核磁共振量子计算机与并行量子计算

在本文，我们首先回顾了量子计算的发展历史，阐述了核磁共振量子计算的原理．在叙述了利用有效纯态方法进行核磁共振量子计算之后，我们阐述了利用混合态进行核磁共振的量子计算的方法．首先是刘维尔量子计算方法，它是由Madi，Brushweiler，Ernst等人1998年提出的，在这一模式中，可以对搜索算法进行加速算法，Brushweilet。提出了一个指数速度的搜索算法．我们在3个比特的量子计算机中实现了这一搜索算法．我们在这一模式中提出了一个只需要一次搜索即可找标记物的直接拿取算法，并且在7个比特的核磁共振的量子计算机中实现了这一直接拿取算法．本文提出了在一个核磁共振量子计算机，或者更一般地一个系统量子计算机中实现多个量子计算机的并行计算．我们着重对量子搜索算法和Shor。的大数分解算法进行了并行实现．在并行量子计算中，一部分量子比特处在纯态，一部分量子比特处在混合态．如果所有的量子比特都处在纯态上，则就是有效纯态量子计算，如果所有的量子比特都处在混合态上，则就是刘维尔量子计算．在这两个极限中间，相当于2个到N／2个量子计算机的并行计算．量子搜索方法可以很有效地进行并行计算，而Shor算法则只能在小的范围内进行并行计算．     

Cluster 态的核磁共振实验制备

利用一种优化的幺正算符制备了一种高度纠缠态--cluster 态,这个优化的幺正算符因为只需要施加非选择性脉冲,其所用的时间被明显缩短．该文选择一个三量子位的自旋体系,在核磁共振仪器上进行了实验验证,实验过程中先制备了一个三量子位的纯态,然后通过施加优化的幺正算符即可得到三量子位的cluster 态,实验结果证明了优化幺正算符的有效性．     

多量子比特核磁共振体系的实验操控技术

随着量子信息与量子计算科学的发展,量子信息处理器被广泛地用于量子计算、量子模拟、量子度量等方面的研究.为了能在实验上实现这些日益复杂的方案,将量子计算机的潜能转化成现实,需要不断提高可操控的量子体系比特位数,实现更复杂的量子操控.核磁共振自旋体系作为一个优秀的量子实验测试平台,提供了丰富而又精密的量子操控手段.近几年来在此平台上进行了不少的多量子比特实验,发展并积累了一系列的多量子比特实验技术.本文首先阐述了核磁共振体系多量子比特实验中的实验困难,然后结合7量子比特标记赝纯态制备以及其他有关实验,对多比特实验过程中应用到的实验技术进行介绍.最后对核磁共振体系多量子比特实验技术方向的进一步研究进行了总结和展望.     

Cluster态的核磁共振实验制备

利用一种优化的幺正算符制备了一种高度纠缠态——cluster态,这个优化的幺正算符因为只需要施加非选择性脉冲,其所用的时间被明显缩短.该文选择一个三量子位的自旋体系,在核磁共振仪器上进行了实验验证,实验过程中先制备了一个三量子位的纯态,然后通过施加优化的幺正算符即可得到三量子位的cluster态,实验结果证明了优化幺正算符的有效性.     

制备三量子位和四量子位核磁共振等效纯态

基于时间平均法,给出了在同核系统中制备三量子位和四量子位核磁共振等效纯态的方案.利用Λn(not)门,本文的方案大大减少了制备等效纯态所需的操作次数在三同核系统中制备三量子位核磁共振等效纯态只需三次操作,在四同核系统中制备四量子位核磁共振等效纯态只需五次操作.然后在一个链状耦合的同核系统中实验制备三量子位核磁共振等效纯态,验证了本文的方案;并且给出了四量子位方案的模拟结果谱图.     

制备三量子位和四量子位核磁共振等效纯态

基于时间平均法,给出了在同核系统中制备三量子位和四量子位核磁共振等效纯态的方案.利用Λn(not)门,本文的方案大大减少了制备等效纯态所需的操作次数:在三同核系统中制备三量子位核磁共振等效纯态只需三次操作,在四同核系统中制备四量子位核磁共振等效纯态只需五次操作.然后在一个链状耦合的同核系统中实验制备三量子位核磁共振等效纯态,验证了本文的方案 并且给出了四量子位方案的模拟结果谱图     

核磁共振量子计算中的赝纯态制备

研究了少数量子位赝纯态的制备方案,比较两种不同的逻辑标志赝纯态的差异,分析了形成“垃圾块”的原因,提出了减少甚至消除“垃圾块”的方法． 关键词：     

能级间同时存在衰变和跃迁时的消相干特性

二能级原子在量子信息中可视为量子位.本文基于约化密度矩阵理论,利用量子纯态和混合态分析方法,针对二能级原子能级间同时存在衰变和跃迁的情况,研究原子消相干特性.     

从混合态构造相应的系统-热库纠缠纯态的新方法

在量子统计学和低温物理学中,常用密度算符(或混合态)来表示物理系综.本文旨在提出一个新方法能将混合态转化为系统与热库相纠缠的量子纯态,这样做不但可以彰显环境对系统的影响,探寻新的物理态,尤其是纠缠态,而且能将求系综平均的复杂计算转化为较为简洁的求纯态平均.我们的新方法是将相干态和有序算符内的积分理论结合起来,就可直接将混合态扩充为自由度加倍的纯态.     

热场动力学理论中的Husimi分布函数及Wehrl熵的研究

利用量子相空间技术和信息熵理论,研究了热场动力学理论中量子纯态与相应混合态的Husimi分布函数及Wehrl熵的一致性问题.结果表明,热相干态与相应混合态的Husimi分布函数及Wehrl熵完全相同,支持了热场动力学理论.且热相干态的Wehrl熵与平移因子无关,故在热相干态中,量子系统的可观测量的量子涨落及不确定关系也与平移因子无关.     

Use of non-adiabatic geometric phase for quantum computing by NMR

Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of error. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using the non-adiabatic geometric phase we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system.     

Experimental realization of single-shot nonadiabatic holonomic gates in nuclear spins

Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors.However,all the previous schemes have to use at least two sequentially implemented gates to realize a general one-qubit gate.Based on two recent reports,we construct two Hamiltonians and experimentally realized nonadiabatic holonomic gates by a single-shot implementation in a two-qubit nuclear magnetic resonance(NMR)system.Two noncommuting one-qubit holonomic gates,rotating along x?and z?axes respectively,are implemented by evolving a work qubit and an ancillary qubit nonadiabatically following a quantum circuit designed.Using a sequence compiler developed for NMR quantum information processor,we optimize the whole pulse sequence,minimizing the total error of the implementation.Finally,all the nonadiabatic holonomic gates reach high unattenuated experimental fidelities over 98%.     

Scheme for Implementing Quantum Search Algorithm in a Cluster State Quantum Computer

Using cluster state and single qubit measurement one can perform the one-way quantum computation. Here we give a detailed scheme for realizing a modified Grover search algorithm using measurements on cluster state. We give the measurement pattern for the cluster-state realization of the algorithm and estimated the number of measurement needed for its implementation. It is found that O（2^3n/^2n^2） number of single qubit measurements is required for its realization in a cluster-state quantum computer.     

Determining the parity of a permutation using an experimental NMR qutrit

We present the NMR implementation of a recently proposed quantum algorithm to find the parity of a permutation. In the usual qubit model of quantum computation, it is widely believed that computational speedup requires the presence of entanglement and thus cannot be achieved by a single qubit. On the other hand, a qutrit is qualitatively more quantum than a qubit because of the existence of quantum contextuality and a single qutrit can be used for computing. We use the deuterium nucleus oriented in a liquid crystal as the experimental qutrit. This is the first experimental exploitation of a single qutrit to carry out a computational task.     

Operating a geometric quantum gate by external controllable parameters

A scheme to perfectly preserve an initial qubit state in geometric quantum computation is proposed for a single-qubit geometric quantum gate in a nuclear magnetic resonance system. At first, by adjusting some magnetic field parameters, one can let the dynamic phase be proportional to the geometric phase. Then, by controlling the azimuthal angle in the initial state, we may realize a geometric quantum gate whose fidelity is equal to one under cyclic evolution. This means that the quantum information is no distortion in the process of geometric quantum computation.     

二维光子晶体中Grover搜索算法的实现

最近,Angelakis等人将光子晶体引入量子计算。本文主要讨论在二维光子晶体中两比特Grover搜索算法的实现。沿用由Angelakis等所提出的量子比特与可控相位门,简单有效的实现了Grover算法。具体的实现方案文中将详细讨论。     

Remote preparation of a Greenberger--Horne--Zeilinger state via a two-particle entangled state

We present two schemes for realizing the remote preparation of a Greenberger--Horne--Zeilinger (GHZ) state. The first scheme is to remotely prepare a general N-particle GHZ state with two steps. One is to prepare a qubit state by using finite classical bits from sender to receiver via a two-particle entangled state, and the other is that the receiver introduces N - 1 additional particles and performs N - 1 controlled-not (C-Not) operations. The second scheme is to remotely prepare an N-atom GHZ state via a two-atom entangled state in cavity quantum electrodynamics (QED). The two schemes require only a two-particle entangled state used as a quantum channel, so we reduce the requirement for entanglement.     

All-optical generation of states for "Encoding a qubit in an oscillator"

Most quantum computation schemes propose encoding qubits in two-level systems. Others exploit the use of an infinite-dimensional system. In "Encoding a qubit in an oscillator" [Phys. Rev. A 64, 012310 (2001)], Gottesman, Kitaev, and Preskill (GKP) combined these approaches when they proposed a fault-tolerant quantum computation scheme in which a qubit is encoded in the continuous position and momentum degrees of freedom of an oscillator. One advantage of this scheme is that it can be performed by use of relatively simple linear optical devices, squeezing, and homodyne detection. However, we lack a practical method to prepare the initial GKP states. Here we propose the generation of an approximate GKP state by using superpositions of optical coherent states (sometimes called "Schr?dinger cat states"), squeezing, linear optical devices, and homodyne detection.