A coloring of a graph is an assignment of colors to vertices such that no two neighboring vertices have the same color. The need for memory-efficient coloring algorithms is motivated by their application in computing clique partitions of graphs arising in quantum computations where the objective is to map a large set of Pauli strings into a compact set of unitaries. We present Picasso, a randomized memory-efficient iterative parallel graph coloring algorithm with theoretical sublinear space guarantees under practical assumptions. The parameters of our algorithm provide a trade-off between coloring quality and resource consumption. To assist the user, we also propose a machine learning model to predict the coloring algorithm’s parameters considering these trade-offs. We provide a sequential and parallel implementation of the proposed algorithm.We perform an experimental evaluation on a 64-core AMD CPU equipped with 512 GB of memory and an Nvidia A100 GPU with 40GB of memory. For a small dataset where existing coloring algorithms can be executed within the 512 GB memory budget, we show up to 68× memory savings. On massive datasets, we demonstrate that GPU-accelerated Picasso can process inputs with 49.5× more Pauli strings (vertex set in our graph) and 2,478× more edges than state-of-the-art parallel approaches.

Variational quantum algorithm (VQA), which is comprised of a classical optimizer and a parameterized quantum circuit, emerges as one of the most promising approaches for harvesting the power of quantum computers in the noisy intermediate scale quantum (NISQ) era. However, the deployment of VQAs on contemporary NISQ devices often faces considerable system and time-dependant noise and prohibitively slow training speeds. On the other hand, the expensive supporting resources and infrastructure make quantum computers extremely keen on high utilization.

The CCSD(T) coupled-cluster model with perturbative triples is considered a gold standard for computational modeling of the correlated behavior of electrons in molecular systems. A fundamental constraint is the relatively small global-memory capacity in GPUs compared to the main-memory capacity on host nodes, necessitating relatively smaller tile sizes for high-dimensional tensor contractions in NWChem's GPU-accelerated implementation of the CCSD(T) method. A coordinated redesign is described to address this limitation and associated data movement overheads, including a novel fused GPU kernel for a set of tensor contractions, along with inter-node communication optimization and data caching. The new implementation of GPU-accelerated CCSD(T) improves overall performance by 3.4×. Finally, we discuss the trade-offs in using this fused algorithm on current and future supercomputing platforms.

We consider an assignment problem arising in Fermionic-swap based mapping of the one-body and two-body interaction terms in simulating time evolution of a sparse second-quantized electronic structure Hamiltonian on a quantum computer. Relative efficiency of different assignment algorithms depends on the relative costs of performing a swap and computing a Hamiltonian interaction term. Under the assumption that the interaction term cost dominates the computation, we develop an iterative algorithm that uses minimum cost linear assignment (MinLA) and matching for one-body interactions, and hypergraph optimal linear arrangement (HOLA) and partial distance-2 coloring for two-body interactions, to exploit arbitrary sparsity in the Hamiltonian for efficient computation. Using a set of 122 problems from computational chemistry, we demonstrate performance improvements up to 100% relative to the state-of-the-art approach for one-body terms and up to 86% utilization for two-body terms relative to a theoretical peak utilization. To the best of our knowledge, this is the first study to exploit arbitrary sparsity in orbital interactions for efficient computation on one-dimensional qubit connectivity layouts. The proposed algorithms lay a foundation for extension to map general k-body interactions that arise in many domains onto generalized qubit connectivity layouts available in current and future quantum systems.

In the article a method of predicting contour error using artificial neural network for a bi-axial positioning system is presented. The machine consists of two linear stages with permanent magnet linear motors controlled by servo drives. The drives are controlled from a PC with real-time operating system via EtherCAT fieldbus. A randomly generated Non-Uniform Rational B-Spline (NURBS) trajectory is used to train offline a NARX-type artificial neural network for each axis. These networks allow prediction of following errors and contour errors of the motion trajectory. Experimental results are presented that validate the viability of the neural network based contour error prediction. The presented contour error predictor will be used in predictive control and velocity optimization algorithms of linear motor based CNC machines.

The four-index integral transform is a fundamental and computationally demanding calculation used in many computational chemistry suites such as NWChem. It transforms a four-dimensional tensor from one basis to another. This transformation is most efficiently implemented as a sequence of four tensor contractions that each contract a four- dimensional tensor with a two-dimensional transformation matrix. Differing degrees of permutation symmetry in the intermediate and final tensors in the sequence of contractions cause intermediate tensors to be much larger than the final tensor and limit the number of electronic states in the modeled systems.

Computational chemistry comprises one of the driving forces of High Performance Computing. In particular, many-body methods, such as Coupled Cluster methods (CC) [1] of the quantum chemistry package NWCHEM [2], are of particular interest for the applied chemistry community.

This paper presents the implementation and performance of the highly accurate CCSD(T) quantum chemistry method on the Intel®Xeon Phi coprocessor within the context of the NWChem computational chemistry package. The widespread use of highly correlated methods in electronic structure calculations is contingent upon the interplay between advances in theory and the possibility of utilizing the ever-growing computer power of emerging heterogeneous architectures. We discuss the design decisions of our implementation as well as the optimizations applied to the compute kernels and data transfers between host and coprocessor. We show the feasibility of adopting the Intel®Many Integrated Core Architecture and the Intel Xeon Phi coprocessor for developing efficient computational chemistry modeling tools. Remarkable scalability is demonstrated by benchmarks. Our solution scales up to a total of 62560 cores with the concurrent utilization of Intel®Xeon®processors and Intel Xeon Phi coprocessors.

The development of reliable tools for excited-state simulations is very important for understanding complex processes in the broad class of light harvesting systems and optoelectronic devices. Over the last years we have been developing equation of motion coupled cluster (EOMCC) methods capable of tackling these problems. In this paper we discuss the parallel performance of EOMCC codes which provide accurate description of excited-state correlation effects. Two aspects are discussed in detail: (1) a new algorithm for the iterative EOMCC methods based on improved parallel task scheduling algorithms, and (2) parallel algorithms for the non-iterative methods describing the effect of triply excited configurations. We demonstrate that the most computationally intensive non-iterative part can take advantage of 210,000 cores of the Cray XT5 system at the Oak Ridge Leadership Computing Facility (OLCF), achieving over 80% parallel efficiency. In particular, we demonstrate the importance of the computationally demanding non-iterative many-body methods in matching experimental level of accuracy for several porphyrin-based systems.

Tensor contractions are generalized multidimensional matrix multiplication operations that widely occur in quantum chemistry. Efficient execution of tensor contractions on GPUs requires tackling several challenges to be addressed, including index permutation and small dimension-sizes reducing thread block utilization. In this paper, we present our approach to automatically generate CUDA code to execute tensor contractions on GPUs, including management of data movement between CPU and GPU. GPU-enabled code is generated for the most expensive contractions in CCSD(T), a key coupled cluster method, and incorporated into NW Chem, a popular computational chemistry suite. We demonstrate speedup over a factor of 8.4 using one core per node and over 2.6 when utilizing the entire system using hybrid CPU+GPU solution with 2 GPUs and 5 cores. Finally, we analyze the implementation behavior on future GPU systems.