We present hybrid quantum–classical algorithms to compute time-dependent Møller wavepacket correlation functions via digital quantum simulation. Reactant and product channel wavepackets are encoded as qubit states, evolved under a discretized molecular Hamiltonian, and their correlation is reconstructed using both a modified Hadamard test and a multi-fidelity estimation (MFE) protocol. The method is applied to the collinear H + H2 exchange reaction on a London–Eyring–Polanyi–Sato potential energy surface. Quantum-estimated correlation functions show quantitative agreement with high-resolution classical wavepacket simulations across the full time domain, reproducing both short-time scattering peaks and long-time oscillatory dynamics. The ancilla-free MFE protocol achieves matching results with reduced circuit depth. These results provide a proof of principle that digital quantum circuits can be used to accurately calculate the wavepacket correlation functions for a benchmark chemical reaction system.
We present hybrid quantum–classical algorithms to compute time-dependent Møller wavepacket correlation functions via digital quantum simulation. Reactant and product channel wavepackets are encoded as qubit states, evolved under a discretized molecular Hamiltonian, and their correlation is reconstructed using both a modified Hadamard test and a multi-fidelity estimation (MFE) protocol. The method is applied to the collinear H + H2 exchange reaction on a London–Eyring–Polanyi–Sato potential energy surface. Quantum-estimated correlation functions show quantitative agreement with high-resolution classical wavepacket simulations across the full time domain, reproducing both short-time scattering peaks and long-time oscillatory dynamics. The ancilla-free MFE protocol achieves matching results with reduced circuit depth. These results provide a proof of principle that digital quantum circuits can be used to accurately calculate the wavepacket correlation functions for a benchmark chemical reaction system.
Studying chemical reactions, particularly in the gas phase, relies heavily on computing scattering matrix elements. These elements are essential for characterizing molecular reactions and accurately determining reaction probabilities. However, the intricate nature of quantum interactions poses challenges, necessitating the use of advanced mathematical models and computational approaches to tackle the inherent complexities. In this study, we develop and apply a quantum computing algorithm for the calculation of scattering matrix elements. In our approach, we employ the time-dependent method based on the Møller operator formulation where the S-matrix element between the respective reactant and product channels is determined through the time correlation function of the reactant and product Møller wavepackets. We successfully apply our quantum algorithm to calculate scattering matrix elements for 1D semi-infinite square well potential and on the colinear hydrogen exchange reaction. As we navigate the complexities of quantum interactions, this quantum algorithm is general and emerges as a promising avenue, shedding light on new possibilities for simulating chemical reactions on quantum computers.
The electronic energies of molecules have been successfully evaluated on quantum computers. However, more attention is paid to the dynamics simulation of molecules in practical applications. Based on the variational quantum eigensolver (VQE) algorithm, Fedorov et al. proposed a correlated sampling (CS) method and demonstrated the vibrational dynamics of H2 molecules [J. Chem. Phys. 154, 164103 (2021)]. In this study, we have developed a quantum approach by extending the CS method based on the VQE algorithm (labeled eCS-VQE) for simulating chemical reaction dynamics. First, the CS method is extended to the three-dimensional cases for calculation of first-order energy gradients, and then, it is further generalized to calculate the second-order gradients of energies. By calculating atomic forces and vibrational frequencies for H2, LiH, H+ + H2, and Cl- + CH3Cl systems, we have seen that the approach has achieved the CCSD level of accuracy. Thus, we have simulated dynamics processes for two typical chemical reactions, hydrogen exchange and chlorine substitution, and obtained high-precision reaction dynamics trajectories consistent with the classical methods. Our eCS-VQE approach, as measurement expectations and ground-state wave functions can be reused, is less demanding in quantum computing resources and is, therefore, a feasible means for the dynamics simulation of chemical reactions on the current noisy intermediate-scale quantum-era quantum devices.
Quantum computers offer the potential to simulate chemical systems beyond the capabilities of classical computers. However, current quantum computing approaches to ab initio molecular dynamics (AIMD) and vibrational analysis largely rely on the Variational Quantum Eigensolver (VQE), whose circuit depth, iterative optimization, and measurement overhead hinder the practical simulation of molecular systems. Here, we extend Sample-based Quantum Diagonalization (SQD), a quantum sampling-based electronic-structure method, to AIMD and vibrational analysis on noisy quantum hardware. The resulting framework enables nuclear forces and Hessians to be derived from quantum-computed electronic energies, facilitating molecular dynamics and characterization of potential energy surfaces. We demonstrate the approach using diverse molecular processes, including H2 bond vibration, the proton-exchange reaction (H+ + H2), the bimolecular nucleophilic substitution (SN2) reaction (Cl- + CH3Cl), and proton-transfer dynamics between two water molecules involving transient formation of the Zundel cation (H2O···H+···OH2). Across these systems, SQD-AIMD trajectories and vibrational frequencies obtained with noisy quantum hardware/noise-models show excellent agreement with classical reference calculations and substantially improved accuracy relative to previously reported VQE-based simulations. Importantly, the SQD-based approach eliminates costly variational optimization and significantly reduces measurement requirements relative to VQE, enabling AIMD simulations spanning approximately 500 timesteps (∼200 fs), substantially longer than previously reported AIMD simulations on quantum hardware. These results establish SQD-AIMD and SQD-vibrational analysis as practical and scalable frameworks for simulating chemical reaction dynamics and elucidating reaction mechanisms on near-term quantum hardware, extending quantum computing applications beyond static electronic structure calculations.
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.
Simulating chemical dynamics such as atomic and molecular scattering is a natural target for quantum computation, where conventional (classical) hardware faces exponential cost. We present a product-formula quantum algorithm that models single-channel helium-helium scattering by real-time evolution of a Gaussian wavepacket, requiring no precomputation of eigenstates. Interaction with the Lennard-Jones potential and centrifugal barrier is applied unitarily with closed-form circuits, with the evolution processed directly with error-free quantum circuit compilation. Tracking the wave function results in converged phase shifts, from which the deflection function, scattering amplitude, and differential cross section are calculated. Identical-boson integral cross sections agree with time-independent Numerov and log-derivative benchmarks to 6.1%, with a localized residual in s-wave scattering. The construction realizes any potential of the form ∑ir-mi with the same gate count as a single 1/r term, scales efficiently to multichannel dynamics, and provides a ground-truth operator for benchmarking approximate quantum simulation.
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.