Quantum reversible circuit of AES-128

An explicit quantum design of AES-128 is presented in this paper. The design is structured to utilize the lowest number of qubits. First, the main components of AES-128 are designed as quantum circuits and then combined to construct the quantum version of AES-128. Some of the most efficient approaches in classical hardware implementations are adopted to construct the circuits of the multiplier and multiplicative inverse in \({\mathbb {F}}_{2}[x]/(x^8+x^4+x^3+x+1)\). The results show that 928 qubits are sufficient to implement AES-128 as a quantum circuit. Moreover, to maintain the key uniqueness when the quantum AES-128 is employed as a Boolean function within a Black-box in other key searching quantum algorithms, a method with a cost of 930 qubits is also proposed.     

基于量子门线路的量子神经网络模型及算法

提出一种量子神经网络模型及算法.该模型为一组量子门线路.输入信息用量子位表示,经量子旋转门进行相位旋转后作为控制位,控制隐层量子位的翻转;隐层量子位经量子旋转门进行相位旋转后作为控制位,控制输出层量子位的翻转.以输出层量子位中激发态的概率幅作为网络输出,基于梯度下降法构造了该模型的学习算法.仿真结果表明,该模型及算法在收敛能力和鲁棒性方面均优于普通BP网络.     

Quantum cooperative search algorithm for 3-SAT

Grover's search algorithm, one of the most popular quantum algorithms, provides a good solution to solve NP complexity problems, but requires a large number of quantum bits (qubits) for its functionality. In this paper, a novel algorithm called quantum cooperative search is proposed to make Grover's search algorithm work on 3-SAT problems with a small number of qubits. The proposed algorithm replaces some qubits with classical bits and finds assignments to these classical bits using the traditional 3-SAT algorithms including evolutionary algorithms and heuristic local search algorithms. In addition, the optimal configuration of the proposed algorithm is suggested by mathematical analysis. The experimental results show that the quantum cooperative search algorithm composed by Grover's search and heuristic local search performs better than other pure traditional 3-SAT algorithms in most cases. The mathematical analysis of the appropriate number of qubits is also verified by the experiments.     

Line ordering of reversible circuits for linear nearest neighbor realization

Real quantum computing technologies have different restrictions and constraints which need to be considered during circuit synthesis. In certain technologies, only physically adjacent qubits can interact, which restricts their realizations to only linear nearest neighbor (LNN) architecture. In this work, we formulate the line ordering problem in LNN architecture as task assignment problem to find a mapping (permutation) between task graph and processor graph with minimum cost. We propose two different approaches, a greedy heuristic and a meta-heuristic algorithm based on Harmony Search to solve the task assignment problem. Experimental results show that our algorithms were able to reduce the quantum cost of benchmark circuits by approximately 30 % on average. Moreover, the proposed algorithms were compared to one recently proposed ordering algorithm and were found to further improve the cost by approximately 16 %.     

Implementing gate operations between uncoupled qubits in linear nearest neighbor arrays using a learning algorithm

We propose a new scheme to implement gate operations in a one dimensional linear nearest neighbor array, by using dynamic learning algorithm. This is accomplished by training quantum system using a back propagation technique, to find the system parameters that implement gate operations directly. The key feature of our scheme is that, we can reduce the computational overhead of a quantum circuit by finding the parameters to implement the desired gate operation directly, without decomposing them into a sequence of elementary gate operations. We show how the training algorithm can be used as a tool for finding the parameters for implementing controlled-NOT (CNOT) and Toffoli gates between next-to-nearest neighbor qubits in an Ising-coupled linear nearest neighbor system. We then show how the scheme can be used to find parameters for realizing swap gates first, between two adjacent qubits and then, between two next-to-nearest-neighbor qubits, in each case without decomposing it into 3 CNOT gates. Finally, we show how the scheme can be extended to systems with non-diagonal interactions. To demonstrate, we train a quantum system with Heisenberg interactions to find the parameters to realize a swap operation.     

基于量子位Bloch坐标的量子遗传算法及其应用

提出了一种基于量子位Bloch坐标的量子遗传算法. 该方法用量子位构成染色体; 用量子位的Bloch坐标构成染色体上的基因位; 用量子旋转门进行染色体上量子位的更新; 用量子非门进行染色体变异. 对于量子旋转门的转角大小及方向的确定, 提出了一种简易快捷的新方法; 对旋转和变异操作, 提出了基于量子位Bloch坐标的新算子. 该算法将量子位的3个Bloch 坐标都看作基因位, 每条染色体包含3条并列的基因链, 每条基因链代表1个优化解.在染色体数目相同时, 可加速优化进程. 以函数极值优化和神经网络权值优化为例, 仿真结果表明该方法在搜索能力和优化效率两个方面优于普通量子遗传算法和简单遗传算法.     

量子可逆逻辑综合的关键技术及其算法

最优化量子可逆逻辑的关键在于用最小的量子代价自动构造量子可逆逻辑.为了提高可逆逻辑自动生成与优化的效率,提出了类模板技术和一种快速算法.模板技术是一个有效的优化工具,类模板技术可以显著提高模板技术的匹配效率;R-M算法是可逆逻辑综合的一种较好的迭代方法,基于R-M算法的原始思想,构造了一个Hash函数,并在此基础上提出了一种可逆逻辑综合的快速算法.实验结果表明,在同等实验环境下使用类模板技术与快速算法,其优化的效果与效率远远优于已知的其他算法.     

Towards quantum reversible ternary coded decimal adder

Quantum ternary logic is a promising emerging technology for the future quantum computing. Ternary reversible logic circuit design has potential advantages over the binary ones like its logarithmic reduction in the number of qudits. In reversible logic all computations are done in an invertible fashion. In this paper, we propose a new quantum reversible ternary half adder with quantum cost of only 7 and a new quantum ternary full adder with a quantum cost of only 14. We termed it QTFA. Then we propose 3-qutrit parallel adders. Two different structures are suggested: with and without input carry. Next, we propose quantum ternary coded decimal (TCD) detector circuits. Two different approaches are investigated: based on invalid numbers and based on valid numbers. Finally, we propose the quantum realization of TCD adder circuits. Also here, two approaches are discussed. Overall, the proposed reversible ternary full adder is the best between its counterparts comparing the figures of merits. The proposed 3-qutrit parallel adders are compared with the existing designs and the improvements are reported. On the other hand, this paper suggested the quantum reversible TCD adder designs for the first time. All the proposed designs are realized using macro-level ternary Toffoli gates which are built on the top of the ion-trap realizable ternary 1-qutrit gates and 2-qutrit Muthukrishnan–Stroud gates.     

基于改进量子遗传算法的过程神经元网络训练

针对过程神经元网络由于模型参数较多BP算法不易收敛的问题,提出一种基于量子位Bloch坐标的量子遗传算法.将该算法融合于过程神经网络的训练.按权值参数的个数确定量子染色体上的基因数并完成种群编码,通过新的量子旋转门完成个体的更新.算法中的每条染色体携带3条基因链,因此可扩展对解空间的遍历性,加速优化进程.以两组二维三角函数的模式分类问题为例,仿真结果表明该方法不仅收敛速度快,而且寻优能力强.     

Efficient quantum computing between remote qubits in linear nearest neighbor architectures

We propose a new scheme for implementing gate operations between remote qubits in linear nearest neighbor (LNN) architectures, one that does not require qubits to be adjacent to each other in order to perform a gate operation between them. The key feature of our scheme is a new two-control, one-target controlled-unitary gate operation, which we refer to as the C²(?I) gate. The gate operation can be implemented easily in a single step, requiring only a single control parameter of the system Hamiltonian. Using the C²(?I) gate, we show how to implement CNOT gate operations between remote qubits that do not have any direct coupling between them, along an LNN array. Since this is achieved without requiring swap operations or additional ancilla qubits in the circuit, the quantum cost of our circuit can be more than 50 % lower than those using conventional swap methods. All CNOT gate operations between remote qubits can be achieved with fidelity greater than 99.5 %.     

Synthesis of quantum circuits for linear nearest neighbor architectures

While a couple of impressive quantum technologies have been proposed, they have several intrinsic limitations which must be considered by circuit designers to produce realizable circuits. Limited interaction distance between gate qubits is one of the most common limitations. In this paper, we suggest extensions of the existing synthesis flow aimed to realize circuits for quantum architectures with linear nearest neighbor interaction. To this end, a template matching optimization, an exact synthesis approach, and two reordering strategies are introduced. The proposed methods are combined as an integrated synthesis flow. Experiments show that by using the suggested flow, quantum cost can be improved by more than 50% on average.     

Least significant qubit algorithm for quantum images

To study the feasibility of the classical image least significant bit (LSB) information hiding algorithm on quantum computer, a least significant qubit (LSQb) information hiding algorithm of quantum image is proposed. In this paper, we focus on a novel quantum representation for color digital images (NCQI). Firstly, by designing the three qubits comparator and unitary operators, the reasonability and feasibility of LSQb based on NCQI are presented. Then, the concrete LSQb information hiding algorithm is proposed, which can realize the aim of embedding the secret qubits into the least significant qubits of RGB channels of quantum cover image. Quantum circuit of the LSQb information hiding algorithm is also illustrated. Furthermore, the secrets extracting algorithm and circuit are illustrated through utilizing control-swap gates. The two merits of our algorithm are: (1) it is absolutely blind and (2) when extracting secret binary qubits, it does not need any quantum measurement operation or any other help from classical computer. Finally, simulation and comparative analysis show the performance of our algorithm.     

量子协同免疫动态优化算法

基于协同策略和量子免疫计算理论,提出量子协同免疫动态优化算法,并从理论上证明算法的全局收敛性.该算法采用量子比特编码表达种群中的抗体,并采用量子旋转门和动态调整旋转步长策略来演化抗体,加速原有克隆算子的收敛.该算法中引入协同策略增强子群体间的信息交流,提高种群的多样性,同时利用量子编码种群的关联性,使算法具有更强的稳定性,能够较好地适应于动态问题的求解.文中通过一系列动态背包测试问题和交叉验证(t检验)实验表明,量子协同免疫动态优化算法具有更强的鲁棒性和适应性,显示出较优越的性能.     

A lower bound method for quantum circuits

Quantum circuits, which are shallow, limited in the number of gates and additional workspace qubits, are popular for quantum computation because they form the simplest possible model similar to the classical model of a network of Boolean gates and capable of performing non-trivial computation. We give a new lower bound technique for such circuits and use it to give another proof that deterministic computation of the parity function cannot be performed by such circuits.     

Disassembly Sequencing Using Tabu Search

End-of-life disassembly has developed into a major research area within the sustainability paradigm, resulting in the emergence of several algorithms and structures proposing heuristics techniques such as Genetic Algorithm (GA), Ant Colony Optimization (ACO) and Neural Networks (NN). The performance of the proposed methodologies heavily depends on the accuracy and the flexibility of the algorithms to accommodate several factors such as preserving the precedence relationships during disassembly while obtaining near- optimal and optimal solutions. This paper improves a previously proposed Genetic Algorithm model for disassembly sequencing by utilizing a faster metaheuristic algorithm, Tabu search, to obtain the optimal solution. The objectives of the proposed algorithm are to minimize (1) the traveled distance by the robotic arm, (2) the number of disassembly method changes, and (3) the number of robotic arm travels by combining the identical-material components together and hence eliminating unnecessary disassembly operations. In addition to improving the quality of optimum sequence generation, a comprehensive statistical analysis comparing the previous Genetic Algorithm and the proposed Tabu Search Algorithm is also included     

Efficient schemes for the quantum teleportation of a sub-class of tripartite entangled states

In this paper we propose two schemes for teleportation of a sub-class of tripartite states, the first one with the four-qubit cluster state and the second one with two Bell pairs as entanglement channels. A four-qubit joint measurement in the first case and two Bell measurements in the second are performed by the sender. Appropriate unitary operations on the qubits at the receiver’s end along with an ancilla qubit result in the perfect teleportation of the tripartite state. Analysis of the quantum circuits employed in these schemes reveal that in our technique the desired quantum tasks are achieved with lesser quantum cost, gate count and classical communication bits compared with other similar schemes.     

Evolving quantum circuits at the gate level with a hybrid quantum-inspired evolutionary algorithm

This paper proposes an approach to evolve quantum circuits at the gate level, based on a hybrid quantum-inspired evolutionary algorithm. This approach encodes quantum gates as integers and combines the cost and correctness of quantum circuits into the fitness function. A fast algorithm of matrix multiplication with Kronecker product has been proposed to speed up the calculation of matrix multiplication in individuals evaluation. This algorithm is shown to be better than the known best algorithm for matrix multiplication when a certain condition holds. The approach of evolving quantum circuits is validated by some experiments and the effects of some parameters are investigated. And finally, some features of the approach are also discussed.     

Maximum density of quantum information in a scalable CMOS implementation of the hybrid qubit architecture

Scalability from single-qubit operations to multi-qubit circuits for quantum information processing requires architecture-specific implementations. Semiconductor hybrid qubit architecture is a suitable candidate to realize large-scale quantum information processing, as it combines a universal set of logic gates with fast and all-electrical manipulation of qubits. We propose an implementation of hybrid qubits, based on Si metal-oxide-semiconductor (MOS) quantum dots, compatible with the CMOS industrial technological standards. We discuss the realization of multi-qubit circuits capable of fault-tolerant computation and quantum error correction, by evaluating the time and space resources needed for their implementation. As a result, the maximum density of quantum information is extracted from a circuit including eight logical qubits encoded by the [[7, 1, 3]] Steane code. The corresponding surface density of logical qubits is 2.6 Mqubit/cm\(^2\).     

基于动态交叉协同的属性量子进化约简与分类学习级联算法

属性约简与规则分类学习是粗糙集理论研究和应用的重要内容。文中充分利用量子计算加速算法速度和混合蛙跳算法高效协同搜索等优势,提出一种基于动态交叉协同的量子蛙跳属性约简与分类学习的级联算法。该算法用量子态比特进行蛙群个体编码,以动态量子角旋转调整策略实现属性染色体快速约简,并在粗糙熵阈值分类标准内采用量子蛙群混合交叉协同进化机制提取和约简分类规则、组合决策规则链等,最后构造属性约简和分类学习双重功能级联模型。仿真实验验证该算法不仅具有较高的全局优化性能,且属性约简与规则分类学习的精度和效率均超过同类算法。