Feasibility of FPGA-based Computations of Transition Densities in Quantum Many-Body Systems

Abstract

This thesis presents the results from a feasibility study of implementing calculations of transition densities for quantum many-body systems on FPGA hardware. Transition densities are of interest in the field of nuclear physics as a tool when calculating expectation values for different operators. Specifically, this report focuses on transition densities for bound states of neutrons. A computational approach is studied, in which FPGAs are used to identify valid connections for one-body operators. Other computational steps are performed on a CPU. Three different algorithms that find connections are presented. These are implemented on an FPGA and evaluated with respect to hardware cost and performance. The performance is also compared to that of an existing CPU-based code, Trdens. The FPGA used to implement the proposed designs was a Xilinx Virtex 6, built into Maxeler’s MAX3 card. It was concluded that the FPGA was able to find the connections of a one-body operator in a fraction of the time used by Trdens, ran on a single CPUcore. However, the CPU-based conversion of the connections to the form in which Trdens presents them, was much more time-consuming. For FPGAs to be feasible, it is hence necessary to accelerate the CPU-based computations or include them into the FPGA-implementations. Therefore, we recommend further investigations regarding calculations of the final representation of transition densities on FPGAs, without the use of an off-FPGA computation.