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The foundation of this research is the quantum implementation of two hashing algorithms, namely Secure Hash Algorithm (SHA1) and Message Digest (MD5). Quantum cryptography is a challenging topic in network security for future networks. Quantum cryptography is an outgrowth of two broad topics—cryptology and cryptanalysis. In this paper, SHA1 and MD5 algorithms are designed and implemented for quantum computers. The main aim is to study and investigate the time requirement to build a hash and the bit rate at which a hash value is sent through. In this paper, a comprehensive analysis of these two algorithms is performed. Experiments have been done to compare and contrast the performances of the classical and proposed algorithms. In the experiment, it was found that the total time of execution of quantum SHA1 and quantum MD5 is much higher than the classical SHA1 and MD5. During quantum MD5 execution, it is observed that the time doubles when the number of chunks is increased from 1 to 2. Another experimental observation is that the execution time of the implemented algorithms depends upon the processor's speed. [ABSTRACT FROM AUTHOR]

The quantum phase estimation algorithm has been utilized by a variety of quantum algorithms, most notably Shor's algorithm, to obtain information regarding the period of a function that is appropriately encoded into a unitary operator. In many cases, it is desired to estimate whether a specific state exhibits a certain pattern quickly. In this paper, we exhibit a methodology based on the QPE algorithm to identify certain patterns. In particular, starting from a properly encoded state, we demonstrate how to construct unitary operators whose eigenvectors correspond to states with proper diagonals. QPE will then output an eigenphase equal to zero with certainty for these states, thereby identifying this class of matrices. For partial matches, our algorithm, based on the tolerance threshold used, will show areas of high similarity, and it will outperform classical ones when the number of mismatches defined by the tolerance is significantly low when compared to the size of the diagonal. [ABSTRACT FROM AUTHOR]

Clustering, a well-studied problem in the machine learning community, becomes even more intriguing with the emergence of quantum machine learning. Specifically, exploring clustering techniques for quantum data, such as quantum states, holds great interest. This paper introduces a quantum state clustering algorithm that utilizes variational quantum circuits. Our algorithm transforms the clustering problem into a parameter optimization task involving parametric quantum circuits. Each cluster is represented by a variational quantum circuit (VQC), which learns to extract the distinctive feature of its corresponding cluster during the optimization process. To guide the optimization of circuit parameters, we design an objective function that encourages each cluster's feature extractor to produce features similar to states within its own cluster and dissimilar to states in other clusters. We construct four quantum state datasets for testing the effectiveness of our algorithm. The numerical results demonstrate that our algorithm can achieve satisfying performance. [ABSTRACT FROM AUTHOR]

Quantum multidimensional scaling is a quantum dimensionality reduction algorithm. Its complex quantum circuit design structure and excessive qubits consumption make it difficult to run on the current quantum computers. In order to solve this problem, this paper proposes the variational quantum multidimensional scaling algorithm based on the variational quantum algorithm. Utilizing the parallel advantages of quantum computing to quickly compute low-dimensional embeddings of high-dimensional data, the variational quantum multidimensional scaling algorithm can provide lower time complexity; compared with the non-variational quantum multidimensional scaling algorithm, the variational quantum multidimensional scaling algorithm provides a simpler quantum circuit. In the noisy intermediate scale quantum era, the algorithm can run on a quantum computer. In addition, the article finally implemented the variational quantum multidimensional scaling algorithm on the Qiskit framework, proving the correctness of the algorithm. [ABSTRACT FROM AUTHOR]

Quantum approximate optimization algorithms are hybrid quantum-classical variational algorithms designed to approximately solve combinatorial optimization problems such as the MAX-CUT problem. In spite of its potential for near-term quantum applications, it has been known that quantum approximate optimization algorithms have limitations for certain instances to solve the MAX-CUT problem, at any constant level p. Recently, the recursive quantum approximate optimization algorithm, which is a non-local version of quantum approximate optimization algorithm, has been proposed to overcome these limitations. However, it has been shown by mostly numerical evidences that the recursive quantum approximate optimization algorithm outperforms the original quantum approximate optimization algorithm for specific instances. In this paper, we analytically prove that the recursive quantum approximate optimization algorithm is more competitive than the original one to solve the MAX-CUT problem for complete graphs with respect to the approximation ratio. [ABSTRACT FROM AUTHOR]

Data mining has reached a state that is difficult to break through, while the scale of data is growing rapidly, due to the lack of traditional computing power and limited data storage space. Efficient and accurate extraction of valuable information from massive data has become a challenge. Researchers have combined quantum computing with data mining to address this problem, hence the concept of quantum data mining has emerged. The fundamental tenets of quantum physics are adhered to for information transmission and computing operations in quantum data mining, which use the states of minuscule particles to represent and process information. Quantum data mining are based on the characteristics of quantum computing, such as superposition and entanglement, which make the ability of computational and information extraction effectively improved. The paper discusses and summarizes the relevant literature on quantum data mining in recent 3 years. After introducing relevant basic concepts of quantum computing, quantum data mining is presented in five aspects: quantum data classification, quantum data clustering, quantum dimensionality reduction, quantum association rules, quantum linear regression, and quantum causal analysis. These approaches, based on quantum computing, offer new perspectives and tools for handling complex data mining tasks. In conclusion, the development of quantum data mining is promising and crucial to overcome the difficulties associated with large-scale data mining. [ABSTRACT FROM AUTHOR]

Popular Secp256k1 and Schnorr algorithms offer strong security in current Blockchains. However, they are vulnerable to quantum attacks. To solve this problem, several quantum-resistant algorithms have been proposed. However, the performance evaluations and tangible analyses of these algorithms on current Blockchains have not been studied yet. In this context, a performance analysis of quantum-resistant algorithms on a Blockchain can provide valuable insight into the efficiency of quantum-resistant algorithms in real-world scenarios. To address this need, we prototyped and analyzed a quantum-resistant Blockchain using the Falcon algorithm. Falcon is selected because it provides smaller signature and key size compared to Crystals-Dilithium and Sphincs+. We then measured in real-time the key size, transaction signature size, and transaction verification time. The paper also discusses the potential scalability limitations of the proposed quantum-resistant Blockchain and suggests an approach to select quantum-resistant algorithms based on different Blockchain use cases. Our approach and benchmark results have implications for the future development and adoption of quantum-resistant Blockchains. [ABSTRACT FROM AUTHOR]