High-performance quantum simulation for coupled Josephson junctions on the earth simulator; A Challenge to the Schrdinger equation on grids

Imamura, Toshiyuki*; Kano, Takuma*; Yamada, Susumu; Okumura, Masahiko*; Machida, Masahiko

International Journal of High Performance Computing Applications, 24(3), p.319 - 334, 2010/08

https://doi.org/10.1177/1094342009352483

In order to explore quantum dynamics of coupled Josephson junctions, we develop a program solving directly the time-dependent Schrdinger equation by diagonalizing the Hamiltonian matrix and obtaining its ground and multiple low-lying excitation states. The Schrdinger equation is defined on grids, in which is the number of grid points discretized on a characteristic phase space of each junction and is the number of coupled junctions. In this paper, the calculated maximum system is that and , i.e. the number of degrees of freedom reaches (=4,294,967,296). We examine possible effective numerical schemes and make a parallel tuning to optimize the communication on the Earth Simulator. We sustain floating-point operation performance exceeding 20% of the peak on 512 nodes (4,096 PEs). From systematic calculations, we find a new concept that "quantum-assisted synchronization" occurs with downsizing the junction plane. This is a discovery adding a quantum flavor to the classical concept "synchronization".