Diagrammatic Coupled Cluster Monte Carlo

We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker--Campbell--Hausdorff expansion of the similarity transformed Hamiltonian by construction of coupled cluster diagrams on the fly. Our new approach -- diagCCMC -- allows propagation to be performed using only the connected components of the similarity-transformed Hamiltonian, greatly reducing the memory cost associated with the stochastic solution of the coupled cluster equations. We show that for perfectly local, noninteracting systems, diagCCMC is able to represent the coupled cluster wavefunction with a memory cost that scales linearly with system size. The favorable memory cost is observed with the only assumption of fixed stochastic granularity and is valid for arbitrary levels of coupled cluster theory. Significant reduction in memory cost is also shown to smoothly appear with dissociation of a finite chain of helium atoms. This approach is also shown not to break down in the presence of strong correlation through the example of a stretched nitrogen molecule. Our novel methodology moves the theoretical basis of coupled cluster Monte Carlo closer to deterministic approaches.Comment: 31 pages, 6 figure

Diagrammatic Coupled Cluster Monte Carlo.

We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker-Campbell-Hausdorff expansion of the similarity-transformed Hamiltonian by construction of coupled cluster diagrams on the fly. Our new approach-diagCCMC-allows propagation to be performed using only the connected components of the similarity-transformed Hamiltonian, greatly reducing the memory cost associated with the stochastic solution of the coupled cluster equations. We show that for perfectly local, noninteracting systems diagCCMC is able to represent the coupled cluster wavefunction with a memory cost that scales linearly with system size. The favorable memory cost is observed with the only assumption of fixed stochastic granularity and is valid for arbitrary levels of coupled cluster theory. Significant reduction in memory cost is also shown to smoothly appear with dissociation of a finite chain of helium atoms. This approach is also shown not to break down in the presence of strong correlation through the example of a stretched nitrogen molecule. Our novel methodology moves the theoretical basis of coupled cluster Monte Carlo closer to deterministic approaches.Sims Fun

Numerical evaluation of the bispectrum in multiple field inflation

We present a complete framework for numerical calculation of the power spectrum and bispectrum in canonical inflation with an arbitrary number of light or heavy fields. Our method includes all relevant effects at tree-level in the loop expansion, including (i) interference between growing and decaying modes near horizon exit; (ii) correlation and coupling between species near horizon exit and on superhorizon scales; (iii) contributions from mass terms; and (iv) all contributions from coupling to gravity. We track the evolution of each correlation function from the vacuum state through horizon exit and the superhorizon regime, with no need to match quantum and classical parts of the calculation; when integrated, our approach corresponds exactly with the tree-level Schwinger or 'in-in' formulation of quantum field theory. In this paper we give the equations necessary to evolve all two- and three-point correlation functions together with suitable initial conditions. The final formalism is suitable to compute the amplitude, shape, and scale dependence of the bispectrum in models with |fNL| of order unity or less, which are a target for future galaxy surveys such as Euclid, DESI and LSST. As an illustration we apply our framework to a number of examples, obtaining quantitatively accurate predictions for their bispectra for the first time. Two accompanying reports describe publicly-available software packages that implement the method

Development of Relativistic Electronic Structure Methods for Accurate Calculations of Molecules Containing Heavy Elements

The dissertation focuses on an efficient implementation of relativistic spin-orbit coupled-cluster methods (SO-CC) widely applicable to molecules containing heavy elements. SO-CC methods have high computational time and storage requirements with a bottleneck associated with the storage and processing of large molecular orbital (MO) integral matrices. These high computational requirements limit the application of SO-CC methods to relatively small molecules compared with their non-relativistic counterparts. Inspired by atomic orbital (AO)-based algorithms in non-relativistic methods, AO-based algorithms have been developed to enhance the computational efficiency of SO-CC methods in the framework of the exact two-component (X2C) theory, with the following advances: 1. The AO-based scheme avoids the evaluation and storage of large MO integral matrices. 2. It lowers the formal floating-point operation count of the computationally significant "ladder term" by a factor of four. 3. It allows the use of sparsity in the AO integral matrix to further reduce the storage requirements and formal operation count. This dissertation develops the formulation and implementation of the AO-based algorithms for SO-CC methods, leveraging the spin-free nature of AO two-electron integrals and sparsity in the AO integral matrix to eliminate the storage bottleneck and reduce the formal operation count. This implementation has been parallelized using shared memory (OpenMP)-based parallelization. In addition, the development of an automatic expression generation library, named AutoGen, and its application to the derivation of working equations in unitary coupled-cluster (UCC) singles and doubles-based third-order polarization propagator theory (UCC3) is discussed in the dissertation. Derivation and implementation of working equations has become a limiting factor in developing several classes of quantum chemistry methods. The number of tensor contraction expressions reaches hundreds and even thousands in many methods including the UCC-based methods. Derivation and implementation of such a large number of expressions is time-consuming and error-prone. The Python-based library developed is driven by string-based manipulation of creation and annihilation operators to bring them to normal order using Wick's theorem. Working equations can be extracted in a simple object form, allowing easy extension and integration with other software packages

W Boson Polarization Studies for Vector Boson Scattering at LHC: from Classical Approaches to Quantum Computing

The Large Hadron Collider (LHC) at the European Organization for Nuclear Research (CERN) has, in the recent years, delivered unprecedented high-energy proton-proton collisions that have been collected and studied by two multi-purpose experiments, ATLAS and CMS. In this thesis, we focus on one physics process in particular, the Vector Boson Scattering (VBS), which is one of the keys to probe the ElectroWeak sector of the Standard Model in the TeV regime and to shed light on the mechanism of ElectroWeak symmetry breaking. VBS measurement is extremely challenging, because of its low signal yields, complex final states and large backgrounds. Its understanding requires a coordinated effort of theorists and experimentalists, to explore all possible information about inclusive observables, kinematics and background isolation. The present work wants to contribute to Vector Boson Scattering studies by exploring the possibility to disentangle among W boson polarizations when analyzing a pure VBS sample. This work is organized as follows. In Chapter1, we overview the main concepts related to the Standard Model of particle physics. We introduce the VBS process from a theoretical perspective in Chapter2, underlying its role with respect to the known mechanism of ElectroWeak Symmetry Breaking. We emphasize the importance of regularizing the VBS amplitude by canceling divergences arising from longitudinally polarized vector bosons at high energy. In the same Chapter, we discuss strategies to explore how to identify the contribution of longitudinally polarized W bosons in the VBS process. We investigate the possibility to reconstruct the event kinematics and to thereby develop a technique that would efficiently discriminate between the longitudinal contribution and the rest of the participating processes in the VBS. In Chapter 3, we perform a Montecarlo generator comparison at different orders in perturbation theory, to explore the state-of-art of VBS Montecarlo programs and to provide suggestions and limits to the experimental community. In the last part of the same Chapter we provide an estimation of PDF uncertainty contribution to VBS observables. Chapter 4 introduces the phenomenological study of this work. We perform an extensive study on polarization fraction extraction and on reconstruction of the W boson reference frame. We first make use of traditional kinematic approaches, moving then to a Deep Learning strategy. Finally, in Chapter 5, we test a new technological paradigm, the Quantum Computer, to evaluate its potential in our case study and overall in the HEP sector. This work has been carried on in the framework of a PhD Executive project, in partnership between the University of Pavia and IBM Italia, and has therefore received supports from both the institutions. This work has been funded by the European Community via the COST Action VBSCan, created with the purpose of connecting all the main players involved in Vector Boson Scattering studies at hadron colliders, gathering a solid and multidisciplinary community and aiming at providing the worldwide phenomenological reference on this fundamental process

A toolchain for the automatic generation of computer codes for correlated wavefunction calculations

In this work, the automated generator environment for ORCA (ORCA‐AGE) is described. It is a powerful toolchain for the automatic implementation of wavefunction‐based quantum chemical methods. ORCA‐AGE consists of three main modules: (1) generation of “raw” equations from a second quantized Ansatz for the wavefunction, (2) factorization and optimization of equations, and (3) generation of actual computer code. We generate code for the ORCA package, making use of the powerful functionality for wavefunction‐based correlation calculations that is already present in the code. The equation generation makes use of the most elementary commutation relations and hence is extremely general. Consequently, code can be generated for single reference as well as multireference approaches and spin‐independent as well as spin‐dependent operators. The performance of the generated code is demonstrated through comparison with efficient hand‐optimized code for some well‐understood standard configuration interaction and coupled cluster methods. In general, the speed of the generated code is no more than 30% slower than the hand‐optimized code, thus allowing for routine application of canonical ab initio methods to molecules with about 500–1000 basis functions. Using the toolchain, complicated methods, especially those surpassing human ability for handling complexity, can be efficiently and reliably implemented in very short times. This enables the developer to shift the attention from debugging code to the physical content of the chosen wavefunction Ansatz. Automatic code generation also has the desirable property that any improvement in the toolchain immediately applies to all generated code