基于STQ系統(tǒng)的一個四比特簇態(tài)制備方案

陳 娟，郭琰博，姜年權(quán)

基于STQ系統(tǒng)的一個四比特簇態(tài)制備方案

*陳 娟，郭琰博，姜年權(quán)

(溫州大學物理與電子信息工程學院，浙江，溫州 325035)

Transmon 比特通過電容與一個超導TLR（transmission line resonator）耦合。本文采用Transmon 比特與TLR之間有更強的耦合常量，提出了一個在STQ（superconducting transmon qubit）系統(tǒng)中制備四比特糾纏簇態(tài)（cluster state）的簡單方案。與已有的方案相比，此方案有更長的消相干時間。又由于Transmon 比特和TLR有以上的屬性，此方案在實驗上更可行。

cluster態(tài)；超導Transmon比特；傳輸線型諧振腔

量子糾纏因其獨特的性質(zhì)而成為量子信息處理的重要資源[1]。其中，三體或多體糾纏不僅可以用于檢驗量子力學非局域理論[2]，而且被用于許多量子信息處理方案中。比如：量子隱形傳態(tài)[3-4]，量子糾纏交換[5]和量子稠密編碼等[6-7]。因此, 探究和制備多體糾纏態(tài)具有重要意義。在近年來的研究中，已有多種不同的多體糾纏態(tài)被提出，如：Greenberger-Horne-Zeilinger (GHZ)態(tài)[8-9]、W 態(tài)[10]和cluster 態(tài)[11]等。其中，Briegel 和 Raussendor[11]提出的cluster 態(tài)比GHZ 態(tài)對消相干更不敏感[12-13]，而且量子計算機能通過cluster 態(tài)來實現(xiàn)[12]，正因為如此，cluster 態(tài)備受人們的關(guān)注。其在不同的物理系統(tǒng)（如：腔量子電動力學系統(tǒng)（QED））中的制備方案已經(jīng)被提出[14-21]。在文獻[20]中，Yang 等人提出了一個在熱腔QED中制備四原子cluster 態(tài)的方案，此方案包括兩個單比特操作和四個兩比特操作；在文獻[14-19,21]中，提出了需要三步來制備一個四比特cluster態(tài)的方案；鄭曉娟等提出了一個在腔QED中通過兩個三比特操作制備四比特cluster態(tài)的方案[22]。

(a)

(b)

圖 1 (a)Transmon量子比特基本的線路圖；(b)N個Transmon量子比特與TLR耦合的電路圖，其中頻率為d的微波輸入到TLR

Fig. 1 (a) The basic circuit of transmon qubit; (b) The circuit of N transmon qubits coupled with the TLR, in which a microwave ?eld of frequencydis applied to the input wire of the TRL

本文將基于STQ系統(tǒng)提出了一個有效地制備四比特糾纏cluster態(tài)的方案，與上述已有方案相比，該方案僅包括兩個三比特操作，方案中超導TLR被選為量子數(shù)據(jù)總線（QDB）[25]，并且Transmon量子位和QDB之間的耦合常數(shù)非常大[26]。因此，方案具有更長的消相干時間和更短的操作時間。本文將在第二部分給出系統(tǒng)的模型和它的哈密頓量，在第三部分介紹如何制備四比特糾纏cluster態(tài)，最后討論此方案在實驗中的可行性。

1 模型和哈密頓量

因此，總系統(tǒng)的哈密頓量為

2 制備四比特糾纏cluster態(tài)

現(xiàn)將介紹如何在一個由四個STQ和一個TLR組成的系統(tǒng)中制備四比特糾纏cluster態(tài)。利用前面已經(jīng)寫出的系統(tǒng)的哈密頓量，選取

這些條件在實驗上能很容易實現(xiàn)。因此，哈密頓量 (4) 變?yōu)?/p>

應(yīng)用上面相同的理論，得到演化算符為

因此，任意初態(tài)演化為

這是一個四比特糾纏cluster態(tài)。

3 討論和結(jié)論

很明顯非常小。所以說，在第一步中只有三個Transmon比特演化。第一個Transmon比特一直處于基態(tài)。同理可得第二步中Transmon比特被激發(fā)的可能性

所以方案是可行的。

總之，本文提出了一個在STQ系統(tǒng)中制備四比特糾纏cluster態(tài)的方案。因為所用的量子比特有更長的消相干時間和更大的耦合量，所以該方案在實驗上更加可行。同時也計算了無關(guān)Transmon比特被激發(fā)的可能性，發(fā)現(xiàn)對于態(tài)的制備來說，影響非常小。

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Scheme To PreparE four-qubit cluster states Based On STQ sYstem

*CHEN Juan，GUO Yan-bo，JIANG Nian-quan

( College of Physics and Electronic Information Engineering of Wenzhou University, Wenzhou, Zhejiang 325035,China)

Transmon qubits capacitively coupled to a superconducting transmission line resonator (TLR). We adopt transmon qubits which have much stronger coupling constant with TLR and propose a simple scheme to prepare a four-qubit entangled cluster state in superconducting transmon qubit (STQ) system. Compared with the scheme firstly introduced by Zheng Xiao-Juan et al, our schemes have longer dephasing time. Based on the favorable properties of transmons and TLR, our method is more feasible in experiment.

cluster states; superconducting Transmon qubit; transmission line resonator

O413.1

A

10.3969/j.issn.1674-8085.2014.03.006

1674-8085(2014)03-0027-05

2013-12-09；

2014-01-11

國家自然科學基金項目(10947017/A05)

*陳 娟(1989-)，女，江西撫州人，碩士生，主要從事量子信息研究(E-mail: 214386945@qq.com);

郭琰博(1990-)，男，甘肅天水人，碩士生，主要從事量子信息研究(E-mail:344516047@qq.com);

姜年權(quán)(1966-)，男，安徽安慶人，教授，博士，主要從事量子信息和太陽能電池研究(E-mail:jiangnq@wzu.edu.cn).