High-Performance Quantum Simulation for Coupled Josephson Junctions on the Earth Simulator: a Challenge To the Schrödinger Equation On 2564 Grids

Abstract

In order to explore quantum dynamics of coupled Josephson junctions, we develop a program solving directly the time-dependent Schrödinger equation by diagonalizing the Hamiltonian matrix and obtaining its ground and multiple low-lying excitation states. The Schrödinger equation is defined on mn grids, in which m is the number of grid points discretized on a characteristic phase space of each junction and n is the number of coupled junctions. In this paper, the calculated maximum system is that m = 256 and n = 4, i.e. the number of degrees of freedom reaches 2564 (=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”.