openGroupCode( )

Current versions developed and maintained by Brad Chase.

SDE Integrators

Computer simulations of quantum measurement require the integration of stochastic differential equations (SDE). Since such simulations are common in our research, we developed the following libraries to abstract away the details. The code is meant to integrate equations of the form

.

The C++ package is an abstract class which performs integration once a concrete class implements the coefficients and . The Matlab version provides a function which also requires the implementation of the SDE coefficient, as well as useful hooks for driving the integration via an innovations process and storing limited data about the state.

• C++ SDE Integrator, requires (and tar includes) the RandomLib random number generator library.
• Matlab SDE Integrator

Mathematica Packages

The following packages were developed to better double-check analytical calculations and are used in worksheets posted elsewhere on the site. To use, extract the contents of the tar (or place the .m file) in Mathematica's Applications directory. On OSX, this is in ~/Library/Mathematica/Applications. To use a package, launch Mathematica and type

<<PackageName`

and to see a list of provided functions type

?PackageName`*

Packages:

• Ricatti Matrix Differential Equation Solver, attempts to symbolically solve matrix differential equations of the form
• Ito Calculus Package, provides notation and Ito table rules for easily manipulating Ito differentials
• Quantum Operator Package, provides notation and functionality for manipulating quantum operator expressions, simplifying commutation relations, dealing with operators for multipartite systems and expressing the quantum filtering equation