易實(shí)現(xiàn).通過對(duì)相位門保真度的分析得知，該方案對(duì)腔衰減更加魯棒，在中度耦合條件下，它的保真度可以達(dá)到1.最后，本文討論了在當(dāng)前實(shí)驗(yàn)條件下該方案的可行性. 無消相干子空間； 原子與光子的相互作用； 多量子比特相位門 O431

文獻(xiàn)標(biāo)識(shí)碼：A

1單邊腔的輸入輸出過程

考慮2個(gè)相同的二能級(jí)原子與單模腔相互作用的系統(tǒng)，耦合系統(tǒng)的哈密頓可以寫成[28](?=1)：

(1)

(2)

圖1　腔中原子的能級(jí)結(jié)構(gòu)(a)和單邊光學(xué)腔的輸入輸出過程(b)

其中ω是單光子脈沖的頻率， κ/2和γm/2分別為腔衰減率和第m個(gè)原子衰減率.假設(shè)在方程(2)中κ是足夠大的，那么它可以確保原子與光子相互作用后原子布局仍保留在基態(tài)上.原子的衰減率，以及原子與腔模相互作用的耦合強(qiáng)度分別滿足關(guān)系： γ1=γ2=γ， g1=g2=g.在共振條件下ωc=ω0=ω, 反射系數(shù)r(ω)可以寫成：

(3)

其中下角標(biāo)“2”代表2個(gè)原子與腔模相互作用.在強(qiáng)耦合(g?κ,γ)區(qū)域中，發(fā)射系數(shù)r2≈1， 此時(shí)反射出來的光子將會(huì)攜帶一個(gè)φ2=0的相位；在去耦合(g=0)條件下，反射系數(shù)r0≈-1， 此時(shí)反射出來的光子將會(huì)攜帶一個(gè)φ0=π的相位；當(dāng)單光子與腔中的一個(gè)原子相耦合時(shí)，反射系數(shù)r1≈1， 此時(shí)反射出來的光子將攜帶φ1=0的相位[28-29,32-33].

(4)

將方程(4)定義成UR， 它表示的是極化光子和原子躍遷之間的選擇性定則，其目的是實(shí)現(xiàn)一些無消相干子空間中的量子邏輯操作.

2無消相干子空間中多目標(biāo)的受控相位翻轉(zhuǎn)門的實(shí)現(xiàn)

(5)

經(jīng)過這個(gè)模塊以后，腔中的2個(gè)原子就和單光子脈沖糾纏在一起.

圖2　糾纏門的示意圖 (PBS代表極化分束器,QWP代表四分之一波片,HWP22.5°表示半波片)

圖3　實(shí)現(xiàn)三量子比特受控相位門的裝置圖

(6)

(7)

當(dāng)光子脈沖通過模塊Pc后，系統(tǒng)的態(tài)將演化成

(8)

(9)

則方程(8)可以寫成

(10)

最后，光子到達(dá)探測器.當(dāng)探測器Dv響應(yīng)時(shí)，原子態(tài)將塌縮到

(11)

即

(12)

此外，利用圖4的裝置可以將上述的方案拓展到實(shí)現(xiàn)多目標(biāo)邏輯量子比特的受控相位翻轉(zhuǎn)門的情況.多目標(biāo)邏輯量子比特受控相位翻轉(zhuǎn)門可以寫成[11]：

(13)

圖4　實(shí)現(xiàn)多目標(biāo)邏輯量子比特受控相位翻轉(zhuǎn)門的裝置

(14)

利用編碼在無消相干子空間的原子所實(shí)現(xiàn)的上述糾纏態(tài)和量子邏輯門都不受整體退相位的影響，并且也不需要復(fù)雜的操作.

3討論與總結(jié)

(15)

圖5　多目標(biāo)邏輯量子比特受控相位翻轉(zhuǎn)門的保真度F與g/κ的關(guān)系圖

(16)

(17)

從式(17)可以看出，在不同腔中的不同噪聲，不會(huì)使量子態(tài)發(fā)生變化.

本文通過在無消相干子空間中的輸入輸出過程，提出了確定性的實(shí)現(xiàn)光子和原子的糾纏門，以及多目標(biāo)邏輯量子比特的受控相位翻轉(zhuǎn)門的方案.該方案對(duì)環(huán)境噪聲所引起的整體退相位有很好的魯棒性，并且在中度耦合強(qiáng)度下有較高的保真度，所以該方案有望被應(yīng)用于分布式量子計(jì)算網(wǎng)絡(luò)中.

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Deterministic implementation of a controlled phase gate with multi-target qubits in decoherence-free subspace

ZHANG Fengqin,ZHU Aidong*

(DepartmentofPhysics,CollegeofScience,YanbianUniversity,Yanji133002,China)

Abstract：A scheme is proposed for deterministically implementing a controlled-phase flip gate with multi-target logic qubits via the input-output process of the cavity, in which two atoms are trapped and encoded as one logic qubit in the decoherence-free subspace. The scheme is not only robust against the collective dephasing errors, but also easy to implement. The analysis of fidelity for this gate shows the robustness to cavity decay. Under a medium coupling strength it reaches a high fidelity near unity. The discussion on experiment shows its feasibility with current technology.

Keywords：decoherence-free subspace; interactions of atoms with photons; multi-qubit phase gate

文章編號(hào)：1004-4353(2015)04-0300-07

*通信作者：朱愛東(1968—)，女，博士，教授，研究方向?yàn)榱孔庸鈱W(xué)和量子信息學(xué).

收稿日期：2015-10-13基金項(xiàng)目： 國家自然科學(xué)基金資助項(xiàng)目(11564041，61465013，11264042)