Session N03: Electronic Structure in Open Science III

Reduced Scaling Electronic Structure Methods in CFOUR: Theory, Implementation, and Open-Source Software Components

Wavefunction methods such as coupled-cluster and many-body perturbation methods provide accurate electronic properties but suffer from steep polynomial scaling. Cholesky decomposition/resolution-of-the-identity, the canonical polyadic decomposition, rank-reduced coupled cluster, and tensor hypercontraction are some examples of successful approaches which reduce the order of polynomial scaling without losing significant accuracy. Our group has been particularly working towards implementing higher-order rank-reduced as well as grid-based least-squares tensor hypercontraction electronic structure methods within the CFOUR program system. An effective implementation of such methods relies on many complex and inter-related software components such as generation and manipulation of molecular grids, rapid generation of electron repulsion integrals (especially on accelerators), as well as tensor contraction, hyper-contraction, and related linear algebra operations in a variety of precisions and mathematical domains. In this talk we provide an overview of the methods themselves, their implementation in CFOUR, and the reusable and open-source software components which we have developed.   

Block2: an open-source library that extends the boundary of the application of ab initio density matrix renormalization group methods

In this talk I will summarize our recent efforts on the development of an open-source ab initio density matrix renormalization group (DMRG) implementation called block2, which is focused on the easy combination of the highly accurate and scalable DMRG methods with other electronic structure methods such as CCSD, DMET, DMFT, MRCI, and MRPT. The application of this code ranges from high dimensional Heisenberg and Hubbard model simulations, transport property of single impurity Andersen model, and twisted bilayer graphene models, to ab initio simulations for chromium dimer, iron-sulfur catalytic cluster, Kondo problem, and high temperature superconductivity. We found that the connection among different theories is the key to making the expensive ab initio DMRG a unique and practical tool for understanding challenging real-world problems.   

SEAMM, an open-source simulation environment for molecular and atomistic modeling

The move towards open science has been gaining momentum over the last couple decades, pushed in part by government mandates. The importance of open source, open data, and open methods is increasingly recognized. However, a natural consequence of funding models and the focus in academia on new science is that much of the attention has been on new and better methods for solving fundamental problems; on the importance of open source for developers and advanced users to examine and understand the algorithms and science; and in stretching the limits of leading-edge computing to solve massive problems. There has been less focus on the usability of the tools; on getting the newly developed tools into the hands of the broader community, including those in other domains, and ensuring that they can use them productively; and on interoperability, which allows users to choose the best tool for their problem and to combine multiple tools to tackle challenging, often multiscale, problems in their domain.

This talk will present SEAMM – a Simulation Environment for Atomistic and Molecular Modeling – which is an open-source environment for CMS simulations with an emphasis on ease-of-use, productivity, interoperability, reproducibility, and replicability.  SEAMM uses graphical flowcharts for expressing workflows, with a graphical user interfaces (GUIs) for all components, promoting both ease-of-use and interoperability between components. This is certainly a challenging task, particularly since SEAMM covers both of the M’s in CMS: computational molecular and materials science. This talk will outline the challenges and approaches to handling them so that SEAMM can be maintained and expanded as science progresses over the next 20 years or more.

    

Low-depth VQE approach to quantum chemistry on a quantum computer by combining exact UCC factors with Taylor series expansions

The unitary coupled cluster (UCC) approximation is one of the more promising wave function ansätzes for electronic structure calculations on quantum computers via the variational quantum eigensolver algorithm. However, for large systems with many orbitals, the required number of UCC factors still leads to very deep quantum circuits, which can be challenging to implement. Based on the observation that most UCC amplitudes are small for both weakly correlated and strongly correlated molecules, we devise an algorithm that employs a Taylor expansion in the small amplitudes, trading off circuit depth for extra measurements. Strong correlations can be taken into account by performing the expansion about a small set of UCC factors, which are treated exactly. Near equilibrium, the Taylor series expansion often works well without the need to include any exact factors; as the molecule is stretched and correlations increase, we find only a small number of factors need to be treated exactly. In this talk, we will provide a progress report on how we are implementing this strategy.    

Relativistic Quantum Chemistry workflow in PySCF and Dice

PySCF (available at https://github.com/pyscf/pyscf) is an electronic structure package which has the capability to treat 4-component, 2-component as well as scalar relativistic Hamiltonians. With a recently implemented X2CAMF code (available at https://github.com/Warlocat/x2camf.) and its interface to PySCF, PySCF has obtained the ability to evaluate the spin-orbit coupling effects with both low cost and high accuracy. Various standard quantum chemistry methods including MP2, CCSD, EOMCC and TDDFT have been extended to treat the 2c Hamiltonian within PySCF to treat spin-orbit coupling.

Dice (available at https://github.com/sanshar/Dice) is an electronic structure package with an emphasis on stochastic electronic structure methods. Semistochastic Heat-bath Configuration Interaction (SHCI), stochastic variance of N-electron Valence state Perturbation Theory (NEVPT), various quantum Monte Carlo (QMC) methods including Variational Monte Carlo (VMC), Auxiliary-field Quantum Monte Carlo (AFQMC), Green's Function Monte Carlo (GFMF) and Full-Configuration Interaction Quantum Monte Carlo (FCIQMC) are all implemented in the package and the entire workflow is closely related with PySCF. Among these methods, SHCI and AFQMC have been extended to treat relativistic Hamiltonians. One can use SHCI handle over 100 spinors which is close to the relativistic implementation of MRCI at a near FCI quatlity. With AFQMC, correlating hundreds of spinors has also become possible. With selected CI wave function as a trial, the systematic bias in phaseless AFQMC is further reduced and can produce results at near FCI quality with an error at sub-millihartree scale.

PySCF in conjunction with Dice have provided a new toolset to the relativistic community to study more challenging systems with both standard methods and these emerging stochastic methods.

    

Unitary Coupled Cluster State Preparation using a Sparse Wavefunction Circuit Solver

The variational quantum eigenvalue solver (VQE) using the unitary coupled cluster (UCC) wave function ansatz is a powerful hybrid quantum-classical approach that can employ near-term quantum hardware for computing ground state electronic energies for molecular systems. Unfortunately, even for small molecules, the number of variational parameters and qubits required to minimize the electronic energy is beyond the reach of current quantum computers except for small basis sets. For example, a circuit for C₂ using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over  determinants. Here, we propose a new paradigm for state preparation where we explore how much of the optimization can be approximately prepared with classical computers to reduce the number of optimization steps performed using a quantum device. By adapting a recent algorithm for the factorized form of the UCC ansatz [J. Chem. Theory Comput. 2021, 17, 841-847] that allows for efficient UCC optimizations on classical hardware, we can study molecular electronic structure problems employing the UCC ansatz with up to 64 qubits. In this presentation, we will present results using our approach and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.

    

The XtalOpt Evolutionary Algorithm for Crystal Structure Prediction

The past decade has witnessed tremendous advances in first principles calculations, speed-ups in computer hardware, and improvements in algorithms for a priori crystal structure prediction (CSP). These developments have made it possible to predict, without any experimental information, the structure of a crystal given only its composition, opening the door to a new era where materials can be designed rationally prior to their experimental synthesis.

In this contribution we outline the XtalOpt evolutionary algorithm (EA) that has been developed for finding the global minimum structure, and important local minima without experimental information [1-3]. XtalOpt is published under open-source licenses, and the EA searches can be analyzed via the Avogadro chemical editor and visualizer. We describe new algorithmic developments that have made it possible to predict the structures of ever-more complex crystalline lattices. Benchmark tests, which clearly illustrate how the new developments improve the success rate and accelerate the discovery of the global minimum structure, are performed. We describe how XtalOpt has been employed to predict novel ternary hydrides that have the propensity for high-temperature superconductivity under pressure, and superhard materials.