Quantum Algorithm for Mining Frequent Patterns for Association Rule Mining

Maximum frequent pattern generation from a large database of transactions and items for association rule mining is an important research topic in data mining. Association rule mining aims to discover interesting correlations, frequent patterns, associations, or causal structures between items hidden in a large database. By exploiting quantum computing, we propose an efficient quantum search algorithm design to discover the maximum frequent patterns. We modified Grover’s search algorithm so that a subspace of arbitrary symmetric states is used instead of the whole search space. We presented a novel quantum oracle design that employs a quantum counter to count the maximum frequent items and a quantum comparator to check with a minimum support threshold. The proposed derived algorithm increases the rate of the correct solutions since the search is only in a subspace. Furthermore, our algorithm significantly scales and optimizes the required number of qubits in design, which directly reflected positively on the performance. Our proposed design can accommodate more transactions and items and still have a good performance with a small number of qubits.

QUANTUM COLLISION SEARCH ALGORITHM AGAINST NEW FORK-256

In order to improve the attack efficiency of the New FORK-256 function, an algorithm based on Grover's quantum search algorithm and birthday attack is proposed. In this algorithm, finding a collision for arbitrary hash function only needs O(2m/3) expected evaluations, where m is the size of hash space value. It is proved that the algorithm can obviously improve the attack efficiency for only needing O(2 74.7) expected evaluations, and this is more efficient than any known classical algorithm, and the consumed space of the algorithm equals the evaluation.

A Memory-efficient Simulation Method of Grover’s Search Algorithm

Grover’s search algorithm is one of the most significant quantum algorithms,which can obtain quadratic speedup of the extensive search problems.Since Grover's search algorithm cannot be implemented on a real quantum computer at present,its quantum simulation is regarded as an effective method to study the search performance.When simulating the Grover's algorithm,the storage space required is exponential,which makes it difficult to simulate the high-qubit Grover’s algorithm.To this end,we deeply study the storage problem of probability amplitude,which is the core of the Grover simulation algorithm.We propose a novel memory-efficient method via amplitudes compression,and validate the effectiveness of the method by theoretical analysis and simulation experimentation.The results demonstrate that our compressed simulation search algorithm can help to save nearly 87.5%of the storage space than the uncompressed one.Thus under the same hardware conditions,our method can dramatically reduce the required computing nodes,and at the same time,it can simulate at least 3 qubits more than the uncompressed one.Particularly,our memory-efficient simulation method can also be used to simulate other quantum algorithms to effectively reduce the storage costs required in simulation.

Behavior of quantum search algorithm with small phase rotations

When the Grover＇ s original algorithm is applied to search an unordered database, the success probability decreases rapidly with the increase of marked items. Aiming at this problem, a general quantum search algorithm with small phase rotations is proposed. Several quantum search algorithms can be derived from this algorithm according to different phase rotations. When the size of phase rotations are fixed at 0. 01π, the success probability of at least 99. 99% can be obtained in 0（√N/M） iterations.

Grover’s Algorithm in a 4-Qubit Search Space

This paper provides an introduction to a quantum search algorithm,known as Grover’s Algorithm,for unsorted search purposes.The algorithm is implemented in a search space of 4 qubits using the Python-based Qiskit SDK by IBM.While providing detailed proof,the computational complexity of the algorithm is generalized to n qubits.The implementation results obtained from the IBM QASM Simulator and IBMQ Santiago quantum backend are analyzed and compared.Finally,the paper discusses the challenges faced in implementation and real-life applications of the algorithm hitherto.Overall,the implementation and analysis depict the advantages of this quantum search algorithm over its classical counterparts.

Adaptive Phase Matching in Grover’s Algorithm

When the Grover’s algorithm is applied to search an unordered database, the successful probability usually decreases with the increase of marked items. In order to solve this problem, an adaptive phase matching is proposed. With application of the new phase matching, when the fraction of marked items is greater , the successful probability is equal to 1 with at most two Grover iterations. The validity of the new phase matching is verified by a search example.

Distributed exact Grover’s algorithm

Distributed quantum computation has gained extensive attention.In this paper,we consider a search problem that includes only one target item in the unordered database.After that,we propose a distributed exact Grover’s algorithm(DEGA),which decomposes the original search problem into■n/2■parts.Specifically,(i)our algorithm is as exact as the modified version of Grover’s algorithm by Long,which means the theoretical probability of finding the objective state is 100%;(ii)the actual depth of our circuit is 8(n mod 2)+9,which is less than the circuit depths of the original and modified Grover’s algorithms,1+8■π/4√2^(n)■and 9+8■π/4√2^(n)-1/2■,respectively.It only depends on the parity of n,and it is not deepened as n increases;(iii)we provide particular situations of the DEGA on MindQuantum(a quantum software)to demonstrate the practicality and validity of our method.Since our circuit is shallower,it will be more resistant to the depolarization channel noise.

First experimental demonstration of an exact quantum search algorithm in nuclear magnetic resonance system

The success probability of searching an objective item from an unsorted database using standard Grover's algorithm is usually not exactly 1. It is exactly 1 only when it is used to find the target state from a database with four items. Exact search is always important in theoretical and practical applications. The failure rate of Grover's algorithm becomes big when the database is small, and this hinders the use of the commonly used divide-and-verify strategy. Even for large database, the failure rate becomes considerably large when there are many marked items. This has put a serious limitation on the usability of the Grover's algorithm. An important improved version of the Grover's algorithm, also known as the improved Grover algorithm, solves this problem. The improved Grover algorithm searches arbitrary number of target states from an unsorted database with full success rate. Here, we give the first experimental realization of the improved Grover algorithm, which finds a marked state with certainty, in a nuclear magnetic resonance system. The optimal control theory is used to obtain an optimized control sequence. The experimental results agree well with the theoretical predictions.

基于0.1π旋转相位Grover算法的ECC电压毛刺攻击算法

将Grover算法应用到对公钥密码的故障攻击中,提出一种基于固定相位旋转Grover量子算法,当旋转相位为0.1π时,仿真实验搜索成功率提高到99.23%。进一步与故障攻击结合,提出基于0.1π旋转相位Grover算法的椭圆曲线密码电压毛刺攻击算法,仿真实验以100%的概率攻击了NIST公布的Koblitz安全曲线K-163,其计算复杂度呈指数级降低。这是除Shor算法之外量子计算对公钥密码的一种新的有效攻击途径,有助于拓展量子计算对其他公钥密码体制的攻击。

Grover算法改进与应用综述

量子信息科学是一门新兴的交叉学科,它在信息领域中有着独特的性能,在提高运算速度、确保信息安全、增大信息容量和提高检测精度等方面可突破现有经典信息系统的极限。Grover算法是一类典型的量子算法,能够对任意经典暴力穷举搜索问题实现二次加速,进一步推动了量子计算的发展,如何有效地改进和应用Grover算法成为量子计算的一个重要研究领域。文中综述了Grover算法的优化改进和应用,对Grover算法在不同领域应用及不同方面的改进进行了概述,并对Grover算法未来的改进和相关应用的若干研究方向进行了探讨。

MIMO-OFDM系统的联合估计检测算法

针对最大似然检测算法复杂度高,最小二乘信道估计性能较差等缺陷,提出了一种SAGE-IGQS联合估计检测算法,该算法使用LS算法进行信道初始化,采用SAGE算法进行信道迭代估计,并结合改进的Grover量子搜索算法进行信号检测,从而提高了系统的有效性。理论研究和仿真结果表明:该算法在降低系统复杂度的情况下,误比特率性能优于传统的联合检测算法,与理想信道估计下的最大似然检测算法相接近。

量子搜索算法体系及其应用

Grover量子搜索算法正在逐渐演变成一个算法体系,并逐渐进入了实际应用阶段。文章中通过几何法论述了经典Grover算法,通过算符法引申出了该算法的扩展,并在两种情况下对该算法进行了讨论。在分析该算法实际应用基本策略的基础上,论述了函数全局优化问题的改进,提出了通过量子搜索算法改进纯适应搜索算法的新思想。