5:15 PM - 6:45 PM
[PEM17-P08] Development of Universal Boundary Condition Operators for Differential Equation Quantum Algorithms Using Amplitude Encoding Method
In space plasmas, it is known that the kinetic behavior of the plasma often triggers macroscopic dynamics. For example, there are many space plasma phenomena that contain kinetic effects, such as magnetic reconnection, but both theoretical and observational understanding of the detailed physics has yet to be achieved. In order to simulate these phenomena, it is necessary to solve the kinetic effects of plasmas from the microscopic (micro) to the MHD (macro) scale from first principles. The "Vlasov-Maxwell equation" is responsible for this.
However, in order to perform large-scale simulations of the Vlasov-Maxwell equations with kinetic-scale resolution, time-evolving calculations of the six-dimensional distribution function are not realistic even on state-of-the-art supercomputers due to limitations in memory capacity, data storage, and computation time.
Therefore, we focused on the application of quantum computers. In a quantum computer, there is the concept of a qubit, which is based on quantum mechanical principles (superposition principle) corresponding to the classical bits of a classical computer. It allows two pieces of information to exist simultaneously within one qubit. Considering a scalable extension, n qubits can represent pieces of information. This is expected to represent and calculate a huge amount of information in parallel. What is needed to perform calculations on these qubits is a quantum algorithm. In recent years, the development of quantum algorithms has been actively undertaken in many fields such as finance, quantum chemistry, elementary particles, and fluids.
In a previous study [Higuchi et al. (2023)], a quantum algorithm for solving the Vlasov-Maxwell equation system was developed for application to space plasma simulations. They employed a method of differentiating the Vlasov-Maxwell equation system by using quantum walks. It has been suggested that it also automatically satisfies periodic boundary conditions.
However, since the original purpose of quantum computers was to compute quantum systems, the boundary conditions used in numerical calculations in our field have not been developed. In space plasma simulations, appropriate boundary conditions are required depending on the phenomena, such as Neumann and Dirichlet boundary conditions. In this study, we focused on the operators that constitute quantum walks and developed a boundary condition operator that can be used universally by applying appropriate transformations.
In this presentation, we will show the characteristics of the quantum numerical results in addition to the boundary condition operators developed in this study, and discuss the concept of a simulator that includes these boundary condition operators.
However, in order to perform large-scale simulations of the Vlasov-Maxwell equations with kinetic-scale resolution, time-evolving calculations of the six-dimensional distribution function are not realistic even on state-of-the-art supercomputers due to limitations in memory capacity, data storage, and computation time.
Therefore, we focused on the application of quantum computers. In a quantum computer, there is the concept of a qubit, which is based on quantum mechanical principles (superposition principle) corresponding to the classical bits of a classical computer. It allows two pieces of information to exist simultaneously within one qubit. Considering a scalable extension, n qubits can represent pieces of information. This is expected to represent and calculate a huge amount of information in parallel. What is needed to perform calculations on these qubits is a quantum algorithm. In recent years, the development of quantum algorithms has been actively undertaken in many fields such as finance, quantum chemistry, elementary particles, and fluids.
In a previous study [Higuchi et al. (2023)], a quantum algorithm for solving the Vlasov-Maxwell equation system was developed for application to space plasma simulations. They employed a method of differentiating the Vlasov-Maxwell equation system by using quantum walks. It has been suggested that it also automatically satisfies periodic boundary conditions.
However, since the original purpose of quantum computers was to compute quantum systems, the boundary conditions used in numerical calculations in our field have not been developed. In space plasma simulations, appropriate boundary conditions are required depending on the phenomena, such as Neumann and Dirichlet boundary conditions. In this study, we focused on the operators that constitute quantum walks and developed a boundary condition operator that can be used universally by applying appropriate transformations.
In this presentation, we will show the characteristics of the quantum numerical results in addition to the boundary condition operators developed in this study, and discuss the concept of a simulator that includes these boundary condition operators.