Modeling chemical dynamics is essential for understanding, predicting, and optimizing chemical processes. Because realistic chemical systems involve many interacting degrees of freedom, direct propagation of the many-body Schr"{o}dinger equation is intractable for all but the smallest systems. Quantum information platforms offer a fundamentally different representation: a $d$-dimensional state may be encoded using $k=log_2(d)$ qubits rather than storing each amplitude independently. To harness this advantage for chemistry, it is necessary to develop quantum algorithms and hardware architectures capable of simulating the open-system dynamics ubiquitous in condensed-phase and molecular environments. In the first chapter, we develop a theoretical framework for simulating a cavity-modified photoinduced charge-transfer reaction in the carotenoid–porphyrin–C$_{60}$ (CPC$_{60}$) molecular triad dissolved in tetrahydrofuran (THF). Nonequilibrium Fermi’s Golden Rule (NE-FGR) rate coefficients are obtained as a product of cavity-free and cavity-modified correlation functions. We further introduce an approximation based on Instantaneous Marcus Theory (IMT) that closely tracks the full NE-FGR result across all relevant time scales. Population transfer rates computed from the population-only off-diagonal quantum master equation (p-tcl-OD-QME) are shown to be consistent with the NE-FGR predictions. Our results demonstrate that nonequilibrium charge-transfer dynamics are significantly modified by coupling to an optical cavity. The second chapter addresses the integration of linear nonautonomous ordinary differential equations on digital quantum hardware. Rather than classically constructing a nonunitary propagator at each time step and embedding it into a larger unitary operation for execution on quantum hardware, we eliminate this classical–quantum partitioning. We derive and propagate differential equations for the singular value decomposition (SVD) factors of the propagator directly, enabling time evolution to be implemented within a quantum-compatible framework. This approach shifts the locus of time integration from the classical processor to the quantum device. In the third chapter, we investigate the feasibility of simulating chemical reaction dynamics on a parametrically driven bosonic superconducting Kerr-cat device. This analog platform enables direct control over parameters defining an effective double-well free-energy landscape, as well as over environmental factors such as temperature and system–bath coupling strength. We demonstrate that proton transfer dynamics in prototypical benchmark systems, including hydrogen-bonded dimers of malonaldehyde and DNA base pairs, can be accurately reproduced using experimentally accessible Kerr-cat architectures.
Modeling chemical dynamics is essential for understanding, predicting, and optimizing chemical processes. Because realistic chemical systems involve many interacting degrees of freedom, direct propagation of the many-body Schr"{o}dinger equation is intractable for all but the smallest systems. Quantum information platforms offer a fundamentally different representation: a d-dimensional state may be encoded using k=log2(d) qubits rather than storing each amplitude independently. To harness this advantage for chemistry, it is necessary to develop quantum algorithms and hardware architectures capable of simulating the open-system dynamics ubiquitous in condensed-phase and molecular environments. In the first chapter, we develop a theoretical framework for simulating a cavity-modified photoinduced charge-transfer reaction in the carotenoid–porphyrin–C60 (CPC60) molecular triad dissolved in tetrahydrofuran (THF). Nonequilibrium Fermi’s Golden Rule (NE-FGR) rate coefficients are obtained as a product of cavity-free and cavity-modified correlation functions. We further introduce an approximation based on Instantaneous Marcus Theory (IMT) that closely tracks the full NE-FGR result across all relevant time scales. Population transfer rates computed from the population-only off-diagonal quantum master equation (p-tcl-OD-QME) are shown to be consistent with the NE-FGR predictions. Our results demonstrate that nonequilibrium charge-transfer dynamics are significantly modified by coupling to an optical cavity. The second chapter addresses the integration of linear nonautonomous ordinary differential equations on digital quantum hardware. Rather than classically constructing a nonunitary propagator at each time step and embedding it into a larger unitary operation for execution on quantum hardware, we eliminate this classical–quantum partitioning. We derive and propagate differential equations for the singular value decomposition (SVD) factors of the propagator directly, enabling time evolution to be implemented within a quantum-compatible framework. This approach shifts the locus of time integration from the classical processor to the quantum device. In the third chapter, we investigate the feasibility of simulating chemical reaction dynamics on a parametrically driven bosonic superconducting Kerr-cat device. This analog platform enables direct control over parameters defining an effective double-well free-energy landscape, as well as over environmental factors such as temperature and system–bath coupling strength. We demonstrate that proton transfer dynamics in prototypical benchmark systems, including hydrogen-bonded dimers of malonaldehyde and DNA base pairs, can be accurately reproduced using experimentally accessible Kerr-cat architectures.
Accurately simulating molecular dynamics during chemical reactions remains a central challenge in computational chemistry. These processes are inherently quantum mechanical, involving coupled electronic and nuclear motion and non-adiabatic effects. A fully quantum description is therefore required, yet the associated computational cost grows exponentially with system size. Even with modern supercomputers, storing and evolving a molecular wavefunction rapidly becomes intractable, limiting exact simulations of chemical dynamics. Quantum simulation offers a promising alternative by using controllable quantum systems to directly reproduce molecular dynamics. However, fully digital, qubit-based approaches remain impractical for chemistry due to limited qubit numbers, coherence times, and gate fidelities. This motivates the exploration of more resource-efficient quantum architectures. In this thesis, we demonstrate that mixed-qudit-boson (MQB) quantum simulators provide a practical platform for simulating chemical dynamics in the quantum regime. In MQB devices, multilevel qudits encode electronic states while bosonic modes natively represent vibrational degrees of freedom, avoiding costly qubit encodings of nuclear motion and substantially reducing resource requirements. The thesis makes three main contributions. First, it reports the direct observation of geometric-phase interference in non-adiabatic dynamics using an MQB simulation of the Jahn–Teller model. Second, it extends the MQB framework to open-system chemical dynamics through programmable Lindblad dissipation. Third, it presents a resource analysis showing that MQB simulators can reduce resource costs by several orders of magnitude relative to qubit-only approaches. Together, these results establish MQB quantum simulators as a promising route for studying chemical dynamics beyond the reach of classical computation.
Nonautonomous linear ordinary differential equations of the form v˙(t)=A(t)v(t), where A(t) is non-skew-symmetric, are often used to describe nonunitary dynamics in a variety of fields that range from open quantum system dynamics to economic modeling. Because quantum computing hardware is designed to natively implement unitary transformations, existing algorithms for solving such equations on quantum hardware are based on the assumption that the nonunitary propagator is known, and use dilation techniques to embed the nonunitary dynamics within the unitary dynamics of a larger system. However, with the exception of cases where the nonunitary propagator is known in closed form, it needs to be calculated and manipulated on a classical computer at each time step. In this paper, we propose a quantum algorithm that does not require a priori knowledge of the explicit nonunitary propagator and effectively performs the dilation on the quantum hardware. Our algorithm combines a dilation scheme that uses singular value decomposition (SVD) to write the nonunitary propagator as a sum of unitaries with simulating the dynamics of the SVD factors on the quantum hardware. The population-only time-convolutionless quantum master equation describing photoinduced charge transfer in a solvated molecular triad is used as a demonstrative example of the applicability of the algorithm and its sensitivity to noise.
Chemical reactions are commonly described by the reactive flux transferring the population from reactants to products across a double-well free energy barrier. Dynamics often involves barrier recrossing and quantum effects like tunneling, zero-point energy motion, and interference, which traditional rate theories, such as transition-state theory, do not consider. In this study, we investigate the feasibility of simulating reaction dynamics using a parametrically driven bosonic superconducting Kerr-cat device. This approach provides control over parameters defining the double-well free energy profile, as well as external factors like temperature and the coupling strength between the reaction coordinate and the thermal bath of nonreactive degrees of freedom. We demonstrate the effectiveness of this protocol by showing that the dynamics of proton-transfer reactions in prototypical benchmark model systems, such as hydrogen-bonded dimers of malonaldehyde and DNA base pairs, could be accurately simulated on the currently accessible Kerr-cat devices.
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.
Energy and charge transfer processes, which are central to photosynthesis, catalysis, and molecular electronics, are governed by quantum dynamics in contact with complex environments. Interactions with surrounding degrees of freedom give rise to dissipation, decoherence, and energy exchange, shaping the mechanisms that determine chemical reactivity and transport phenomena. In Part IV of the QFlux tutorial series, we extend our study of quantum dynamics to open quantum systems, where time evolution is intrinsically non-unitary. Using the Lindblad master equation as a unifying and practical framework, we show how environmental effects can be modeled, simulated, and visualized with QFlux , an open-source platform that bridges classical and quantum computation. The tutorial presents the theoretical foundations of open-system dynamics, constructs the Lindblad propagator, and implements representative simulations ranging from spin models to chemically relevant double-well potentials. Special attention is given to dilation methods, which embed non-unitary dynamics within an enlarged unitary space through ancillary qubits, enabling open-system simulations on quantum hardware. This installment provides both conceptual insight and computational methodology for exploring dissipative quantum dynamics, laying the groundwork for subsequent parts addressing variational, non-Markovian approaches.
Quantum computers offer a significant advantage in simulating quantum systems compared to classical computers for certain problems, although most current applications are limited to calculating static molecular properties using hybrid quantum-classical hardware. In this work, we establish a framework for the representation of quantum dynamics in molecular and condensed matter systems, designed for execution on topological quantum hardware. By leveraging the non-Abelian braiding statistics of Fibonacci and Ising anyons, we utilize the Solovay-Kitaev algorithm to approximate unitary propagators for a range of systems. We demonstrate the efficacy of these algorithms across a hierarchy of complexity, from two-level systems and one dimensional double-well potentials to condensed phase spin-boson models, simple molecules, and molecular reaction kinetics. These algorithms provide a scalable and robust pathway for simulating many-body condensed phase chemical physics on fault-tolerant quantum devices.