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For the gate becomes the Toffoli gate and calculation of the process matrix is only possible by solving the master equation for the complete qubit register.
The method first builds an approximate map (or model) of the folding energy landscape from which the population kinetics are analyzed by solving the master equation on the map.
To test this approximation we compared the mean-field predictions obtained by solving the Master equation to those obtained by the numerical integration of the deterministic version of the model for the duration of interest (i.e., up to 2009).
By solving the master equations, they obtained the steady-state probabilities and thus the potential landscape.
The data for model construction was obtained by solving the master equation instead of performing MD simulation.
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If one is faced with low laser intensities and thus low intra-cavity excitations, the solution can be obtained by solving the master-equation numerically via an excitation cut-off in the matrix representation of the ladder operators as has been shown in Section 3.
Furthermore, as shown below, in physiologically relevant regimes the fluctuation-dissipation based approximation is highly accurate and in some cases reduces to the Fano factor obtained by exactly solving the master equation.
By solving the kinetic master equation, the kinetic time for binding is obtained and shown to have a U-shape curve-dependence on the temperature.
Instead of solving the master equation, a widely used method is to carry out Monte Carlo simulations using the Gillespie algorithm [ 14].
Perhaps closer to our approach is the recent work of Lepzelter and Wang [ 13], who investigate the same biological problem by solving the reaction-diffusion master equation at steady state.
To this end we use a recently developed formalism and validate first its performance by comparing its predictions to results obtained by solving the Liouville von Neumann master equation.
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