The well-known Riccati differential equations play a key role in many fields,including problems in protein folding,control and stabilization,stochastic control,and cybersecurity(risk analysis and malware propaga-tion)...The well-known Riccati differential equations play a key role in many fields,including problems in protein folding,control and stabilization,stochastic control,and cybersecurity(risk analysis and malware propaga-tion).Quantum computer algorithms have the potential to implement faster approximate solutions to the Riccati equations compared with strictly classical algorithms.While systems with many qubits are still under development,there is significant interest in developing algorithms for near-term quantum computers to determine their accuracy and limitations.In this paper,we propose a hybrid quantum-classical algorithm,the Matrix Riccati Solver(MRS).This approach uses a transformation of variables to turn a set of nonlinear differential equation into a set of approximate linear differential equations(i.e.,second order non-constant coefficients)which can in turn be solved using a version of the Harrow-Hassidim-Lloyd(HHL)quantum algorithm for the case of Hermitian matrices.We implement this approach using the Qiskit language and compute near-term results using a 4 qubit IBM Q System quantum computer.Comparisons with classical results and areas for future research are discussed.展开更多
In the current scenario,data transmission over the network is a challenging task as there is a need for protecting sensitive data.Traditional encryption schemes are less sensitive and less complex thus prone to attack...In the current scenario,data transmission over the network is a challenging task as there is a need for protecting sensitive data.Traditional encryption schemes are less sensitive and less complex thus prone to attacks during transmission.It has been observed that an encryption scheme using chaotic theory is more promising due to its non-linear and unpredictable behavior.Hence,proposed a novel hybrid image encryption scheme with multi-scroll attractors and quantum chaos logistic maps(MSA-QCLM).The image data is classified as inter-bits and intra-bits which are permutated separately using multi scroll attractor&quantum logistic maps to generate random keys.To increase the encryption efficiency,a hybrid chaotic technique was performed.Experimentation is performed in a Qiskit simulation tool for various image sets.The simulation results and theoretical analysis show that the proposed method is more efficient than its classical counterpart,and its security is verified by the statistical analysis,keys sensitivity,and keyspace analysis.The Number of changing pixel rate(NPCR)&the Unified averaged changed intensity(UACI)values were observed to be 99.6%&33.4%respectively.Also,entropy oscillates from 7.9 to 7.901 for the different tested encrypted images.The proposed algorithm can resist brute force attacks well,owing to the values of information entropy near the theoretical value of 8.The proposed algorithm has also passed the NIST test(Frequency Monobit test,Run test and DFT test).展开更多
With the rapid development of quantum theory and technology in recent years,especially the emergence of some quantum cloud computing platforms,more and more researchers are not satisfied with the theoretical derivatio...With the rapid development of quantum theory and technology in recent years,especially the emergence of some quantum cloud computing platforms,more and more researchers are not satisfied with the theoretical derivation and simulation verification of quantum computation(especially quantum algorithms),experimental verification on real quantum devices has become a new trend.In this paper,three representative quantum algorithms,namely Deutsch-Jozsa,Grover,and Shor algorithms,are briefly depicted,and then their implementation circuits are presented,respectively.We program these circuits on python with QISKit to connect the remote real quantum devices(i.e.,ibmqx4,ibmqx5)on IBM Q to verify these algorithms.The experimental results not only show the feasibility of these algorithms,but also serve to evaluate the functionality of these devices.展开更多
文摘The well-known Riccati differential equations play a key role in many fields,including problems in protein folding,control and stabilization,stochastic control,and cybersecurity(risk analysis and malware propaga-tion).Quantum computer algorithms have the potential to implement faster approximate solutions to the Riccati equations compared with strictly classical algorithms.While systems with many qubits are still under development,there is significant interest in developing algorithms for near-term quantum computers to determine their accuracy and limitations.In this paper,we propose a hybrid quantum-classical algorithm,the Matrix Riccati Solver(MRS).This approach uses a transformation of variables to turn a set of nonlinear differential equation into a set of approximate linear differential equations(i.e.,second order non-constant coefficients)which can in turn be solved using a version of the Harrow-Hassidim-Lloyd(HHL)quantum algorithm for the case of Hermitian matrices.We implement this approach using the Qiskit language and compute near-term results using a 4 qubit IBM Q System quantum computer.Comparisons with classical results and areas for future research are discussed.
文摘In the current scenario,data transmission over the network is a challenging task as there is a need for protecting sensitive data.Traditional encryption schemes are less sensitive and less complex thus prone to attacks during transmission.It has been observed that an encryption scheme using chaotic theory is more promising due to its non-linear and unpredictable behavior.Hence,proposed a novel hybrid image encryption scheme with multi-scroll attractors and quantum chaos logistic maps(MSA-QCLM).The image data is classified as inter-bits and intra-bits which are permutated separately using multi scroll attractor&quantum logistic maps to generate random keys.To increase the encryption efficiency,a hybrid chaotic technique was performed.Experimentation is performed in a Qiskit simulation tool for various image sets.The simulation results and theoretical analysis show that the proposed method is more efficient than its classical counterpart,and its security is verified by the statistical analysis,keys sensitivity,and keyspace analysis.The Number of changing pixel rate(NPCR)&the Unified averaged changed intensity(UACI)values were observed to be 99.6%&33.4%respectively.Also,entropy oscillates from 7.9 to 7.901 for the different tested encrypted images.The proposed algorithm can resist brute force attacks well,owing to the values of information entropy near the theoretical value of 8.The proposed algorithm has also passed the NIST test(Frequency Monobit test,Run test and DFT test).
基金This work was supported by the Natural Science Foundation of Jiangsu Province under Grant BK20171458in part by the Natural Science Foundation of China under Grant Nos.61672290 and 61802002+2 种基金the Natural Science Foundation of Jiangsu Higher Education Institutions of China under Grant No.19KJB520028Jiangsu Graduate Scientific Research Innovation Program under Grant No.KYCX20_0978the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD).
文摘With the rapid development of quantum theory and technology in recent years,especially the emergence of some quantum cloud computing platforms,more and more researchers are not satisfied with the theoretical derivation and simulation verification of quantum computation(especially quantum algorithms),experimental verification on real quantum devices has become a new trend.In this paper,three representative quantum algorithms,namely Deutsch-Jozsa,Grover,and Shor algorithms,are briefly depicted,and then their implementation circuits are presented,respectively.We program these circuits on python with QISKit to connect the remote real quantum devices(i.e.,ibmqx4,ibmqx5)on IBM Q to verify these algorithms.The experimental results not only show the feasibility of these algorithms,but also serve to evaluate the functionality of these devices.
