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

Authors:
Toshiyuki Imamura;Takuma Kano;Susumu Yamada;Masahiko Okumura;Masahiko Machida
Affiliations:
DEPARTMENT OF COMPUTER SCIENCE, THE UNIVERSITY OF ELECTRO-COMMUNICATIONS,CHOFU CITY, TOKYO, JAPAN;JAPAN ATOMIC ENERGY AGENCY, CENTER FOR COMPUTATIONALSCIENCE AND E-SYSTEMS, 6-9-3 HIGASHI-UENO, TAITO-KU, TOKYO 110-0015, JAPAN;JAPAN ATOMIC ENERGY AGENCY, CENTER FOR COMPUTATIONALSCIENCE AND E-SYSTEMS, 6-9-3 HIGASHI-UENO, TAITO-KU, TOKYO 110-0015, JAPAN,;JAPAN ATOMIC ENERGY AGENCY, CENTER FOR COMPUTATIONALSCIENCE AND E-SYSTEMS, 6-9-3 HIGASHI-UENO, TAITO-KU, TOKYO 110-0015, JAPAN;JAPAN ATOMIC ENERGY AGENCY, CENTER FOR COMPUTATIONALSCIENCE AND E-SYSTEMS, 6-9-3 HIGASHI-UENO, TAITO-KU, TOKYO 110-0015, JAPAN
Venue:
International Journal of High Performance Computing Applications
Year:
2010

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Abstract

In order to explore quantum dynamics of coupled Josephson junctions, we develop a program solving directly the time-dependent Schr脙露dinger equation by diagonalizing the Hamiltonian matrix and obtaining its ground and multiple low-lying excitation states. The Schr脙露dinger 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 â聙聹quantum-assisted synchronizationâ聙聺 occurs with downsizing the junction plane. This is a discovery adding a quantum flavor to the classical concept â聙聹synchronizationâ聙聺.