I have a HPC (High Performance Computing) cluster with NVIDIA GPU and Xeon CPU partitions.
Is this simulator list complete?
Which do you recommended to use on a HPC cluster?
Will it increase the performance (it has 512GB of memory).
You will find on this website most of them (not commercial ones I think). The choice is all yours and you have to get to know the tools depending on what kind of simulation you want to do. For example if you are going to work on universal quantum computing, write algorithms from scratch or using already available implementations
Quantum++ seems to be a nice library with the use of openMP so that could be something suited for a HPC cluster. With GPUs, look for something integrating openCL like qRack or QCGPU For toolkits, Forest, Qiskit and Microsoft quantum developmenent kit based on Q# would be good candidates to look at.