The generative quantum eigensolver (GQE) and its application for ground state search

We introduce the generative quantum eigensolver (GQE), a novel method for applying classical generative models for quantum simulation. The GQE algorithm optimizes a classical generative model to produce quantum circuits with desired properties. Here, we develop a transformer-based implementation, which we name the generative pre-trained transformer-based (GPT) quantum eigensolver (GPT-QE), leveraging both pre-training on existing datasets and training without any prior knowledge. We demonstrate the effectiveness of training and pre-training GPT-QE in the search for ground states of electronic structure Hamiltonians. GQE strategies can extend beyond the problem of Hamiltonian simulation into other application areas of quantum computing.Comment: 16 pages, 7 figure

Knowledge is power: Quantum chemistry on novel computer architectures

In the first chapter of this thesis, a background of fundamental quantum chemistry concepts is provided. Chapter two contains an analysis of the performance and energy efficiency of various modern computer processor architectures while performing computational chemistry calculations. In chapter three, the processor architectural study is expanded to include parallel computational chemistry algorithms executed across multiple-node computer clusters. Chapter four describes a novel computational implementation of the fundamental Hartree-Fock method which significantly reduces computer memory requirements. In chapter five, a case study of quantum chemistry two-electron integral code interoperability is described. The final chapters of this work discuss applications of quantum chemistry. In chapter six, an investigation of the esterification of acetic acid on acid-functionalized silica is presented. In chapter seven, the application of ab initio molecular dynamics to study the photoisomerization and photocyclization of stilbene is discussed. Final concluding remarks are noted in chapter eight

Knowledge is power: Quantum chemistry on novel computer architectures

In the first chapter of this thesis, a background of fundamental quantum chemistry concepts is provided. Chapter two contains an analysis of the performance and energy efficiency of various modern computer processor architectures while performing computational chemistry calculations. In chapter three, the processor architectural study is expanded to include parallel computational chemistry algorithms executed across multiple-node computer clusters. Chapter four describes a novel computational implementation of the fundamental Hartree-Fock method which significantly reduces computer memory requirements. In chapter five, a case study of quantum chemistry two-electron integral code interoperability is described. The final chapters of this work discuss applications of quantum chemistry. In chapter six, an investigation of the esterification of acetic acid on acid-functionalized silica is presented. In chapter seven, the application of ab initio molecular dynamics to study the photoisomerization and photocyclization of stilbene is discussed. Final concluding remarks are noted in chapter eight

A comparison of the Bravyi-Kitaev and Jordan-Wigner transformations for the quantum simulation of quantum chemistry

The ability to perform classically intractable electronic structure calculations is often cited as one of the principal applications of quantum computing. A great deal of theoretical algorithmic development has been performed in support of this goal. Most techniques require a scheme for mapping electronic states and operations to states of and operations upon qubits. The two most commonly used techniques for this are the Jordan-Wigner transformation and the Bravyi-Kitaev transformation. However, comparisons of these schemes have previously been limited to individual small molecules. In this paper we discuss resource implications for the use of the Bravyi-Kitaev mapping scheme, specifically with regard to the number of quantum gates required for simulation. We consider both small systems which may be simulatable on near-future quantum devices, and systems sufficiently large for classical simulation to be intractable. We use 86 molecular systems to demonstrate that the use of the Bravyi-Kitaev transformation is typically at least approximately as efficient as the canonical Jordan-Wigner transformation, and results in substantially reduced gate count estimates when performing limited circuit optimisations.Comment: 46 pages, 11 figure

Modeling structural and electronic properties of nano-scale systems

Computergestütze Modellierung von organischen elektronsichen Materialien durch gezielte Untersuchung mikroskopischer Prozesse und Berechnung molekülspezifischer Materialparameter ermöglicht die effiziente Entwicklung langlebiger, effizienter Bauteile. In dieser Arbeit werden die strukturellen und elektronischen Eigenschaften organischer und metall-organischer Schichten untersucht, sowie effiziente Simulationsmethoden (weiter-)entwickelt

Quantum Computing for Molecular Biology

Molecular biology and biochemistry interpret microscopic processes in the living world in terms of molecular structures and their interactions, which are quantum mechanical by their very nature. Whereas the theoretical foundations of these interactions are very well established, the computational solution of the relevant quantum mechanical equations is very hard. However, much of molecular function in biology can be understood in terms of classical mechanics, where the interactions of electrons and nuclei have been mapped onto effective classical surrogate potentials that model the interaction of atoms or even larger entities. The simple mathematical structure of these potentials offers huge computational advantages; however, this comes at the cost that all quantum correlations and the rigorous many-particle nature of the interactions are omitted. In this work, we discuss how quantum computation may advance the practical usefulness of the quantum foundations of molecular biology by offering computational advantages for simulations of biomolecules. We not only discuss typical quantum mechanical problems of the electronic structure of biomolecules in this context, but also consider the dominating classical problems (such as protein folding and drug design) as well as data-driven approaches of bioinformatics and the degree to which they might become amenable to quantum simulation and quantum computation.Comment: 76 pages, 7 figure