This dissertation is split into two broad topics: the study of exciton transfer in a variety of organic systems, and the classical numerical simulation of quantum algorithms for chemistry. In both parts, the effects of environmental noise played an integral role. For the latter portion, a main focus was to model the implementation of a quantum algorithm on noisy quantum hardware. For the exciton studies, environmental noise was a defining characteristic of the dynamical process being studied. In both of these research areas, advanced numerical methods were often implemented for use on parallel hardware.\nThe first excitonic system we present is the chlorosome, a large photosynthetic antennae found in some species of green sulfur bacteria, containing tens of thousands of molecules. Using a method capable of simulating massive open quantum systems, we modeled the dynamics of an exciton's migration across this unusual supramolecular object. The chlorosome's unique concentric-roll structure leads to some anomalous effects with respect to initial conditions, and the study is a demonstration that these numerical methods can be directly applied to other very large excitonic simulations.\nIn a theoretical-experimental effort, our next system is a rationally designed DNA-based excitonic system. We designed a coherent "building block'' in which we demonstrated that an exciton can delocalize across multiple pseudoisocyanine molecules, which are non-covalently attached to the DNA backbone. With a combination of computational and experimental evidence, we show that these building blocks can be used to create complex DNA structures with somewhat tunable excitonic properties.\nIn the final excitonics project discussed in this dissertation, we designed a novel ``exciton gate.'' The design is similar in principle to a traditional transistor, and is the first excitonic transistor that can be activated by external light or via an auxiliary flow of excitons. This concept provides a method for a user to regulate the magnitude and direction of excitonic current in a chromophoric system. We show how to overcome the two potential challenges: short-lived second excited states and errors in the precision of orienting molecules relative to each other. Additionally, we show how a universal set of binary logic gates can be constructed, leading to universal classical computation. This new invention may lead to new developments in bioimaging, complex directed photocatalyis, phototherapeutics, and/or chemical sensing.\nIn the second portion of this dissertation, we developed two parallel software packages for the simulation of quantum algorithms. Such simulation packages are essential for the numerical study of quantum algorithms, since a viable large-scale quantum computer has not yet been built. The first package is called the Quantum High-Performance Software Testing Environment (qHiPSTER), which simulates the full Hilbert space of the quantum circuit's state. We simulated 40 qubits, which was the largest simulation of its kind at the time.\nThe second quantum computation software package, the Quantum TensOR Contraction Handler (qTorch), implements a tensor network contraction algorithm. Using the Quantum Approximate Optimization Algorithm (QAOA)/Max-Cut and the Hubbard model as test cases, we found heuristic trends that help a user determine which circuits will benefit most from a tensor network simulation approach.\nFinally, we investigated the effects of noise on chemical state preparation in quantum algorithms. Chemical state preparation is necessary for both of the main quantum algorithmic approaches to chemistry: the variational quantum eigensolver and the quantum phase estimation algorithm. Trends were elucidated with respect to mapping types (Jordan-Wigner versus Bravyi-Kitaev), noise types, and chemical properties.\nWe end with a short discussion of the future of rational excitonic design and classical simulation of quantum phenomena.
This dissertation is split into two broad topics: the study of exciton transfer in a variety of organic systems, and the classical numerical simulation of quantum algorithms for chemistry. In both parts, the effects of environmental noise played an integral role. For the latter portion, a main focus was to model the implementation of a quantum algorithm on noisy quantum hardware. For the exciton studies, environmental noise was a defining characteristic of the dynamical process being studied. In both of these research areas, advanced numerical methods were often implemented for use on parallel hardware.\nThe first excitonic system we present is the chlorosome, a large photosynthetic antennae found in some species of green sulfur bacteria, containing tens of thousands of molecules. Using a method capable of simulating massive open quantum systems, we modeled the dynamics of an exciton's migration across this unusual supramolecular object. The chlorosome's unique concentric-roll structure leads to some anomalous effects with respect to initial conditions, and the study is a demonstration that these numerical methods can be directly applied to other very large excitonic simulations.\nIn a theoretical-experimental effort, our next system is a rationally designed DNA-based excitonic system. We designed a coherent "building block'' in which we demonstrated that an exciton can delocalize across multiple pseudoisocyanine molecules, which are non-covalently attached to the DNA backbone. With a combination of computational and experimental evidence, we show that these building blocks can be used to create complex DNA structures with somewhat tunable excitonic properties.\nIn the final excitonics project discussed in this dissertation, we designed a novel ``exciton gate.'' The design is similar in principle to a traditional transistor, and is the first excitonic transistor that can be activated by external light or via an auxiliary flow of excitons. This concept provides a method for a user to regulate the magnitude and direction of excitonic current in a chromophoric system. We show how to overcome the two potential challenges: short-lived second excited states and errors in the precision of orienting molecules relative to each other. Additionally, we show how a universal set of binary logic gates can be constructed, leading to universal classical computation. This new invention may lead to new developments in bioimaging, complex directed photocatalyis, phototherapeutics, and/or chemical sensing.\nIn the second portion of this dissertation, we developed two parallel software packages for the simulation of quantum algorithms. Such simulation packages are essential for the numerical study of quantum algorithms, since a viable large-scale quantum computer has not yet been built. The first package is called the Quantum High-Performance Software Testing Environment (qHiPSTER), which simulates the full Hilbert space of the quantum circuit's state. We simulated 40 qubits, which was the largest simulation of its kind at the time.\nThe second quantum computation software package, the Quantum TensOR Contraction Handler (qTorch), implements a tensor network contraction algorithm. Using the Quantum Approximate Optimization Algorithm (QAOA)/Max-Cut and the Hubbard model as test cases, we found heuristic trends that help a user determine which circuits will benefit most from a tensor network simulation approach.\nFinally, we investigated the effects of noise on chemical state preparation in quantum algorithms. Chemical state preparation is necessary for both of the main quantum algorithmic approaches to chemistry: the variational quantum eigensolver and the quantum phase estimation algorithm. Trends were elucidated with respect to mapping types (Jordan-Wigner versus Bravyi-Kitaev), noise types, and chemical properties.\nWe end with a short discussion of the future of rational excitonic design and classical simulation of quantum phenomena.
Applications of the concepts of quantum information theory are usually related to the powerful and counter-intuitive quantum mechanical effects of superposition, interference and entanglement. In this thesis, I examine the role of coherence and entanglement in complex chemical systems. The research has focused mainly on two related projects: The first project is developing a theoretical model to explain the recent ultrafast experiments on excitonic migration in photosynthetic complexes that show long-lived coherence of the order of hundreds of femtoseconds and the second project developing the Grover algorithm for global optimization of complex systems. The first part can be divided into two sections. The first section is investigating the theoretical frame about the transfer of electronic excitation energy through the Fenna-Matthews-Olson (FMO) pigment-protein complex. The new developed modified scaled hierarchical equation of motion (HEOM) approach is employed for simulating the open quantum system. The second section is investigating the evolution of entanglement in the FMO complex based on the simulation result via scaled HEOM approach. We examine the role of multipartite entanglement in the FMO complex by direct computation of the convex roof optimization for a number of different measures, including pairwise, triplet, quadruple and quintuple sites entanglement. Our results support the hypothesis that multipartite entanglement is maximum primary along the two distinct electronic energy transfer pathways. The second part of this thesis can be separated into two sections. The first section demonstrated that a modified Grover's quantum algorithm can be applied to real problems of finding a global minimum using modest numbers of quantum bits. Calculations of the global minimum of simple test functions and Lennard-Jones clusters have been carried out on a quantum computer simulator using a modified Grover's algorithm. The second section is implementing the basic quantum logical gates upon arrays of trapped ultracold polar molecules as qubits for the quantum computer. Utilized herein is the Multi-Target Optimal Control Theory (MTOCT) as a means of manipulating the initial-to-target transition probability via external laser field. The detailed calculation is applied for the SrO molecule, an ideal candidate in proposed quantum computers using arrays of trapped ultra-cold polar molecules.
The 20th century saw the first revolution of quantum mechanics, setting the rules for our understanding of light, matter, and their interaction. The 21st century is focused on using these quantum mechanical laws to develop technologies which allows us to solve challenging practical problems. One of the directions is the use quantum devices which promise to surpass the best computers and best known classical algorithms for solving certain tasks. Crucial to the design of realistic devices and technologies is to account for the open nature of quantum systems and to cope with their interactions with the environment. In the first part of this dissertation, we show how to tackle classical optimization problems of interest in the physical sciences within one of these quantum computing paradigms, known as quantum annealing (QA). We present the largest implementation of QA on a biophysical problem (six different experiments with up to 81 superconducting quantum bits). Although the cases presented here can be solved on a classical computer, we present the first implementation of lattice protein folding on a quantum device under the Miyazawa-Jernigan model. This is the first step towards studying optimization problems in biophysics and statistical mechanics using quantum devices. In the second part of this dissertation, we focus on the problem of excitonic energy transfer. We provide an intuitive platform for engineering exciton transfer dynamics and we show that careful consideration of the properties of the environment leads to opportunities to engineer the transfer of an exciton. Since excitons in nanostructures are proposed for use in quantum information processing and artificial photosynthetic designs, our approach paves the way for engineering a wide range of desired exciton dy- namics. Finally, we develop the theory for a two-dimensional electronic spectroscopic technique based on fluorescence (2DFS) and challenge previous theoretical results claiming its equivalence to the two-dimensional photon echo (2DPE) technique which is based on polarization. Experimental realization of this technique confirms our the- oretical predictions. The new technique is more sensitive than 2DPE as a tool for conformational determination of excitonically coupled chromophores and o↵ers the possibility of applying two-dimensional electronic spectroscopy to single-molecules.
Determining properties of molecules and materials is one of the premier applications of quantum computing. A major question in the thesis is: how might we use long- and near-term quantum computers to solve problems of chemical interest? First, we give an overview of the standard model in electronic structure theory. Electronic structure methods have been improved significantly in the last decades; however, it is still a non-trivial task to fit experimental results for complex molecular systems. Second, we introduce quantum computation and quantum algorithms as an alternative device to solve the electronic structure problem. In the remaining part of the thesis, we describe the research projects. The thesis covers two (rather different) research directions: software and hardware projects. For the software part, we contribute with two new algorithms: Phase-Estimation Interval Target Energy Readout (PHILTER) and Recursive Variational Series Estimation (RVSE), where both are designed to be run on a quantum digital computer and extract materials and molecular properties. The PHILTER algorithm is a modification of the Quantum Phase Estimation and is designed to compute excited state energies within a target energy-interval for cases where good approximations for the states in the target energy-interval are either unknown or hard to prepare. For the RVSE algorithm, we pose the question: how might we use imperfect near-term quantum computers to solve problems of practical value? In this work, we introduce a method to compute expectation values of general functions of a Hamiltonian with respect to an input state using low depth quantum circuits suitable for noisy intermediate-scale quantum computers. For the hardware part, we propose a new chemical quantum computer by using molecular electronics as a basis for quantum computing. In this work, we pose the question: can scattering of electrons in molecules produce quantum gates? We construct one-qubit gates using one-electron scattering in molecules, and two-qubit controlled-phase gates using electron-electron scattering along metallic leads. We show initial applications of the framework by illustrating one-qubit gates using the molecular electronic structure of molecular hydrogen as a baseline model.
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of optimization, material science, chemistry, and biology. Thus, the realization of large-scale, reliable quantum-computers will likely have a significant impact on the world. For this reason, the focus of this dissertation is on the development of quantum-computing applications and robust, scalable quantum-architectures. I begin by presenting an overview of the language of quantum computation. I then, in joint work with Ojas Parekh, analyze the performance of the quantum approximate optimization algorithm (QAOA) on a graph problem called Max Cut. Next, I present a new stabilizer simulation algorithm that gives improved runtime performance for topological stabilizer codes. After that, in joint work with Andrew Landahl, I present a new set of procedures for performing logical operations called "color-code lattice-surgery." Finally, I describe a software package I developed for studying, developing, and evaluating quantum error-correcting codes under realistic noise.
The advancements in classical computational components such as CPUs and GPUs have had a reverberating impact on the democratization of computational power available, with the field of computational chemistry reaping significant benefits from the propulsion of the limits of systems studied. The accurate prediction of chemical properties and reaction dynamics through computational simulation is now a centerpiece of modern chemical research, significantly accelerating discoveries research areas of materials science and drug development, as well as industrially relevant processes such as the emission of aldehydes from soft foams, flame retardants and pyrolysis and the carbonylation of epoxides. These achievements of computational chemistry still are overshadowed in the face of fundamental bottlenecks where classical methods remain constrained by the exponential scaling when treating large and/or strongly correlated quantum many-body systems. This innate computational complexity often constitutes chemically accurate calculations based on first principles impractical, or plain impossible, for systems beyond modest sizes. Quantum computing offers a potential pathway around these limitations, originally formally formulated by David Deutsch as a tool for simulating quantum systems, with the first quantum algorithms indicating speed-ups compared to classical counterparts arising from Peter Shor and Lov Grover for the prime factorization of an integer number and unstructured search respectively. Relying on fundamental theorems by Claude Shannon, it has been demonstrated that through the use of error-correcting codes fault-tolerant quantum computers are able to safeguard information against noise and decoherence, strongly indicating towards exponential speedups in solving central computational chemistry problems, such as determining ground state energies or reaction pathways of chemical systems. Substantial strides in experimental quantum computing over the past decade, including proof-of-principle demonstrations of quantum error correction, mean to bring full-scale fault-tolerant quantum computing within the grasp of humanity. The breakthroughs needed to attain scalable, error-corrected quantum computation with capabilities exceeding those of classical methods in real-world scenarios is likely still some years away. While striving to address the engineering challenges standing in the way of achieving fault tolerant quantum computing, substantial effort has been focused toward developing and benchmarking hybrid algorithms tailored for the Noisy Intermediate- Scale Quantum (NISQ) devices, available now to researchers. These hybrid quantum-classical algorithms, with the most notable being the Variational Quantum Eigensolver (VQE), allow the probing of quantum computing’s utility in computational chemistry even in the face of significant hardware noise and limited coherence times. The work presented in this thesis introduces several key additions the VQE framework, geared especially towards to NISQ hardware, where the mindful use of available resources is imperative. First, the implementation of the Conjugate Model Search optimizer is described, an optimization method that integrates simple models that are surrogate to the original function, combined with conjugate gradient optimization to navigate effectively parameter landscapes typical of variational algorithms, prone to noise. Second, this thesis contains the proposal and extensive study of a hyperparameter tuning procedure employing genetic algorithms, allowing for comprehensive simulation benchmarks that augment the robustness and efficiency of VQE implementations with respect to convergence time through real wall-time models of quantum processors. Continuing, a bridge is presented between quantum simulation and quantum chemistry, through qubit-to-fermion mappings of existing quantum gates, further enabling the direct and accurate modeling of chemical systems on trapped atom quantum hardware with the added arsenal provided by techniques designed for qubit architectures. Additionally, experimental data contained in this thesis include detailed benchmarking data collected from state-of-the-art trapped ion quantum processors available at the Johannes Gutenberg Universität Mainz, demonstrating the actual viability and performance of various methodologies for extracting results. Lastly, the state of VQE is examined, as it served as a springboard for a plethora of advancements in the development of quantum computing hardware, as well as the direction the field of simulation of computational quantum chemistry via quantum devices is headed towards in the coming years.
Quantum computers have the potential to simulate chemical systems beyond the capability of classical computers. Recent developments in hybrid quantum-classical approaches enable the determinations of the ground or low energy states of molecular systems. Here, we extend near-term quantum simulations of chemistry to time-dependent processes by simulating energy transfer in organic semiconducting molecules. We developed a multiscale modeling workflow that combines conventional molecular dynamics and quantum chemistry simulations with hybrid variational quantum algorithm to compute the exciton dynamics in both the single excitation subspace (i.e., Frenkel Hamiltonian) and the full-Hilbert space (i.e., multiexciton) regimes. Our numerical examples demonstrate the feasibility of our approach, and simulations on IBM Q devices capture the qualitative behaviors of exciton dynamics, but with considerable errors. We present an error mitigation technique that combines experimental results from the variational and Trotter algorithms, and obtain significantly improved quantum dynamics. Our approach opens up new opportunities for modeling quantum dynamics in chemical, biological, and material systems with quantum computers.