Quantum algorithms offer more enhanced computational efficiency in comparison to their classical counterparts when solving specific tasks.In this study,we implement the quantum permutation algorithm utilizing a polar ...Quantum algorithms offer more enhanced computational efficiency in comparison to their classical counterparts when solving specific tasks.In this study,we implement the quantum permutation algorithm utilizing a polar molecule within an external electric field.The selection of the molecular qutrit involves the utilization of field-dressed states generated through the pendular modes of SrO.Through the application of multi-target optimal control theory,we strategically design microwave pulses to execute logical operations,including Fourier transform,oracle U_(f)operation,and inverse Fourier transform within a three-level molecular qutrit structure.The observed high fidelity of our outcomes is intricately linked to the concept of the quantum speed limit,which quantifies the maximum speed of quantum state manipulation.Subsequently,we design the optimized pulse sequence to successfully simulate the quantum permutation algorithm on a single SrO molecule,achieving remarkable fidelity.Consequently,a quantum circuit comprising a single qutrit suffices to determine permutation parity with just a single function evaluation.Therefore,our results indicate that the optimal control theory can be well applied to the quantum computation of polar molecular systems.展开更多
This research presents,and claries the application of two permutation algorithms,based on chaotic map systems,and applied to a le of speech signals.They are the Arnold cat map-based permutation algorithm,and the Baker...This research presents,and claries the application of two permutation algorithms,based on chaotic map systems,and applied to a le of speech signals.They are the Arnold cat map-based permutation algorithm,and the Baker’s chaotic map-based permutation algorithm.Both algorithms are implemented on the same speech signal sample.Then,both the premier and the encrypted le histograms are documented and plotted.The speech signal amplitude values with time signals of the original le are recorded and plotted against the encrypted and decrypted les.Furthermore,the original le is plotted against the encrypted le,using the spectrogram frequencies of speech signals with the signal duration.These permutation algorithms are used to shufe the positions of the speech les signals’values without any changes,to produce an encrypted speech le.A comparative analysis is introduced by using some of sundry statistical and experimental analyses for the procedures of encryption and decryption,e.g.,the time of both procedures,the encrypted audio signals histogram,the correlation coefcient between specimens in the premier and encrypted signals,a test of the Spectral Distortion(SD),and the Log-Likelihood Ratio(LLR)measures.The outcomes of the different experimental and comparative studies demonstrate that the two permutation algorithms(Baker and Arnold)are sufcient for providing an efcient and reliable voice signal encryption solution.However,the Arnold’s algorithm gives better results in most cases as compared to the results of Baker’s algorithm.展开更多
Quantum algorithms provide a more efficient way to solve computational tasks than classical algorithms. We experimentally realize quantum permutation algorithm using light＇s orbital angular momentum degree of freedom...Quantum algorithms provide a more efficient way to solve computational tasks than classical algorithms. We experimentally realize quantum permutation algorithm using light＇s orbital angular momentum degree of freedom. By exploiting the spatial mode of photons, our scheme provides a more elegant way to understand the principle of quantum permutation algorithm and shows that the high dimension characteristic of light＇s orbital angular momentum may be useful in quantum algorithms. Our scheme can be extended to higher dimension by introducing more spatial modes and it paves the way to trace the source of quantum speedup.展开更多
Tradeoffs between time complexities and solution optimalities are important when selecting algorithms for an NP-hard problem in different applications. Also, the distinction between theoretical upper bound and actual ...Tradeoffs between time complexities and solution optimalities are important when selecting algorithms for an NP-hard problem in different applications. Also, the distinction between theoretical upper bound and actual solution optimality for realistic instances of an NP-hard problem is a factor in selecting algorithms in practice. We consider the problem of partitioning a sequence of n distinct numbers into minimum number of monotone （increasing or decreasing） subsequences. This problem is NP-hard and the number of monotone subsequences can reach [√2n＋1/1-1/2]in the worst case. We introduce a new algorithm, the modified version of the Yehuda-Fogel algorithm, that computes a solution of no more than [√2n＋1/1-1/2]monotone subsequences in O（n^1.5） time. Then we perform a comparative experimental study on three algorithms, a known approximation algorithm of approximation ratio 1.71 and time complexity O（n^3）, a known greedy algorithm of time complexity O（n^1.5 log n）, and our new modified Yehuda-Fogel algorithm. Our results show that the solutions computed by the greedy algorithm and the modified Yehuda-Fogel algorithm are close to that computed by the approximation algorithm even though the theoretical worst-case error bounds of these two algorithms are not proved to be within a constant time of the optimal solution. Our study indicates that for practical use the greedy algorithm and the modified Yehuda-Fogel algorithm can be good choices if the running time is a major concern.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.92265209,11174081 and 62305285the Natural Science Foundation of Chongqing under Grant No.CSTB2024NSCQ-MSX0643the Shanghai Municipal Science and Technology Major Project under Grant No.2019SHZDZX01。
文摘Quantum algorithms offer more enhanced computational efficiency in comparison to their classical counterparts when solving specific tasks.In this study,we implement the quantum permutation algorithm utilizing a polar molecule within an external electric field.The selection of the molecular qutrit involves the utilization of field-dressed states generated through the pendular modes of SrO.Through the application of multi-target optimal control theory,we strategically design microwave pulses to execute logical operations,including Fourier transform,oracle U_(f)operation,and inverse Fourier transform within a three-level molecular qutrit structure.The observed high fidelity of our outcomes is intricately linked to the concept of the quantum speed limit,which quantifies the maximum speed of quantum state manipulation.Subsequently,we design the optimized pulse sequence to successfully simulate the quantum permutation algorithm on a single SrO molecule,achieving remarkable fidelity.Consequently,a quantum circuit comprising a single qutrit suffices to determine permutation parity with just a single function evaluation.Therefore,our results indicate that the optimal control theory can be well applied to the quantum computation of polar molecular systems.
文摘This research presents,and claries the application of two permutation algorithms,based on chaotic map systems,and applied to a le of speech signals.They are the Arnold cat map-based permutation algorithm,and the Baker’s chaotic map-based permutation algorithm.Both algorithms are implemented on the same speech signal sample.Then,both the premier and the encrypted le histograms are documented and plotted.The speech signal amplitude values with time signals of the original le are recorded and plotted against the encrypted and decrypted les.Furthermore,the original le is plotted against the encrypted le,using the spectrogram frequencies of speech signals with the signal duration.These permutation algorithms are used to shufe the positions of the speech les signals’values without any changes,to produce an encrypted speech le.A comparative analysis is introduced by using some of sundry statistical and experimental analyses for the procedures of encryption and decryption,e.g.,the time of both procedures,the encrypted audio signals histogram,the correlation coefcient between specimens in the premier and encrypted signals,a test of the Spectral Distortion(SD),and the Log-Likelihood Ratio(LLR)measures.The outcomes of the different experimental and comparative studies demonstrate that the two permutation algorithms(Baker and Arnold)are sufcient for providing an efcient and reliable voice signal encryption solution.However,the Arnold’s algorithm gives better results in most cases as compared to the results of Baker’s algorithm.
基金supported by the Fundamental Research Funds for the Central Universitiesthe National Natural Science Foundation of China(Grant Nos.11374008,11374238,11374239,and 11534008)
文摘Quantum algorithms provide a more efficient way to solve computational tasks than classical algorithms. We experimentally realize quantum permutation algorithm using light＇s orbital angular momentum degree of freedom. By exploiting the spatial mode of photons, our scheme provides a more elegant way to understand the principle of quantum permutation algorithm and shows that the high dimension characteristic of light＇s orbital angular momentum may be useful in quantum algorithms. Our scheme can be extended to higher dimension by introducing more spatial modes and it paves the way to trace the source of quantum speedup.
文摘Tradeoffs between time complexities and solution optimalities are important when selecting algorithms for an NP-hard problem in different applications. Also, the distinction between theoretical upper bound and actual solution optimality for realistic instances of an NP-hard problem is a factor in selecting algorithms in practice. We consider the problem of partitioning a sequence of n distinct numbers into minimum number of monotone （increasing or decreasing） subsequences. This problem is NP-hard and the number of monotone subsequences can reach [√2n＋1/1-1/2]in the worst case. We introduce a new algorithm, the modified version of the Yehuda-Fogel algorithm, that computes a solution of no more than [√2n＋1/1-1/2]monotone subsequences in O（n^1.5） time. Then we perform a comparative experimental study on three algorithms, a known approximation algorithm of approximation ratio 1.71 and time complexity O（n^3）, a known greedy algorithm of time complexity O（n^1.5 log n）, and our new modified Yehuda-Fogel algorithm. Our results show that the solutions computed by the greedy algorithm and the modified Yehuda-Fogel algorithm are close to that computed by the approximation algorithm even though the theoretical worst-case error bounds of these two algorithms are not proved to be within a constant time of the optimal solution. Our study indicates that for practical use the greedy algorithm and the modified Yehuda-Fogel algorithm can be good choices if the running time is a major concern.
