多量子位Grover量子搜索算法的NMR仿真实现

核磁共振（NMR）技术目前是能有效实现量子计算的物理体系之一。多量子算符代数理论可以将幺正变换分解为一系列有限的单量子门和对角双量子门的组合。本文以核磁共振和多量子算符代数理论为基础,提出了实现多量子位Grover量子搜索算法的核磁共振脉冲序列设计方法,并在量子计算仿真程序上进行了3量子位的Grover量子搜索算法的实验验证。     

多量子位量子小波变换逻辑线路及仿真实现

由于量子计算相比于经典计算的突出优越性,量子小波变换的实现对于小波变换的理论完善和实际应用具有重要的意义,而逻辑线路是该变换实现的基础。应用多量子算符代数理论设计了3量子位Haar和D^（4）小波变换的逻辑线路,进而将逻辑线路转化成核磁共振系统可以实现的脉冲序列,并在量子计算仿真器（QCE）上进行了模拟实现,验证了逻辑线路的合理性。     

自旋量子系统的可控李代数计算

动态系统可控性同是经典和量子控制中研究的一个基本问题,本文研究了单自旋和双自旋量子系统的可控李代数的计算.首先基于量子系统可控的等价性条件,通过单量子系统Hamiltonian算符的李括号运算,给出了与基系数相关的系统可控的充要条件.然后利用Cartan分解方法构造了李代数su(4)的矩阵基,同时根据可控性基本定理提出了Hamiltonian算符多重李括号的计算方法及系统的可控性判据.     

Grover量子搜索算法的仿真实现

利用核磁共振(NMR)实验技术来实现量子计算,是当前各种验证量子算法最为有效的方法之一,但这个方法首先必须把量子算法编译成在现代超导核磁共振谱仪上能够直接执行的NMR脉冲序列,即NMR量子计算程序。在NMR技术中通常只要施加合适的射频脉冲,便可以达到使核自旋翻转以实现某种逻辑功能的目的,该文讨论了如何设计多量子位核磁共振(NMR)脉冲序列来实现Grower量子搜索算法,并在量子仿真器(QCE)上进行了实验验证。     

量子衍生布谷鸟搜索算法

为提高布谷鸟搜索算法的寻优能力,通过在经典布谷鸟搜索算法中引入量子计算机制,提出了一种量子衍生布谷鸟搜索算法.该算法采用量子比特编码个体,采用泡利矩阵确定旋转轴,采用Levy飞行原理确定旋转角度,采用量子比特在Bloch球面上的绕轴旋转实现个体更新.标准函数极值优化的实验结果表明,与传统布谷鸟搜索算法相比,该算法的搜索能力确有明显提升.     

量子控制非门核磁共振脉冲序列设计与验证

在核磁共振条件下解单体含时薛定谔方程,给出核自旋绕[x]轴和[y]轴转动[π/2]的单量子位转动门,根据量子控制非门的定义,设计出实现量子控制非门的核磁共振脉冲序列。利用两个核自旋之间的相互作用时间远小于射频脉冲作用时间这个条件,通过在旋转参考系中近似求解核磁共振时的两体含时薛定谔方程,给出量子控制非门核磁共振脉冲序参数取值。利用Suzuki对称乘积公式,对含时薛定谔方程进行数值计算,数值计算结果验证了量子控制非门脉冲序列设计与参数取值的正确性。     

基于受控旋转门的量子神经网络模型算法及应用

提出一种量子神经网络模型及算法．首先借鉴受控非门的含义提出一种受控量子旋转门,基于该门的物理意义,提出一种量子神经元模型,该模型包含对输入量子比特相位的旋转角度和对旋转角度的控制量两种设计参数;然后基于上述量子神经元提出一种量子神经网络模型,基于梯度下降法详细设计了该模型的学习算法：最后通过模式识别和时间序列预测两个仿...     

混合多值可逆逻辑中广义Toffoli门仅用CNOT门的实现

混合多值量子可逆逻辑电路综合问题中,Toffoli门的合成是整个合成过程中最为关键的一步。针对混合多值5-qubits量子可逆逻辑电路综合问题,构造了PMX量子门,验证了CNOT门的合成能力,实现了对Toffoli门的合成,并设计了双向的BDS搜索算法,高效实现了量子电路的最优或者较优综合。     

量子纠缠遗传算法在微带耦合器中的应用

结合量子纠缠理论,提出了量子纠缠遗传算法。利用多粒子的量子纠缠W态,探讨了量子染色体的纠缠编码方式;给出了量子更新算符、量子变异算符和量子交叉算符的具体形式;给出了量子纠缠遗传算法的具体步骤。最后,将量子纠缠遗传算法应用到微带耦合器设计中,其结果表明量子纠缠遗传算法优化速度很快,能够得到很好的优化结果。     

量子衍生布谷鸟算法及在地层对比中的应用

为提高布谷鸟搜索算法的寻优能力,通过在经典布谷鸟搜索算法中引入量子计算机制,提出一种量子衍生布谷鸟搜索算法。该算法采用量子比特编码个体,采用泡利矩阵确定旋转轴,采用Levy飞行原理确定旋转角度,采用量子比特在Bloch球面上的绕轴旋转实现个体更新。针对钻井剖面地层对比的具体特点及需要满足的约束条件,提出应用量子衍生布谷鸟算法进行地层对比优化的实施方案,该方法既能对比不同地层之间的相似性,也能处理对比井地层因断层或尖灭等因素造成的缺失。实验结果表明,在复杂地质情况下,该算法是有效的和可行的。      

Circuit QED: implementation of the three-qubit refined Deutsch–Jozsa quantum algorithm

We propose a protocol to construct the 35 \(f\) -controlled phase gates of a three-qubit refined Deutsch–Jozsa (DJ) algorithm, by using single-qubit \(\sigma _z\) gates, two-qubit controlled phase gates, and two-target-qubit controlled phase gates. Using this protocol, we discuss how to implement the three-qubit refined DJ algorithm with superconducting transmon qutrits resonantly coupled to a single cavity. Our numerical calculation shows that implementation of this quantum algorithm is feasible within the present circuit QED technique. The experimental realization of this algorithm would be an important step toward more complex quantum computation in circuit QED.     

Constructing quantum logic gates using q-deformed harmonic oscillator algebras

We study two-level q-deformed angular momentum states, and using q-deformed harmonic oscillators, we provide a framework for constructing qubits and quantum gates. We also present the construction of some basic one-qubit and two-qubit quantum logic gates.     

Towards a NMR implementation of a quantum lattice gas algorithm

Recent theoretical results suggest that an array of quantum information processors communicating via classical channels can be used to solve fluid dynamics problems. Quantum lattice-gas algorithms (QLGA) running on such architectures have been shown to solve the diffusion equation and the nonlinear Burgers equations. In this report, we describe progress towards an ensemble nuclear magnetic resonance (NMR) implementation of a QLGA that solves the diffusion equation. The methods rely on NMR techniques to encode an initial mass density into an ensemble of two-qubit quantum information processors. Using standard pulse techniques, the mass density can then manipulated and evolved through the steps of the algorithm. We provide the experimental results of our first attempt to realize the NMR implementation. The results qualitatively follow the ideal simulation, but the observed implementation errors highlight the need for improved control.     

Exact canonical decomposition of two-qubit operators in terms of CNOT

The canonical decomposition for two-qubit operators has proven very useful for applications in quantum computing. This decomposition generates equivalence classes up to local quantum gates. We provide a variety of complete, explicit decompositions of given two-qubit operators in terms of single, double, and triple controlled-NOT (CNOT) gates. By analytically addressing the needed pre- and post-tensor product factors, we demonstrate that exact results are possible, even when a parameter is included. The examples given are of interest to superconducting qubit, spin-based, dipolar molecule, and other quantum information processing systems.     

Construction of quantum gates for concatenated Greenberger–Horne–Zeilinger-type logic qubit

Concatenated Greenberger–Horne–Zeilinger (C-GHZ) state is a kind of logic qubit which is robust in noisy environment. In this paper, we encode the C-GHZ state as the logic qubit and design two kinds of quantum gates for such logic qubit. The first kind is the single logic-qubit gate which contains the logic-qubit bit-flip gate and phase-flip gate. The second kind is the logic-qubit controlled-not (CNOT) gate. We exploit the single quantum gate for physical qubit, such as bit-flip gate and phase-flip gate, and two-qubit CNOT gate to realize the logic-qubit gate. We also calculated the success probability of such logic-qubit gate based on the imperfect physical quantum gate. This protocol may be useful for future quantum computation.     

On the role of the four-qubit state in two-qubit gate teleportation

The full analysis of quantum protocols requires the knowledge of the role of quantum states, bases of measurement and quantum gates involved. In what concerns the famous two-qubit quantum gate teleportation protocol, the role of the basis of measurement was considered in a recent work by Mendes and Ramos. In this work, we analyze the role of the four-qubit state used as resource. We show that the quantum two-qubit gate teleportation divides the set of pure four-qubit states in two classes. For one class, deterministic and probabilistic teleportation can be achieved, while for the other class, probabilistic remote two-qubit gate preparation is achieved.     

Quantum computation in the decoherence-free subspaces with cavity QED

We present a scheme to implement quantum computation in decoherence-free subspaces (DFSs) with four atoms in a single-mode cavity. A four-dimensional DFS is constituted to protect quantum information when the full symmetry of interaction between system and environment is broken in a specific way, and entangling two-qubit logic gates and noncommuting single-qubit gates are implemented in such DFS. The gate fidelity is numerically calculated, and the feasibility of the approximations taken in this work is verified based on the numerical calculations.     

Direct implementation of an N-qubit controlled-unitary gate in a single step

We present a new scheme to implement an N-qubit controlled-unitary operation directly in a single step. The main advantage of our scheme is that we do not use conventional gate decomposition protocols to break an N-qubit controlled-unitary gate into one- and two-qubit gates. This greatly reduces the number of computational steps in implementing quantum algorithms and error-correcting codes, which use multi-control unitary operations. We show how to find analytic solutions to the time evolution of the system, so that system parameters can be found to realize the desired N-qubit controlled-unitary operations.