Search

The parallel computing power of quantum computing and the special properties of qubits provide an effective solution for image processing tasks. This paper presents a quantum image encryption algorithm based on Fisher–Yates algorithm and Logistic mapping. Firstly, the Fisher–Yates algorithm is used to generate three key sequences, one of which is used to encode the coordinate qubits of the image. Using the other two keys and the preset rules, the quantum coordinate scrambling operation is designed based on the encoded coordinate qubit, which effectively scrambles the spatial information of the plaintext image. Next, another set of key sequences is generated, one of which is used to encode the color qubits of the image. Using two other key sequences and different rules, a qubit plane scrambling operation based on coded color qubits is designed, and the color information of image is scrambled successfully. Finally, the quantum key image is generated based on Logistic mapping, and the key image is scrambled based on Fisher–Yates algorithm to improve the key complexity. The final ciphertext image is obtained by performing XOR operation between the original image and the scrambled key image. The complete quantum circuit diagram of the scheme is given in this paper. The experimental results and security analysis prove the effectiveness of the scheme, which provides a large key space and the computational complexity is only O(n). [ABSTRACT FROM AUTHOR]

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]

Since Grover developed a quantum search algorithm for unstructured data, generalizing the algorithm to structured datasets, which can be represented as graphs, has been an important research topic. Recently, Krovi et al. introduced a quantum algorithm that can find a marked vertex on any ergodic and reversible graph by using absorbing marked vertices, replacing the marked vertices with partially absorbing vertices. The algorithm was extended to finding marked vertices in any graph with multiple marked vertices using the quantum fast-forwarding technique (QFF). However, the proof of this result based on QFF does not provide much intuition about the underlying mechanism. In this paper, to obtain the underlying mechanism of the quantum search with absorbing marked vertices, we consider, as a nontrivial example, the complete bipartite graph consisting of two sets X 1 and X 2 with the marked vertices being on both vertex sets. By analytically finding the spectral information of the quantum walk, we propose an approximate optimal search parameter s o . We demonstrate that the quantum algorithm at the optimal search parameter s o shows a quadratic speedup compared to the corresponding classical search method if the number of marked vertices is smaller than the total number of vertices. Additionally, we find that the quantum search is described in terms of a two-state model for that case. [ABSTRACT FROM AUTHOR]

Quantum computing has made many important achievements in the field of cryptanalysis. However, due to the limitations of current physical system and technology, the realization of large-scale universal quantum computers is a long way off. Currently, small-scale quantum computers are easier to implement than large-scale universal quantum computers. Distributed quantum computing proposes an implementation architecture, which attempts to break down large-scale tasks into many sub-tasks distributed across multiple small-scale quantum computers. How to use small-scale quantum computers with fewer qubits and shallower quantum depths to complete large-scale tasks and improve the success rate of attacking symmetric cryptosystems is our concern. In this paper, we propose a distributed exact Simon's algorithm, apply it to achieve quantum key recovery attacks on single-permutation-based pseudorandom cryptographic schemes with classical birthday bound security, and estimate the quantum resources of quantum circuits. Furthermore, we combine distributed exact Grover's algorithm and distributed exact Simon's algorithm to achieve quantum key recovery attacks on two-permutation-based pseudorandom cryptographic schemes with classical beyond birthday bound security and estimate the corresponding quantum resources. Our results show that (1) our algorithms are exact which means that the theoretical success probability of attacking pseudorandom cryptographic schemes is 100%; (2) the depth of circuit is in polynomial time which means that the theoretical depth of attacking symmetric cryptosystems is exponentially accelerated relative to the previous results; (3) the qubits of circuit don't increase significantly. Our work is of great importance. It could lead to the rapid realization of effective quantum attacks against symmetric cryptosystems on small-scale quantum computers. [ABSTRACT FROM AUTHOR]

In the domain of quantum computing, two widely employed techniques for encoding a normalized vector of length N, denoted as { α i } , are one-hot encoding and binary encoding. The one-hot encoding state is represented as | ψ OH (N) ⟩ and can be expressed as: | ψ OH (N) ⟩ = ∑ i = 0 N - 1 α i | 0 ⟩ ⊗ N - i - 1 | 1 ⟩ | 0 ⟩ ⊗ i . On the other hand, the binary encoding state is symbolized as | ψ BI (N) ⟩ and is defined as: | ψ BI (N) ⟩ = ∑ i = 0 N - 1 α i | b i ⟩ , where b i corresponds to the binary representation of i. In this paper, we introduce a method for converting between the one-hot encoding state and the binary encoding state, utilizing the Domain Wall state as an intermediary. The Domain Wall state, denoted as | ψ DW (N) ⟩ , is defined as: | ψ DW (N) ⟩ = ∑ i = 0 N - 1 α i | 0 ⟩ ⊗ N - i - 1 | 1 ⟩ ⊗ i . Our proposed circuit achieves a depth of O (log 2 N) and a size of O(N).Kindly check and confirm that the corresponding author mail id is correctly identified. [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]