Implementation of the conjugate gradient algorithm on FPGA devices

Results of porting parts of the Lattice Quantum Chromodynamics code to modern FPGA devices are presented. A single-node, double precision implementation of the Conjugate Gradient algorithm is used to invert numerically the Dirac-Wilson operator on a 4-dimensional grid on a Xilinx Zynq evaluation board. The code is divided into two software/hardware parts in such a way that the entire multiplication by the Dirac operator is performed in programmable logic, and the rest of the algorithm runs on the ARM cores. Optimized data blocks are used to efficiently use data movement infrastructure allowing to reach intervals of 1 clock cycle. We show that the FPGA implementation can offer a comparable performance compared to that obtained using Intel Xeon Phi KNL.Comment: Proceedings of the 36th Annual International Symposium on Lattice Field Theory - LATTICE201

Investigating the Dirac operator evaluation with FPGAs

In recent years the computational capacity of single Field Programmable Gate Arrays (FPGA) devices as well as their versatility has increased significantly. Adding to that the High Level Synthesis frameworks allowing to program such processors in a high level language like C++, makes modern FPGA devices a serious candidate as building blocks of a general purpose High Performance Computing solution. In this contribution we describe benchmarks which we performed using a Lattice QCD code, a highly compute-demanding HPC academic code for elementary particle simulations. We benchmark the performance of a single FPGA device running in two modes: using the external or embedded memory. We discuss both approaches in detail using the Xilinx U250 device and provide estimates for the necessary memory throughput and the minimal amount of resources needed to deliver optimal performance depending on the available hardware platform.Comment: 8 pages, 5 figure

Towards Lattice Quantum Chromodynamics on FPGA devices

In this paper we describe a single-node, double precision Field Programmable Gate Array (FPGA) implementation of the Conjugate Gradient algorithm in the context of Lattice Quantum Chromodynamics. As a benchmark of our proposal we invert numerically the Dirac-Wilson operator on a 4-dimensional grid on three Xilinx hardware solutions: Zynq Ultrascale+ evaluation board, the Alveo U250 accelerator and the largest device available on the market, the VU13P device. In our implementation we separate software/hardware parts in such a way that the entire multiplication by the Dirac operator is performed in hardware, and the rest of the algorithm runs on the host. We find out that the FPGA implementation can offer a performance comparable with that obtained using current CPU or Intel's many core Xeon Phi accelerators. A possible multiple node FPGA-based system is discussed and we argue that power-efficient High Performance Computing (HPC) systems can be implemented using FPGA devices only.Comment: 17 pages, 4 figure

Solutions of D=2 supersymmetric Yang-Mills quantum mechanics with SU(N) gauge group

We describe the generalization of the recently derived solutions of D=2 supersymmetric Yang-Mills quantum mechanics with SU(3) gauge group to the generic case of SU(N) gauge group. We discuss the spectra and eigensolutions in bosonic as well as fermionic sectors.Comment: 21 pages, no figure

The CLS 2+1 flavor simulations

We report on the status of large volume simulations with 2+1 dynamical fermions which are being performed by the CLS initiative. The algorithmic details include: open boundary conditions, twisted mass reweighting and RHMC, whereas the main feature of the simulation strategy is the approach to the physical point along a trajectory of constant trace of the mass matrix. We comment on the practical side of the above issues using as examples some of the newly generated ensembles, which presently cover lattice spacings between 0.05 fm and 0.11 fm and pion masses between 150 MeV and 415 MeV.Comment: 8 pages, 6 figures, talk presented at the 32nd International Symposium on Lattice Field Theory, 23-28 June, 2014, Columbia University New York, NY. appears in PoS(LATTICE2014)02

Gauge invariant plane-wave solutions in supersymmetric Yang-Mills quantum mechanics

We derive the spectra of D=2, SU(3) supersymmetric Yang-Mills quantum mechanics in all fermionic sectors. Moreover, we provide exact expressions for the corresponding eigenvectors in the sectors with none and one fermionic quantum. We also generalize our results obtained in a cut Fock space to the infinite cut-off limit.Comment: 38 pages, 1 figur

Analytic calculation of Witten index in D=2 supersymmetric Yang-Mills quantum mechanics

We propose a method for the evaluation of Witten index in D=2 supersymmetric Yang-Mills quantum mechanics. We rederive a known result for the SU(2) gauge group and generalize it to any SU(N) gauge group.Comment: 21 pages, 5 figure

Exact solutions to D=2 Supersymmetric Yang-Mills Quantum Mechanics with SU(3) gauge group

In this article we present the cut Fock space approach to the D=d+1=2, Supersymmetric Yang-Mills Quantum Mechanics (SYMQM). We start by briefly introducing the main features of the framework. We concentrate on those properties of the method which make it a convenient set up not only for numerical calculations but also for analytic computations. In the main part of the article a sample of results are discussed, namely, analytic and numerical analysis of the D=2, SYMQM systems with SU(2) and SU(3) gauge symmetry.Comment: Proceedings of the XLIX Cracow School of Theoretical Physics, 200

Eigenvalues and eigenvectors of the Laplace operator in d-dimensional cut Fock basis

We present exact expressions for the eigenvalues and eigenvectors of the d-dimensional Laplace operator in a cut Fock basis.Comment: 13 pages, 2 figure