Search-based Model-driven Loop Optimizations for Tensor Contractions

Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. The Tensor Contraction Engine (TCE) is a high-level program synthesis system that facilitates the generation of high-performance parallel programs from tensor contraction equations. We are developing a new software infrastructure for the TCE that is designed to allow experimentation with optimization algorithms for modern computing platforms, including for heterogeneous architectures employing general-purpose graphics processing units (GPGPUs). In this dissertation, we present improvements and extensions to the loop fusion optimization algorithm, which can be used with cost models, e.g., for minimizing memory usage or for minimizing data movement costs under a memory constraint. We show that our data structure and pruning improvements to the loop fusion algorithm result in significant performance improvements that enable complex cost models being use for large input equations. We also present an algorithm for optimizing the fused loop structure of handwritten code. It determines the regions in handwritten code that are safe to be optimized and then runs the loop fusion algorithm on the dependency graph of the code. Finally, we develop an optimization framework for generating GPGPU code consisting of loop fusion optimization with a novel cost model, tiling optimization, and layout optimization. Depending on the memory available on the GPGPU and the sizes of the tensors, our framework decides which processor (CPU or GPGPU) should perform an operation and where the result should be moved. We present extensive measurements for tuning the loop fusion algorithm, for validating our optimization framework, and for measuring the performance characteristics of GPGPUs. Our measurements demonstrate that our optimization framework outperforms existing general-purpose optimization approaches both on multi-core CPUs and on GPGPUs

Transport Coefficients from Large Deviation Functions

We describe a method for computing transport coefficients from the direct evaluation of large deviation function. This method is general, relying on only equilibrium fluctuations, and is statistically efficient, employing trajectory based importance sampling. Equilibrium fluctuations of molecular currents are characterized by their large deviation functions, which is a scaled cumulant generating function analogous to the free energy. A diffusion Monte Carlo algorithm is used to evaluate the large deviation functions, from which arbitrary transport coefficients are derivable. We find significant statistical improvement over traditional Green-Kubo based calculations. The systematic and statistical errors of this method are analyzed in the context of specific transport coefficient calculations, including the shear viscosity, interfacial friction coefficient, and thermal conductivity.Comment: 11 pages, 5 figure

Transport Coefficients from Large Deviation Functions

We describe a method for computing transport coefficients from the direct evaluation of large deviation function. This method is general, relying on only equilibrium fluctuations, and is statistically efficient, employing trajectory based importance sampling. Equilibrium fluctuations of molecular currents are characterized by their large deviation functions, which is a scaled cumulant generating function analogous to the free energy. A diffusion Monte Carlo algorithm is used to evaluate the large deviation functions, from which arbitrary transport coefficients are derivable. We find significant statistical improvement over traditional Green-Kubo based calculations. The systematic and statistical errors of this method are analyzed in the context of specific transport coefficient calculations, including the shear viscosity, interfacial friction coefficient, and thermal conductivity.Comment: 11 pages, 5 figure

Logical Abstractions for Noisy Variational Quantum Algorithm Simulation

Due to the unreliability and limited capacity of existing quantum computer prototypes, quantum circuit simulation continues to be a vital tool for validating next generation quantum computers and for studying variational quantum algorithms, which are among the leading candidates for useful quantum computation. Existing quantum circuit simulators do not address the common traits of variational algorithms, namely: 1) their ability to work with noisy qubits and operations, 2) their repeated execution of the same circuits but with different parameters, and 3) the fact that they sample from circuit final wavefunctions to drive a classical optimization routine. We present a quantum circuit simulation toolchain based on logical abstractions targeted for simulating variational algorithms. Our proposed toolchain encodes quantum amplitudes and noise probabilities in a probabilistic graphical model, and it compiles the circuits to logical formulas that support efficient repeated simulation of and sampling from quantum circuits for different parameters. Compared to state-of-the-art state vector and density matrix quantum circuit simulators, our simulation approach offers greater performance when sampling from noisy circuits with at least eight to 20 qubits and with around 12 operations on each qubit, making the approach ideal for simulating near-term variational quantum algorithms. And for simulating noise-free shallow quantum circuits with 32 qubits, our simulation approach offers a $66\times$ reduction in sampling cost versus quantum circuit simulation techniques based on tensor network contraction.Comment: ASPLOS '21, April 19-23, 2021, Virtual, US

Computational methods and software systems for dynamics and control of large space structures

Two key areas of crucial importance to the computer-based simulation of large space structures are discussed. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area involves massively parallel computers

MHV, CSW and BCFW: field theory structures in string theory amplitudes

Motivated by recent progress in calculating field theory amplitudes, we study applications of the basic ideas in these developments to the calculation of amplitudes in string theory. We consider in particular both non-Abelian and Abelian open superstring disk amplitudes in a flat space background, focusing mainly on the four-dimensional case. The basic field theory ideas under consideration split into three separate categories. In the first, we argue that the calculation of alpha'-corrections to MHV open string disk amplitudes reduces to the determination of certain classes of polynomials. This line of reasoning is then used to determine the alpha'^3-correction to the MHV amplitude for all multiplicities. A second line of attack concerns the existence of an analog of CSW rules derived from the Abelian Dirac-Born-Infeld action in four dimensions. We show explicitly that the CSW-like perturbation series of this action is surprisingly trivial: only helicity conserving amplitudes are non-zero. Last but not least, we initiate the study of BCFW on-shell recursion relations in string theory. These should appear very naturally as the UV properties of the string theory are excellent. We show that all open four-point string amplitudes in a flat background at the disk level obey BCFW recursion relations. Based on the naturalness of the proof and some explicit results for the five-point gluon amplitude, it is expected that this pattern persists for all higher point amplitudes and for the closed string.Comment: v3: corrected erroneous statement about Virasoro-Shapiro amplitude and added referenc