@techreport{oai:ipsj.ixsq.nii.ac.jp:00235058,
 author = {Yuki, Sato and Ruho, Kondo and Ikko, Hamamura and Tamiya, Onodera and Naoki, Yamamoto and Yuki, Sato and Ruho, Kondo and Ikko, Hamamura and Tamiya, Onodera and Naoki, Yamamoto},
 issue = {11},
 month = {Jun},
 note = {This paper addresses the challenge of solving partial differential equations (PDEs) for large-scale classical conservative systems, a fundamental task in advancing engineering applications. Quantum computing, particularly through Hamiltonian simulation, has the potential for providing a promising solution to achieve these computations within feasible timescales. Previous efforts in Hamiltonian simulation have hinted at potential speedups but lacked clarity in implementation details. In our work, we contribute a detailed scheme for the explicit implementation of quantum circuits that simulate classical conservative systems. We focus on the construction of quantum gates that represent the time evolution by differential operators discretized by the finite difference method. Our analysis shows that the space and time complexity of our approach is exponentially lower than that of conventional classical algorithms. We also provide numerical experiments and a real-device implementation for simulating the wave equation., This paper addresses the challenge of solving partial differential equations (PDEs) for large-scale classical conservative systems, a fundamental task in advancing engineering applications. Quantum computing, particularly through Hamiltonian simulation, has the potential for providing a promising solution to achieve these computations within feasible timescales. Previous efforts in Hamiltonian simulation have hinted at potential speedups but lacked clarity in implementation details. In our work, we contribute a detailed scheme for the explicit implementation of quantum circuits that simulate classical conservative systems. We focus on the construction of quantum gates that represent the time evolution by differential operators discretized by the finite difference method. Our analysis shows that the space and time complexity of our approach is exponentially lower than that of conventional classical algorithms. We also provide numerical experiments and a real-device implementation for simulating the wave equation.},
 title = {Scalable quantum circuits for Hamiltonian simulation of classical conservative systems},
 year = {2024}
}