Disconnected Diagrams in Lattice Qcd

In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called disconnected diagrams and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements of the nucleon at two different values of the lattice spacing. Finally, we employ these algorithms to do a high-precision study of strange sigma terms in light nuclei; to our knowledge this is the first calculation of its kind from Lattice QCD

Quantum annealing for systems of polynomial equations

Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct matrix inversion or iteratively with judicious preconditioning. However, the convergence of iterative algorithms is highly variable and depends, in part, on the condition number. We present a direct method for solving general systems of polynomial equations based on quantum annealing, and we validate this method using a system of second-order polynomial equations solved on a commercially available quantum annealer. We then demonstrate applications for linear regression, and discuss in more detail the scaling behavior for general systems of linear equations with respect to problem size, condition number, and search precision. Finally, we define an iterative annealing process and demonstrate its efficacy in solving a linear system to a tolerance of $10^{-8}$.Comment: 11 pages, 4 figures. Added example for a system of quadratic equations. Supporting code is available at https://github.com/cchang5/quantum_poly_solver . This is a post-peer-review, pre-copyedit version of an article published in Scientific Reports. The final authenticated version is available online at: https://www.nature.com/articles/s41598-019-46729-

Simulating the weak death of the neutron in a femtoscale universe with near-Exascale computing

The fundamental particle theory called Quantum Chromodynamics (QCD) dictates everything about protons and neutrons, from their intrinsic properties to interactions that bind them into atomic nuclei. Quantities that cannot be fully resolved through experiment, such as the neutron lifetime (whose precise value is important for the existence of light-atomic elements that make the sun shine and life possible), may be understood through numerical solutions to QCD. We directly solve QCD using Lattice Gauge Theory and calculate nuclear observables such as neutron lifetime. We have developed an improved algorithm that exponentially decreases the time-to solution and applied it on the new CORAL supercomputers, Sierra and Summit. We use run-time autotuning to distribute GPU resources, achieving 20% performance at low node count. We also developed optimal application mapping through a job manager, which allows CPU and GPU jobs to be interleaved, yielding 15% of peak performance when deployed across large fractions of CORAL.Comment: 2018 Gordon Bell Finalist: 9 pages, 9 figures; v2: fixed 2 typos and appended acknowledgement

First lattice QCD study of the gluonic structure of light nuclei

The role of gluons in the structure of the nucleon and light nuclei is investigated using lattice quantum chromodynamics (QCD) calculations. The first moment of the unpolarized gluon distribution is studied in nuclei up to atomic number A = 3 at quark masses corresponding to pion masses of m(pi) similar to 450 and 806 MeV. Nuclear modification of this quantity defines a gluonic analogue of the EMC effect and is constrained to be less than similar to 10% in these nuclei. This is consistent with expectations from phenomenological quark distributions and the momentum sum rule. In the deuteron, the combination of gluon distributions corresponding to the b(1) structure function is found to have a small first moment compared with the corresponding momentum fraction. The first moment of the gluon transversity structure function is also investigated in the spin-1 deuteron, where a nonzero signal is observed at m(pi) similar to 806 MeV. This is the first indication of gluon contributions to nuclear structure that can not be associated with an individual nucleon

Scale setting the M\"obius Domain Wall Fermion on gradient-flowed HISQ action using the omega baryon mass and the gradient-flow scales t0t_0 and w0w_0

We report on a sub-percent scale determination using the omega baryon mass and gradient-flow methods. The calculations are performed on 22 ensembles of $N_f=2+1+1$ highly improved, rooted staggered sea-quark configurations generated by the MILC and CalLat Collaborations. The valence quark action used is M\"obius Domain-Wall fermions solved on these configurations after a gradient-flow smearing is applied with a flowtime of $t_{\rm gf}=1$ in lattice units. The ensembles span four lattice spacings in the range $0.06 \lesssim a \lesssim 0.15$ fm, six pion masses in the range $130 \lesssim m_\pi \lesssim 400$ MeV and multiple lattice volumes. On each ensemble, the gradient-flow scales $t_0/a^2$ and $w_0/a$ and the omega baryon mass $a m_\Omega$ are computed. The dimensionless product of these quantities is then extrapolated to the continuum and infinite volume limits and interpolated to the physical light, strange and charm quark mass point in the isospin limit, resulting in the determination of $\sqrt{t_0}=0.1422(14)$ fm and $w_0 = 0.1709(11)$ fm with all sources of statistical and systematic uncertainty accounted for. The dominant uncertainty in this result is the stochastic uncertainty, providing a clear path for a few-per-mille uncertainty, as recently obtained by the Budapest-Marseille-Wuppertal Collaboration.Comment: v3: Published version; v2: Added determination of t_0 as well as w_0; v1: 13 pages plus appendices. The correlation function data, mass results and analysis code accompanying this publication can be found at this github repository: https://github.com/callat-qcd/project_scale_setting_mdwf_his

Detailed analysis of excited state systematics in a lattice QCD calculation of gAg_A

Excited state contamination remains one of the most challenging sources of systematic uncertainty to control in lattice QCD calculations of nucleon matrix elements and form factors. Most lattice QCD collaborations advocate for the use of high-statistics calculations at large time separations ($t_{\rm sep}\gtrsim1$ fm) to combat the signal-to-noise degradation. In this work we demonstrate that, for the nucleon axial charge, $g_A$, the alternative strategy of utilizing a large number of relatively low-statistics calculations at short to medium time separations ($0.2\lesssim t_{\rm sep}\lesssim1$ fm), combined with a multi-state analysis, provides a more robust and economical method of quantifying and controlling the excited state systematic uncertainty, including correlated late-time fluctuations that may bias the ground state. We show that two classes of excited states largely cancel in the ratio of the three-point to two-point functions, leaving the third class, the transition matrix elements, as the dominant source of contamination. On an $m_\pi\approx310$ MeV ensemble, we observe the expected exponential suppression of excited state contamination in the Feynman-Hellmann correlation function relative to the standard three-point function; the excited states of the regular three-point function reduce to the 1% level for $t_{\rm sep} >2$ fm while, for the Feynman-Hellmann correlation function, they are suppressed to 1% at $t_{\rm sep}\approx1$ fm. Independent analyses of the three-point and Feynman-Hellmann correlators yield consistent results for the ground state. However, a combined analysis allows for a more detailed and robust understanding of the excited state contamination, improving the demonstration that the ground state parameters are stable against variations in the excited state model, the number of excited states, and the truncation of early-time or late-time numerical data.Comment: v1: 13 pages plus appendices. The correlation function data and analysis code accompanying this publication can be accessed at this github repository: https://github.com/callat-qcd/project_fh_vs_3p