量子信息处理方案研究及其应用

【作者】 陈清；

【导师】 汪克林；

【作者基本信息】 中国科学技术大学 ， 理论物理， 2006， 博士

【摘要】 量子信息处理利用量子力学规律表示和操作信息，其能力大大超过了经典信息处理方式，因而激发了研究者对此研究领域的极大兴趣。在本论文中，我们主要讨论了两种不基于量子逻辑网络的量子信息处理方案——自由演化模型方案和一次性的量子计算机。 自由演化模型的特点很鲜明：优点是在处理过程中，无需对系统做任何含时的调控(除了某些情况下做单比特测量之外)，这样系统能够很好的独立于外界，而且对于那些实验上很难调控内部相互作用大小的系统，这种方案无疑更为容易实现；缺点是需要针对具体的任务来设计系统的具体属性，包括系统的构型，作用于其上的哈密顿量和初态等，从而影响了它的通用性。 一次性的量子计算机则是普适的，当这种量子计算机的初态即二维的cluster态制备完成之后，剩下的工作就仅仅只是一序列的单qubit测量。一次性的量子计算机没有量子输入，量子输出，量子寄存器，也不包含量子门。但是，由于利用了纠缠态作为它的核心物理资源，它的确实现了量子计算机的功能。 在第二章中，我们讨论了如何利用自由演化模型实现几项比较重要的量子信息处理任务，即量子态传输、量子态克隆、量子纠缠态制备。在量子态传输一节里介绍了如何利用具有镜像对称性的自旋网络来实现精确态传输。而在量子态克隆和量子纠缠态制备这两节里，我们利用星形自旋网络实现了最佳的1→M相位协变克隆(PCC)和W态的制备。另外，我们采用N个辅助粒子与M个目标粒子相互作用的自旋网络结构，使得需要制备的对称态在对辅助粒子进行单比特测量后能以一定的概率精确制备到目标粒子上。进一步的，我们提出“重复直到成功”的策略，即制备失败后不需要恢复系统到初始状态，继续演化并对对辅助粒子继续测量，最终能制备出所需的对称态。 鉴于图态在一次性的量子计算机中的重要性，我们在第三章中介绍了图态的一些性质，尤其是图态的测量性质和图态的等价类划分。我们还讨论了图态在量子博弈中的应用。特别地，我们详细分析了以星形结构的图态作为纠缠源的量子少数者博弈，发现当选手的数目为偶数时，选手在Nash平衡下能够得到比经典情况更多的收益。进一步的，我们研究了4qubit的图态，发现无论在哪种4更多还原

【Abstract】 Quantum information processing employs quantum mechanics to express and manipulate information, and it appeals much more powerful than the classic information processing. Recently, this field has drawn increasing attention. In this thesis, we mainly investigate two quantum information processing schemes: free evolution model and the one-way quantum computer, both of which do not involve quantum logic network.In the free evolution model, the time dependent external control (except for single qubit measurements) is not needed, which ensures the whole computation process can be implemented while isolated from environment. Moreover, for those systems where the interaction between qubits is difficult to modulate, this scheme provides a relative easier alternative. Meanwhile, this scheme is less flexible than the traditional approach with quantum gates. One needs to design a different system including the structure of the system, the Hamiltonian and the initial state for each different computation task.The one-way quantum computer, in the other hand, is universal. When the initial state, a two dimensional cluster state, has been prepared, all left work is to perform a series of single qubit measurements upon chosen qubits. This scheme consists no quantum input, output and quantum register, even unitary gates from some universal sets are not necessary. However, by utilizing quantum entangled states as its kernel physical resource, it does realize all required functions of the genuine quantum computer.In Chapter 2 we show how to implement several important quantum informationprocessing tasks--quantum state transfer, quantum state cloning and the generationof quantum entangled states, within the free evolution model. We describe that perfect state transfer can be carried out in spin networks which has the mirror inversion symmetry. Later, we demonstrate that star like spin network is capable of implementing optimal 1 → M Phase Covariant Cloning (PCC), also it can also be used to generate arbitrary W states. Further, we proposed a "repeat-until-success" scheme which provides a persistent approach to arbitrary symmetric states without any modulated control.Since the Graph state plays an crucial role in one-way quantum computer, we in-更多还原