We explore how the fundamental problems in quantum molecular dynamics can be modeled using classical simulators (emulators) of quantum computers and the actual quantum hardware available to us today. The list of problems we tackle includes propagation of a free wave packet, vibration of a harmonic oscillator, and tunneling through a barrier. Each of these problems starts with the initial wave packet setup. Although Qiskit provides a general method for initializing wave functions, in most cases it generates deep quantum circuits. While these circuits perform well on noiseless simulators, they suffer from excessive noise on quantum hardware. To overcome this issue, we designed a shallower quantum circuit for preparing a Gaussian-like initial wave packet, which improves the performance of real hardware. Next, quantum circuits are implemented to apply the kinetic and potential energy operators for the evolution of a wave function over time. The results of our modeling on classical emulators of quantum hardware agree perfectly with the results obtained using the traditional (classical) methods. This serves as a benchmark and demonstrates that the quantum algorithms and Qiskit codes we developed are accurate. However, the results obtained on the actual quantum hardware available today, such as IBM's superconducting qubits and IonQ's trapped ions, indicate large discrepancies due to hardware limitations. This work highlights both the potential and challenges of using quantum computers to solve fundamental quantum molecular dynamics problems.
We explore how the fundamental problems in quantum molecular dynamics can be modeled using classical simulators (emulators) of quantum computers and the actual quantum hardware available to us today. The list of problems we tackle includes propagation of a free wave packet, vibration of a harmonic oscillator, and tunneling through a barrier. Each of these problems starts with the initial wave packet setup. Although Qiskit provides a general method for initializing wave functions, in most cases it generates deep quantum circuits. While these circuits perform well on noiseless simulators, they suffer from excessive noise on quantum hardware. To overcome this issue, we designed a shallower quantum circuit for preparing a Gaussian-like initial wave packet, which improves the performance of real hardware. Next, quantum circuits are implemented to apply the kinetic and potential energy operators for the evolution of a wave function over time. The results of our modeling on classical emulators of quantum hardware agree perfectly with the results obtained using the traditional (classical) methods. This serves as a benchmark and demonstrates that the quantum algorithms and Qiskit codes we developed are accurate. However, the results obtained on the actual quantum hardware available today, such as IBM's superconducting qubits and IonQ's trapped ions, indicate large discrepancies due to hardware limitations. This work highlights both the potential and challenges of using quantum computers to solve fundamental quantum molecular dynamics problems.
Quantum computers hold the potential of solving problems that are intractable using classical means. Yet, to date no quantum computer has actually solved a problem of general interest that could not have been solved otherwise. Bridging this gap from promised theoretical usefulness to practical relevance is an interdisciplinary challenge, requiring experimental progress, solutions of classical software challenges as well as advances in quantum algorithm design. It is these final two points in which this thesis aims to contribute. One of the most promising quantum computing architectures is based on trapping ions in surface-electrode ion-traps. In order to productively operate such trapped-ion quantum computers, we develop and benchmark a compiler that optimizes ion shuttling sequences in order to efficiently map abstract quantum circuits onto a physical trapped-ion chip. This is a necessary component of the infrastructure of a quantum computing setup, however it is alone not sufficient to execute arbitrary quantum algorithms. In particular, a very promising class of quantum algorithms are so-called hybrid quantum-classical algorithms which leverage the computational resources of both quantum and classical computers. To effectively implement such algorithms, a suitable software setup is necessary to allow for tight interplay between the two types of computers without wasting precious coherence time. To solve this challenge, we propose, implement and benchmark our setup for Interpreted Quantum-Classical Computations (IQCCs), demonstrating its feasibility for trapped-ion quantum computers. For the second part of this thesis we focus on the development of quantum algorithms that make use of this setup. As a first application, we investigate quantum simulations of gauge theories. Such theories are prevalent throughout modern physics and are characterized by local constraints that the dynamics are subject to. Errors in noisy simulations of such theories results in these constraints being violated and the simulations becoming unphysical. We show that this problem can be remedied by measuring gauge operators, decoding possible errors on a classical computer and actively correcting them, which reduces simulation errors. Additionally we interpret the scheme as a sympathetic cooling setup, which allows thermal control of the simulation. We finally turn to the task of preparing ground states of frustration-free Hamiltonians in quantum computers. Studying ground states of various systems is of paramount importance for solving optimization problems and understanding phenomena such as magnetism, superconductivity and superfluidity. We frame the ground-state preparation problem as an error correction problem, wherein energy is measured locally, measurements are decoded and corrections are applied to reduce the energy. In physically relevant examples we show up to exponentially improved runtimes over previous, similar algorithms and give a general run-time bound in terms of the Hamiltonian gap.
Quantum computing has emerged as a transformative paradigm capable of solving complex computational problems that are intractable for classical computers. Central to the advancement of this technology is the development of efficient quantum algorithms and high fidelity simulations that enable the design, testing, and optimization of quantum solutions before deployment on physical hardware. This study focuses on the design and implementation of quantum algorithms tailored for solving a variety of quantum problems, including quantum chemistry, optimization, and cryptography. Using state of the art simulation platforms such as Qiskit, Cirq, and Pennylane, algorithm performance was evaluated in terms of accuracy, execution time, scalability, and resilience to noise. Benchmarks demonstrate that algorithms such as the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA) achieve significant speedups in problem specific domains, while hybrid quantum–classical methods provide robust pathways for near term quantum advantage. Simulation results reveal that algorithmic efficiency can be significantly improved through optimized circuit depth, qubit connectivity mapping, and advanced error mitigation techniques. The findings highlight the potential of simulation driven quantum algorithm development in accelerating the practical realization of quantum computing applications across disciplines such as materials discovery, molecular modeling, secure communications, and complex optimization tasks.
Quantum Hamiltonian simulation is one of the most promising applications of quantum computing and forms the basis for many quantum algorithms. Benchmarking them is an important gauge of progress in quantum computing technology. We present a methodology and software framework to evaluate various facets of the performance of gate-based quantum computers on Trotterized quantum Hamiltonian evolution. We propose three distinct modes for benchmarking: (i) comparing simulation on a real device to that on a noiseless classical simulator, (ii) comparing simulation on a real device with exact diagonalization results, and (iii) using scalable mirror circuit techniques to assess hardware performance in scenarios beyond classical simulation methods. We demonstrate this framework on five Hamiltonian models from the HamLib library: the Fermi and Bose-Hubbard models, the transverse field Ising model, the Heisenberg model, and the Max3SAT problem. Experiments were conducted using Qiskit's Aer simulator, BlueQubit's CPU cluster and GPU simulators, and IBM's quantum hardware. Our framework, extendable to other Hamiltonians, provides comprehensive performance profiles that reveal hardware and algorithmic limitations and measure both fidelity and execution times, identifying crossover points where quantum hardware outperforms CPU/GPU simulators.
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.
The theoretical investigation of nonadiabatic processes is hampered by the complexity of the coupled electron-nuclear dynamics beyond the Born-Oppenheimer approximation. Classically, the simulation of such reactions is limited by the unfavorable scaling of the computational resources as a function of the system size. While quantum computing exhibits proven quantum advantage for the simulation of real-time dynamics, the study of quantum algorithms for the description of nonadiabatic phenomena is still unexplored. In this Letter, we propose a quantum algorithm for the simulation of fast nonadiabatic chemical processes together with an initialization scheme for quantum hardware calculations. In particular, we introduce a first-quantization method for the time evolution of a wave packet on two coupled harmonic potential energy surfaces (Marcus model). In our approach, the computational resources scale polynomially in the system dimensions, opening up new avenues for the study of photophysical processes that are classically intractable.
We investigate one-dimensional quantum wave-packet dynamics using a grid-based encoding of the wave function onto qubit registers. Time evolution is implemented using a split operator approach, with the kinetic energy operator realized via the Quantum Fourier Transform (QFT) and arbitrary discretized potentials represented by commuting Pauli-Z gates. The algorithm is benchmarked against classical grid-based simulations and validated using a noiseless Qiskit Statevector simulator before being implemented on current quantum hardware (IBM Quantum and IonQ) for qubit counts ranging from two to five. Good agreement with benchmark calculations is obtained for two- and three-qubit implementations, while deviations increase at larger qubit counts due to hardware noise and increased circuit depth. Among the devices examined, the algorithm maintains closer agreement with the benchmark on the trapped-ion IonQ Forte processor as the number of qubits increases.