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

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

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

Detailed study of a transition point in the Veneziano-Wosiek model of Planar Quantum Mechanics

Following a model recently investigated by Veneziano and Wosiek we briefly introduce Planar Quantum Mechanics (PQM). Then, we present high precision numerical results in the sectors with two and three fermions. We confirm, that the transition point in the 't Hooft's coupling constant lambda in these sectors occurs at lambda = 1, as was expected.Comment: 10 pages, 8 figures, submitted to Acta Physica Polonic

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

On one-loop corrections to matching conditions of Lattice HQET including 1/m_b terms

HQET is an effective theory for QCD with N_f light quarks and a massive valence quark if the mass of the latter is much bigger than Lambda_QCD. As any effective theory, HQET is predictive only when a set of parameters has been determined through a process called matching. The non-perturbative matching procedure including 1/m_b terms, developped by the ALPHA collaboration, consists of 19 carefully chosen observables which are precisely computable in lattice QCD as well as in lattice HQET. The matching conditions are then a set of 19 equations which relate the QCD and HQET values of these observables. We present a study of one-loop corrections to two generic matching observables involving correlation function with an insertion of the A_0 operator. Our results enable us to quantify the quality of the relevant observables in view of the envisaged non-perturbative implementation of this matching procedure.Comment: 7 pages, 4 figures; presented at th 31st International Symposium on Lattice Field Theory (LATTICE2013), 29 July - 3 August 2013, Mainz, German