Quantum Computation
Some of the most likely first applications of future quantum computers may be in quantum chemistry. Even with currently available quantum computers consisting of just a few qubits, it is possible to address certain simple problems, but most of the development has occurred in systems using superconducting qubits. Hempel et al. used up to four qubits encoded by trapped ions to calculate the ground-state energies of two simple molecules, H2 and LiH. They made use of a hybrid classical-quantum method called the variational quantum eigensolver, which relegates parts of the computation such as preprocessing and optimization to a classical computer.
Phys. Rev. X 8 , 031022 (2018).
Quantum Computation
Some of the most likely first applications of future quantum computers may be in quantum chemistry. Even with currently available quantum computers consisting of just a few qubits, it is possible to address certain simple problems, but most of the development has occurred in systems using superconducting qubits. Hempel et al. used up to four qubits encoded by trapped ions to calculate the ground-state energies of two simple molecules, H2 and LiH. They made use of a hybrid classical-quantum method called the variational quantum eigensolver, which relegates parts of the computation such as preprocessing and optimization to a classical computer.
Phys. Rev. X 8 , 031022 (2018).
Over the last few decades, quantum chemistry has progressed through the development of computational methods based on modern digital computers. However, these methods can hardly fulfill the exponentially-growing resource requirements when applied to large quantum systems. As pointed out by Feynman, this restriction is intrinsic to all computational models based on classical physics. Recently, the rapid advancement of trapped-ion technologies has opened new possibilities for quantum control and quantum simulations. Here, we present an efficient toolkit that exploits both the internal and motional degrees of freedom of trapped ions for solving problems in quantum chemistry, including molecular electronic structure, molecular dynamics, and vibronic coupling. We focus on applications that go beyond the capacity of classical computers, but may be realizable on state-of-the-art trapped-ion systems. These results allow us to envision a new paradigm of quantum chemistry that shifts from the current transistor to a near-future trapped-ion-based technology.
Using quantum computers to tackle problems in chemistry is one of the first and most promising fields of application for near-term available quantum computers in the noisy intermediate-scale quantum computer (NISQ) era. To present applications, we start from small examples well known in classical computing and move to open questions we—all of humanity—face in solving issues like reducing the amount of energy needed to produce fertilizers and optimizing the underlying chemical reaction. We begin with the general process of simulating chemical molecules with quantum computers. Our first goal is to use potential energy surface calculation to determine the bonding energy of H2. We then adapt the example to CO2 and the metal—organic frameworks used in direct air capture. We show the adaptions and restrictions for current quantum computer hardware with a limited number of qubits during the NISQ era. We present the Haber— Bosch process and its importance for all humanity and investigate how and in which areas quantum computing can be applied in future research. We conclude the chapter by outlining what still needs to be done in research to constructively apply quantum computing in chemistry.
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.
We present computational chemistry data for small molecules (CO, HCl, F2, NH4+, CH4, NH3, H3O+, H2O, BeH2, LiH, OH−, HF, HeH+, H2), obtained by implementing the Unitary Coupled Cluster method with Single and Double excitations (UCCSD) on a quantum computer simulator. We have used the Variational Quantum Eigensolver (VQE) algorithm to extract the ground state energies of these molecules. This energy data represents the expected ground state energy that a quantum computer will produce for the given molecules, on the STO-3G basis. Since there is a lot of interest in the implementation of UCCSD on quantum computers, we hope that our work will serve as a benchmark for future experimental implementations.
The design of new materials and chemicals derived entirely from computation has long been a goal of computational chemistry, and the governing equation whose solution would permit this dream is known. Unfortunately, the exact solution to this equation has been far too expensive and clever approximations fail in critical situations. Quantum computers offer a novel solution to this problem. In this work, we develop not only new algorithms to use quantum computers to study hard problems in chemistry, but also explore how such algorithms can help us to better understand and improve our traditional approaches.\n\nIn particular, we first introduce a new method, the variational quantum eigensolver, which is designed to maximally utilize the quantum resources available in a device to solve chemical problems. We apply this method in a real quantum photonic device in the lab to study the dissociation of the helium hydride (HeH+) molecule. We also enhance this methodology with architecture specific optimizations on ion trap computers and show how linear-scaling techniques from traditional quantum chemistry can be used to improve the outlook of similar algorithms on quantum computers.\n\nWe then show how studying quantum algorithms such as these can be used to understand and enhance the development of classical algorithms. In particular we use a tool from adiabatic quantum computation, Feynman's Clock, to develop a new discrete time variational principle and further establish a connection between real-time quantum dynamics and ground state eigenvalue problems. We use these tools to develop two novel parallel-in-time quantum algorithms that outperform competitive algorithms as well as offer new insights into the connection between the fermion sign problem of ground states and the dynamical sign problem of quantum dynamics.\n\nFinally we use insights gained in the study of quantum circuits to explore a general notion of sparsity in many-body quantum systems. In particular we use developments from the field of compressed sensing to find compact representations of ground states. As an application we study electronic systems and find solutions dramatically more compact than traditional configuration interaction expansions, offering hope to extend this methodology to challenging systems in chemical and material design.
Accurate and scalable methods for computational quantum chemistry can accelerate research and development in many fields, ranging from drug discovery to advanced material design. Solving the electronic Schrodinger equation is the core problem of computational chemistry. However, the combinatorial complexity of this problem makes it intractable to find exact solutions, except for very small systems. The idea of quantum computing originated from this computational challenge in simulating quantum-mechanics. We propose an end-to-end quantum chemistry pipeline based on the variational quantum eigensolver (VQE) algorithm and integrated with both HPC-based simulators and a trapped-ion quantum computer. Our platform orchestrates hundreds of simulation jobs on compute resources to efficiently complete a set of ab initio chemistry experiments with a wide range of parameterization. Per- and poly-fluoroalkyl substances (PFAS) are a large family of human-made chemicals that pose a major environmental and health issue globally. Our simulations includes breaking a Carbon-Fluorine bond in trifluoroacetic acid (TFA), a common PFAS chemical. This is a common pathway towards destruction and removal of PFAS. Molecules are modeled on both a quantum simulator and a trapped-ion quantum computer, specifically IonQ Aria. Using basic error mitigation techniques, the 11-qubit TFA model (56 entangling gates) on IonQ Aria yields near-quantitative results with milli-Hartree accuracy. Our novel results show the current state and future projections for quantum computing in solving the electronic structure problem, push the boundaries for the VQE algorithm and quantum computers, and facilitates development of quantum chemistry workflows.