A subset of the WP Core Tensor Network QCFD Set: Deliverable 6.1., in relation to the European Union's Horizon Europe research and innovation program (HORIZON-CL4-2021-DIGITAL-EMERGING-02-10) under grant agreement No. 101080085 QCFD (https://doi.org/10.3030/101080085). The dataset covers the computation of small academic examples, namely the Heat equation and the Burgers equation. Simulations for different quantum computing platforms under different noise models are provided, paving the way for future demonstrations