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In-Depth Information
1. An initialization process where a set of parameters regarding the simulation
is defined (e.g., time intervals,
VX
intervals, integration method, definition
of physical parameters, etc.)
2. Generate the system equations or ME
3. Solve the ME using Ordinary Differential Equation (ODE) solvers
4. Computation of the quantum concurrence where a set of system equations
(master equation) to be solved using a specific integration method are gen-
erated and then the concurrence is computed using Wootters concurrence
[4]. Results are temporarily stored in hard disk.
5. From the results stored in hard disk, generate the surface plot using GNU-
plot
2
.
Fig. 3.
Basic flow diagram of QDsim
4 Parallelization Features
The computational complexity of the algorithm depends on several variables (e.g
the degree of freedom of the system, the number of interactions of the QD, the
numerical error of the integrator). The problem is that the complexity is not
easy to derive a priori: the number of equations to generate can be known in
a static manner; on the other hand, the number of terms and factors is only
known at runtime, and worst yet, some of the factors could be simulation-time
dependent functions. Since using the estimated worst-case execution time can be
overly optimistic, a proof-of-concept was implemented using Mathematica
3
,to
