Relief algorithm is a feature selection algorithm used in binary classification proposed by Kira and Rendell, and its computational complexity remarkable increases with both the scale of samples and the number of features. In order to reduce the complexity, a quantum feature selection algorithm based on Relief algorithm, also called quantum Relief algorithm, is proposed. In the algorithm, all features of each sample are superposed by a certain quantum state through the CMP and rotation operations, then the swap test and measurement are applied on this state to get the similarity between two samples. After that, Near-hit and Near-miss are obtained by calculating the maximal similarity, and further applied to update the feature weight vector W T to get W T ′ that determine the relevant features with the threshold τ . In order to verify our algorithm, a simulation experiment based on IBM Q with a simple example is performed. Efficiency analysis shows the computational complexity of our proposed algorithm is O(M), while the complexity of the original Relief algorithm is O(NM), where N is the number of features for each sample, and M is the size of the sample set. Obviously, our quantum Relief algorithm has superior acceleration than the classical one.
In order to solve the problem of non-ideal training sets (i.e., the less-complete or overcomplete sets) and implement one-iteration learning, a novel efficient quantum perceptron algorithm based on unitary weights is proposed, where the singular value decomposition of the total weight matrix from the training set is calculated to make the weight matrix to be unitary. The example validation of quantum gates {H, S, T, CNOT, Toffoli, Fredkin} shows that our algorithm can accurately implement arbitrary quantum gates within one iteration. The performance comparison between our algorithm and other quantum perceptron algorithms demonstrates the advantages of our algorithm in terms of applicability, accuracy, and availability. For further validating the applicability of our algorithm, a quantum composite gate which consists of several basic quantum gates is also illustrated. INDEX TERMS Quantum perceptron, unitary weight, one-iteration learning, non-ideal training set, singular value decomposition, universal quantum gates.
Cloud computing is a powerful and popular information technology paradigm that enables data service outsourcing and provides higher-level services with minimal management effort. However, it is still a key challenge to protect data privacy when a user accesses the sensitive cloud data. Privacy-preserving database query allows the user to retrieve a data item from the cloud database without revealing the information of the queried data item, meanwhile limiting user's ability to access other ones. In this study, in order to achieve the privacy preservation and reduce the communication complexity, a quantum-based database query scheme for privacy preservation in cloud environment is developed. Specifically, all the data items of the database are firstly encrypted by different keys for protecting server's privacy, and in order to guarantee the clients' privacy, the server is required to transmit all these encrypted data items to the client with the oblivious transfer strategy. Besides, two oracle operations, a modified Grover iteration, and a special offset encryption mechanism are combined together to ensure that the client can correctly query the desirable data item. Finally, performance evaluation is conducted to validate the correctness, privacy, and efficiency of our proposed scheme.
The complex systems with edge computing require a huge amount of multifeature data to extract appropriate insights for their decision making, so it is important to find a feasible feature selection method to improve the computational efficiency and save the resource consumption. In this paper, a quantum-based feature selection algorithm for the multiclassification problem, namely, QReliefF, is proposed, which can effectively reduce the complexity of algorithm and improve its computational efficiency. First, all features of each sample are encoded into a quantum state by performing operations CMP and Ry, and then the amplitude estimation is applied to calculate the similarity between any two quantum states (i.e., two samples). According to the similarities, the Grover–Long method is utilized to find the nearest k neighbor samples, and then the weight vector is updated. After a certain number of iterations through the above process, the desired features can be selected with regards to the final weight vector and the threshold τ. Compared with the classical ReliefF algorithm, our algorithm reduces the complexity of similarity calculation from O(MN) to O(M), the complexity of finding the nearest neighbor from O(M) to OM, and resource consumption from O(MN) to O(MlogN). Meanwhile, compared with the quantum Relief algorithm, our algorithm is superior in finding the nearest neighbor, reducing the complexity from O(M) to OM. Finally, in order to verify the feasibility of our algorithm, a simulation experiment based on Rigetti with a simple example is performed.
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