Extreme Scale Density Matrix Calculations of Coupled Quantum Systems
If a coupled quantum systems shows some level of entanglement, that system can not simply be described by a single state. They exist in mixed states. Furthermore, real quantum systems exhibit dephasing and decoherence, which requires a statistical description of the system. This is done through the density matrix formulation. Density matrices describe the system as a statistical ensemble of several pure quantum states.The time dynamics of the density matrix are governed by the Lindblad master equation, which has involves operator multiplication from both the right and left of the density matrix.
We study the time dynamics of a system consisting of quantum dots coupled to a single plasmon mode. The size of the density matrix grows quickly; a physically reasonable system of 16 quantum dots requires a matrix dimension of 50*2^16. At this size, extreme scale computing must be utilized. Aside from the novel physics applications, we are currently studying how best to treat this system, through different time stepping schemes (RK and exponential time integrator) and different parallelization algorithms.