Using a quantum computer to simulate fermionic systems requires fermion-to-qubit transformations.Usually,lower Pauli weight of transformations means shallower quantum circuits.Therefore,most existing transformations a...Using a quantum computer to simulate fermionic systems requires fermion-to-qubit transformations.Usually,lower Pauli weight of transformations means shallower quantum circuits.Therefore,most existing transformations aim for lower Pauli weight.However,in some cases,the circuit depth depends not only on the Pauli weight but also on the coefficients of the Hamiltonian terms.In order to characterize the circuit depth of these algorithms,we propose a new metric called weighted Pauli weight,which depends on Pauli weight and coefficients of Hamiltonian terms.To achieve smaller weighted Pauli weight,we introduce a novel transformation,Huffman-code-based ternary tree(HTT)transformation,which is built upon the classical Huffman code and tailored to different Hamiltonians.We tested various molecular Hamiltonians and the results show that the weighted Pauli weight of the HTT transformation is smaller than that of commonly used mappings.At the same time,the HTT transformation also maintains a relatively small Pauli weight.The mapping we designed reduces the circuit depth of certain Hamiltonian simulation algorithms,facilitating faster simulation of fermionic systems.展开更多
Evolutionary algorithm is applied for distillation separation sequence optimization synthesis problems with combination explosion. The binary tree data structure is used to describe the distillation separation sequenc...Evolutionary algorithm is applied for distillation separation sequence optimization synthesis problems with combination explosion. The binary tree data structure is used to describe the distillation separation sequence, and it is directly applied as the coding method. Genetic operators, which ensure to prohibit illegal filial generations completely, are designed by using the method of graph theory. The crossover operator based on a single parent or two parents is designed successfully. The example shows that the average ratio of search space from evolutionary algorithm with two-parent genetic operation is lower, whereas the rate of successful minimizations from evolutionary algorithm with single parent genetic operation is higher.展开更多
Small storage space for photographs in formal documents is increasingly necessary in today＇s needs for huge amounts of data communication and storage. Traditional compression algorithms do not sufficiently utilize th...Small storage space for photographs in formal documents is increasingly necessary in today＇s needs for huge amounts of data communication and storage. Traditional compression algorithms do not sufficiently utilize the distinctness of formal photographs. That is, the object is an image of the human head, and the background is in unicolor. Therefore, the compression is of low efficiency and the image after compression is still space-consuming. This paper presents an image compression algorithm based on object segmentation for practical high-efficiency applications. To achieve high coding efficiency, shape-adaptive discrete wavelet transforms are used to transformation arbitrarily shaped objects. The areas of the human head and its background are compressed separately to reduce the coding redundancy of the background. Two methods, lossless image contour coding based on differential chain, and modified set partitioning in hierarchical trees （SPIHT） algorithm of arbitrary shape, are discussed in detail. The results of experiments show that when bit per pixel （bpp）is equal to 0.078, peak signal-to-noise ratio （PSNR） of reconstructed photograph will exceed the standard of SPIHT by nearly 4dB.展开更多
基金supported by the National Key Research and Development Program of China(Grant No.2024YFB4504101)the National Nat-ural Science Foundation of China(Grant No.22303022)the Anhui Province Innovation Plan for Science and Technology(Grant No.202423r06050002).
文摘Using a quantum computer to simulate fermionic systems requires fermion-to-qubit transformations.Usually,lower Pauli weight of transformations means shallower quantum circuits.Therefore,most existing transformations aim for lower Pauli weight.However,in some cases,the circuit depth depends not only on the Pauli weight but also on the coefficients of the Hamiltonian terms.In order to characterize the circuit depth of these algorithms,we propose a new metric called weighted Pauli weight,which depends on Pauli weight and coefficients of Hamiltonian terms.To achieve smaller weighted Pauli weight,we introduce a novel transformation,Huffman-code-based ternary tree(HTT)transformation,which is built upon the classical Huffman code and tailored to different Hamiltonians.We tested various molecular Hamiltonians and the results show that the weighted Pauli weight of the HTT transformation is smaller than that of commonly used mappings.At the same time,the HTT transformation also maintains a relatively small Pauli weight.The mapping we designed reduces the circuit depth of certain Hamiltonian simulation algorithms,facilitating faster simulation of fermionic systems.
文摘Evolutionary algorithm is applied for distillation separation sequence optimization synthesis problems with combination explosion. The binary tree data structure is used to describe the distillation separation sequence, and it is directly applied as the coding method. Genetic operators, which ensure to prohibit illegal filial generations completely, are designed by using the method of graph theory. The crossover operator based on a single parent or two parents is designed successfully. The example shows that the average ratio of search space from evolutionary algorithm with two-parent genetic operation is lower, whereas the rate of successful minimizations from evolutionary algorithm with single parent genetic operation is higher.
基金This work was supported by National Natural Science Foundation of China (No.60372066)
文摘Small storage space for photographs in formal documents is increasingly necessary in today＇s needs for huge amounts of data communication and storage. Traditional compression algorithms do not sufficiently utilize the distinctness of formal photographs. That is, the object is an image of the human head, and the background is in unicolor. Therefore, the compression is of low efficiency and the image after compression is still space-consuming. This paper presents an image compression algorithm based on object segmentation for practical high-efficiency applications. To achieve high coding efficiency, shape-adaptive discrete wavelet transforms are used to transformation arbitrarily shaped objects. The areas of the human head and its background are compressed separately to reduce the coding redundancy of the background. Two methods, lossless image contour coding based on differential chain, and modified set partitioning in hierarchical trees （SPIHT） algorithm of arbitrary shape, are discussed in detail. The results of experiments show that when bit per pixel （bpp）is equal to 0.078, peak signal-to-noise ratio （PSNR） of reconstructed photograph will exceed the standard of SPIHT by nearly 4dB.
