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In this work, calculations of the interaction of positrons with atoms, molecular, and molecular clusters are carried out. Positrons can serve as a probe to the electronic structure of a physical system, however these studies require a systematically improvable treatment of the interaction of positrons with atoms, molecular, and molecular clusters. The approach taken in this work involves both mean-field and improvable post mean-field wave function treatments of multi-component systems. These wave functions are used as trial wave functions for subsequent quantum Monte Carlo calculations. The quantum Monte Carlo calculations were carried out using QMCPACK -- an open source, scalable package that can carry out several varieties of quantum Monte Carlo calculations. The bulk of the work this summer involved improving the generation of trial wave functions including implementation of a method to generate natural orbitals from a multiparticle configuration interaction method and the modification of QMCPACK to handle multicomponent systems.
The Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. A near-optimal solution to the combinatorial optimization problem is achieved by preparing a quantum state through the optimization of quantum circuit parameters. For special instances of the MaxCut problem, we have shown that there exists effective transferability of optimal QAOA parameters. Successful transferability of parameters between different QAOA instances can be explained and predicted based on local properties of graphs, including the type of subgraphs (lightcones) from which graphs are composed, as well as the overall degree of nodes in the graph (parity). To fully exploit graph features, we apply a neural embedding framework (graph2vec) to a pool of pre-optimized graphs, allowing us to project a graph of interest into this embedded space and efficiently obtain pre-optimized parameters. The neural model learns graph structure representations for arbitrary-sized graphs, making this approach widely applicable to many different QAOA instances.
The Maximum Independent Set Problem (MIS) is a well studied combinatorial optimization problem which admits a number of quantum approaches such as Quantum Approximate Optimization Ansatz (QAOA) and Dynamic Quantum Variational Ansatz (DQVA). In this talk, we will introduce a quantum inspired multilevel framework for MIS in order to demenstrate the utility of near term quantum hardware in combinatorial optimization. This framework aims to utilize near term quantum devices for practical application in combinatorial optimization by focusing on the local application of quantum algorithms in order to construct a global solution. Results are compared to the state of the art KaMIS solver for the MIS problem.
Analysis of nuclear reactors depends on neutron transport, heat transfer, and computational fluid dynamics. These three physics are tightly coupled to each other in nuclear systems; the solution in one domain will be dependent on the solution in the other domains. Traditional methodology to analyze multiphysics systems uses codes specializing in one physics at a time, while taking the output of one code and reformatting it to be input into another iteratively. This methodology can be error prone and inefficient. Cardinal manages three codes and wraps them into the MOOSE framework as sub-applications, allowing in-memory data transfer between the solves and much more fluid iteration and geometry representation. Since each physics has different preferences for the most useful mesh, it will be of interest to adaptively refine each domain’s mesh as the problem iterates. This summer internship was spent exploring the adaptivity system in MOOSE and working on code modifications to Cardinal and OpenMC to facilitate adaptive mesh refinement simulations.