The states in quantum systems can be described as a wave function. Calculations on
tensor networks can approximate this function. As these approximations are not always
accurate, especially for tensor networks with large dimensions, symmetries can be exploited.
Integrating these in the tensors used for the network, can improve the approximation and
reduce the resources needed. One symmetry for this purpose is the U(1) group. We will focus
on the integration of this symmetry, specifically for sparse tensors. With this basis, four
elementary operations will be discussed, which are crucial for calculating tensor networks:
permutation of indices, reshaping tenor indices, multiplying matrices, and decomposing a
matrix. However, for the last one, we only cover the theory behind it. Additionally, to
the base implementations, we include approaches for improving the performance of these
methods. These include changes to the underlying algorithms or using multiple threads to
parallelize parts of the methods. As we see in the tests, most of these approaches were not
able to increase the performance of the base implementations and are rather decreasing it.
This happens most likely due to different reasons, one of the major ones being the overhead
that results from the approaches.