To get the quantitive value of abnormal biological tissues, an inverse algorithm about the Young＇s modulus based on the boundary extraction and the image registration technologies is proposed. With the known displace...To get the quantitive value of abnormal biological tissues, an inverse algorithm about the Young＇s modulus based on the boundary extraction and the image registration technologies is proposed. With the known displacements of boundary tissues and the force distribution, the Young＇s modulus is calculated by constructing the unit system and the inverse finite element method （IFEM）. Then a tough range of the modulus for the whole tissue is estimated referring the value obtained before. The improved particle swarm optimizer （PSO） method is adopted to calculate the whole Yong＇s modulus distribution. The presented algorithm overcomes some limitations in other Young＇s modulus reconstruction methods and relaxes the displacements and force boundary condition requirements. The repetitious numerical simulation shows that errors in boundary displacement are not very sensitive to the estimation of next process; a final feasible solution is obtained by the improved PSO method which is close to the theoretical values obtained during searching in an extensive range.展开更多
Quantum algorithms have been developed for efficiently solving linear algebra tasks.However,they generally require deep circuits and hence universal fault-tolerant quantum computers.In this work,we propose variational...Quantum algorithms have been developed for efficiently solving linear algebra tasks.However,they generally require deep circuits and hence universal fault-tolerant quantum computers.In this work,we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum devices.We show that the solutions of linear systems of equations and matrix–vector multiplications can be translated as the ground states of the constructed Hamiltonians.Based on the variational quantum algorithms,we introduce Hamiltonian morphing together with an adaptive ans?tz for efficiently finding the ground state,and show the solution verification.Our algorithms are especially suitable for linear algebra problems with sparse matrices,and have wide applications in machine learning and optimisation problems.The algorithm for matrix multiplications can be also used for Hamiltonian simulation and open system simulation.We evaluate the cost and effectiveness of our algorithm through numerical simulations for solving linear systems of equations.We implement the algorithm on the IBM quantum cloud device with a high solution fidelity of 99.95%.展开更多
In this context,we study three different strategies to improve the time complexity of the widely used adiabatic evolution algorithms when solving a particular class of quantum search problems where both the initial an...In this context,we study three different strategies to improve the time complexity of the widely used adiabatic evolution algorithms when solving a particular class of quantum search problems where both the initial and final Hamiltonians are one-dimensional projector Hamiltonians on the corresponding ground state.After some simple analysis,we find the time complexity improvement is always accompanied by the increase of some other "complexities" that should be considered.But this just gives the implication that more feasibilities can be achieved in adiabatic evolution based quantum algorithms over the circuit model,even though the equivalence between the two has been shown.In addition,we also give a rough comparison between these different models for the speedup of the problem.展开更多
文摘To get the quantitive value of abnormal biological tissues, an inverse algorithm about the Young＇s modulus based on the boundary extraction and the image registration technologies is proposed. With the known displacements of boundary tissues and the force distribution, the Young＇s modulus is calculated by constructing the unit system and the inverse finite element method （IFEM）. Then a tough range of the modulus for the whole tissue is estimated referring the value obtained before. The improved particle swarm optimizer （PSO） method is adopted to calculate the whole Yong＇s modulus distribution. The presented algorithm overcomes some limitations in other Young＇s modulus reconstruction methods and relaxes the displacements and force boundary condition requirements. The repetitious numerical simulation shows that errors in boundary displacement are not very sensitive to the estimation of next process; a final feasible solution is obtained by the improved PSO method which is close to the theoretical values obtained during searching in an extensive range.
基金the Engineering and Physical Sciences Research Council National Quantum Technology Hub in Networked Quantum Information Technology(EP/M013243/1)Japan Student Services Organization(JASSO)Student Exchange Support Program(Graduate Scholarship for Degree Seeking Students)+1 种基金the National Natural Science Foundation of China(U1730449)the European Quantum Technology Flagship project AQTION。
文摘Quantum algorithms have been developed for efficiently solving linear algebra tasks.However,they generally require deep circuits and hence universal fault-tolerant quantum computers.In this work,we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum devices.We show that the solutions of linear systems of equations and matrix–vector multiplications can be translated as the ground states of the constructed Hamiltonians.Based on the variational quantum algorithms,we introduce Hamiltonian morphing together with an adaptive ans?tz for efficiently finding the ground state,and show the solution verification.Our algorithms are especially suitable for linear algebra problems with sparse matrices,and have wide applications in machine learning and optimisation problems.The algorithm for matrix multiplications can be also used for Hamiltonian simulation and open system simulation.We evaluate the cost and effectiveness of our algorithm through numerical simulations for solving linear systems of equations.We implement the algorithm on the IBM quantum cloud device with a high solution fidelity of 99.95%.
基金supported by the National Natural Science Foundation of China (Grant No. 61173050)
文摘In this context,we study three different strategies to improve the time complexity of the widely used adiabatic evolution algorithms when solving a particular class of quantum search problems where both the initial and final Hamiltonians are one-dimensional projector Hamiltonians on the corresponding ground state.After some simple analysis,we find the time complexity improvement is always accompanied by the increase of some other "complexities" that should be considered.But this just gives the implication that more feasibilities can be achieved in adiabatic evolution based quantum algorithms over the circuit model,even though the equivalence between the two has been shown.In addition,we also give a rough comparison between these different models for the speedup of the problem.
