We describe a program for quantum mechanical calculations of very large hydrocarbon polymer systems. It is based on a new algorithmic approach to the quantum mechanical tight binding equations that naturally leads to a very efficient parallel implementation and that scales linearly with respect to the number of atoms. We get both very high single node performance as well as a significant parallel speedup on the SGI Origin 2000 parallel computer.
We describe a program for quantum mechanical calculations of very large hydrocarbon polymer systems. It is based on a new algorithmic approach to the quantum mechanical tight binding equations that naturally leads to a very efficient parallel implementation and that scales linearly with respect to the number of atoms. We get both very high single node performance as well as a significant parallel speedup on the SGI Origin 2000 parallel computer.
Various strategies to implement efficiently quantum Monte Carlo (QMC) simulations for large chemical systems are presented. These include: (i) the introduction of an efficient algorithm to calculate the computationally expensive Slater matrices. This novel scheme is based on the use of the highly localized character of atomic Gaussian basis functions (not the molecular orbitals as usually done), (ii) the possibility of keeping the memory footprint minimal, (iii) the important enhancement of single-core performance when efficient optimization tools are used, and (iv) the definition of a universal, dynamic, fault-tolerant, and load-balanced framework adapted to all kinds of computational platforms (massively parallel machines, clusters, or distributed grids). These strategies have been implemented in the QMC=Chem code developed at Toulouse and illustrated with numerical applications on small peptides of increasing sizes (158, 434, 1056, and 1731 electrons). Using 10-80 k computing cores of the Curie machine (GENCI-TGCC-CEA, France), QMC=Chem has been shown to be capable of running at the petascale level, thus demonstrating that for this machine a large part of the peak performance can be achieved. Implementation of large-scale QMC simulations for future exascale platforms with a comparable level of efficiency is expected to be feasible.
This thesis describes the design and implementation of an environment to allow quantum computation to be simulated on classical computers. Although it is believed that quantum computers cannot in general be efficiently simulated classically, it is nevertheless possible to simulate small but interesting systems, on the order of a few tens of quantum bits. Since the state of the art of physical implementations is less than 10 bits, simulation remains a useful tool for understanding the behavior of quantum algorithms. To create a suitable envrionment for simulation, we constructed a 32-node cluster of workstation class computers linked with a high speed (gigabit Ethernet) network. We then wrote an initial simulation environment based on parallel linear algebra libraries with a Matlab front end. These libraries operated on large matrices representing the problem being simulated. The parallel Matlab environment demonstrated a degree of parallel speedup as we added processors, but overall execution times were high, since the amount of data scaled exponentially with the size of the problem. This increased both the number of operations that had to be performed to compute the simulation, and the volume of data that had to be communicated between the nodes as they were computing. The scaling also affected memory utilization, limiting us to a maximum problem size of 14 qubits. In an attempt to increase simulation efficiency, we revisited the design of the simulation environment. Many quantum algorithms have a structure that can be described using the tensor product operator from linear algebra. We believed that a new simulation environment based on this tensor product structure would be substantially more efficient than one based on large matrices. We designed a new simulation envrionment that exploited this tensor product structure. Benchmarks that we performed on the new simulation environment confirmed that it was substantially more efficient, allowing us to perform simulations of the quantum Fourier transform and the discrete approximation to the solution of 3-SAT by adiabatic evolution up to 25 qubits in a reasonable time. Thesis Supervisor: Stephen A. Benton Title: Professor of Media Arts and Sciences
With advances in algorithms and growing computing powers, quantum Monte Carlo (QMC) methods have become a leading contender for high accuracy calculations for the electronic structure of realistic systems. The performance gain on recent HPC systems is largely driven by increasing parallelism: the number of compute cores of a SMP and the number of SMPs have been going up, as the Top500 list attests. However, the available memory as well as the communication and memory bandwidth per element has not kept pace with the increasing parallelism. This severely limits the applicability of QMC and the problem size it can handle. OpenMP/MPI hybrid programming provides applications with simple but effective solutions to overcome efficiency and scalability bottlenecks on large-scale clusters based on multi/many-core SMPs. We discuss the design and implementation of hybrid methods in QMCPACK and analyze its performance on current HPC platforms characterized by various memory and communication hierarchies.
The unique principles of quantum mechanics may one day enable computers to perform operations that would be impossible on a classical computer. Although no one knows whether it will be possible to build a large-scale, functional, and stable quantum computer, researchers can study quantum-mechanical systems and develop algorithms and circuits by simulating quantum systems in software. Performance and memory bottlenecks prevent most current quantum computer simulators from being able to simulate quantum systems that are large enough to be useful. In this thesis, we develop a matrix-free sequential quantum computer simulator to vastly improve both time and memory performance of sequential code on a single processor. Next, we distribute the matrix-free algorithm over multiple parallel processors using the Message Passing Interface in order to simulate quantum systems that are too large to reside wholly within the memory of a single processor. Finally, we simulate various quantum circuits using the Hamming high-performance computing cluster in order to conduct algorithmic analysis.
The Tight-Binding Propagation Method (TBPM) is a robust computational framework for large-scale quantum simulations with linear scaling in memory and computational time. Building upon shared-memory implementations, this study presents an MPI-accelerated batched TBPM algorithm to exploit distributed-memory high-performance computing systems through domain decomposition and cross-node parallel execution. The approach distributes both the Hamiltonian matrix and wave function states across multiple nodes, enabling memory aggregation and simultaneous utilization of computational resources throughout clusters. The maximum tractable system size is determined primarily by the number of available supercomputing nodes. The batched processing strategy transforms the computational characteristics by reducing matrix access frequency and enhancing computational intensity by a factor of 64, shifting the algorithm from memory-bound to compute-bound regimes. Comprehensive benchmarks on graphene and twisted bilayer graphene demonstrate substantial speedup and memory scalability improvements. Super-linear speedup is consistently observed across both systems, attributed to superior cache efficiency when local Hamiltonian partitions fit within the Last Level Cache, confirming the efficiency and broad applicability of this MPIbased distributed architecture for ultra-large-scale tight-binding calculations.
Graph-based electronic structure theory offers a scalable approach to study large, complex atomistic systems using distributed and hybrid computational platforms. We demonstrate the coupling of graph-based linear scaling electronic structure theory, as implemented in the Scalable Ecosystem, Driver, and Analyzer for Complex Chemistry Simulations (SEDACS), with semiempirical quantum chemistry methods as implemented in the PySEQM code, with Graphics Processing Unit (GPU) acceleration. This powerful combination enables efficient, scalable electronic structure calculations over many nodes, significantly reducing computational cost while naturally harnessing parallelism. Detailed analyses of parallelization efficiency, computational accuracy, and communication overheads are provided, highlighting an order-of-magnitude speedup for systems of up to 10,000 atoms.