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M. Bernard-Schwarz, M. Gröschl:
"FPGA based Linear Algebra functionalities for an atom-cavity application";
in: "Book of Abstracts Conf. on Resonator QED", Conf. on Resonator QED, 2013, S. 88.

A classical approach for the development of control algorithms
is the so-called Hardware-in-the-Loop (HiL) concept.
The HiL simulation is used as a substitute during development
with the advantage to test and modify the control algorithm
even before any part of the real device exists. The
system of interest is a strongly coupled atom-cavity system
where the motion of a two-level atom inside the cavity is controlled.
With the use of the LabVIEW Quantum Optics Toolkit,
a simulation of the atom-cavity experiment of the setup at
the MPQ [1] has been developed. As the HiL simulation has
to react in the sub-microsecond range, as given from the timing
parameters of the real experiment, it is offloaded to the
FPGA platform. This novel application of FPGA usage leads to
new challenges of programming. On the contrary of common
FPGA applications, where the processing speed is maximized,
the focus in our application is to minimize the total latency.
Quantum physics operators correspond to matrices, therefore
the limits of complex valued mathematic and linear algebra
functions are investigated. When looking under the hood of
scientific FPGA programming, the optimized usage of Fixed-
Point data type and the efficient storage of the single matrix
elements are addressed thoroughly.