We develop a time-dependent, grid-based framework for simulating infrared spectra that is specifically designed for quantum computers. The proposed circuit employs a probabilistic strategy for applying the non-unitary dipole operator and an Split Operator-Quantum Fourier Transform time evolution scheme. Using a vibrational model of the water molecule as a test system, our classical emulation results demonstrate accurate determination of fundamental and overtone band positions and intensities via Fourier-transformed dipole-dipole autocorrelation functions. We also identify the optimal time parameters that minimise gate depths while maintaining high fidelity. For further resource reduction, we validate the feasibility of utilising harmonic oscillator approximations in state preparation and dipole operator truncations. With its scalability to higher-dimensional normal mode spaces, this wavefunction-based approach establishes a robust foundation for studying IR spectra on future quantum hardware.
We develop a time-dependent, grid-based framework for simulating infrared spectra that is specifically designed for quantum computers. The proposed circuit employs a probabilistic strategy for applying the non-unitary dipole operator and an Split Operator-Quantum Fourier Transform time evolution scheme. Using a vibrational model of the water molecule as a test system, our classical emulation results demonstrate accurate determination of fundamental and overtone band positions and intensities via Fourier-transformed dipole-dipole autocorrelation functions. We also identify the optimal time parameters that minimise gate depths while maintaining high fidelity. For further resource reduction, we validate the feasibility of utilising harmonic oscillator approximations in state preparation and dipole operator truncations. With its scalability to higher-dimensional normal mode spaces, this wavefunction-based approach establishes a robust foundation for studying IR spectra on future quantum hardware.
This thesis investigates the grid-based Split Operator–Quantum Fourier Transform (SO-QFT) scheme as a general-purpose backbone for time-dependent quantum simulation. We develop an end-to-end algorithmic framework that unifies state preparation on discretised grids, SO-QFT time propagation, and the extraction of observables via autocorrelation functions, with a focus on efficient quantum circuit construction. Classical emulation is used to evaluate the performance and resource demands of this framework across diverse chemical contexts. For vibronic dynamics arising from conical intersections, we assemble a complete workflow that reproduces absorption spectra and population transfer for a well-characterised prototypical polyatomic system. On this basis, we estimate the required quantum resources by mapping grid size, time resolution and spectral precision to qubit budgets, circuit depths and measurement counts. The framework is further tailored to infrared spectroscopy through probabilistic encoding of non-unitary dipole operators and explicit treatment of higher-order Hamiltonian terms via multi-controlled operations. To minimise gate depth, we optimise time discretisation and employ approximation strategies for initial states and dipole truncations, while preserving the fidelity of computed spectra. Importantly, the resource scaling relations derived from the vibronic and infrared simulations generalise to comparable molecular systems, providing a transferable template for predicting resource estimates beyond the specific benchmark studied. Finally, the methodology is extended to Coulombic systems, whose singular potentials challenge grid-based representations. We improve the simulation fidelity by proposing two correction schemes: a Hamiltonian correction that accounts for grid-basis structure, and a modification of the initial wavefunction to better match the discretised Hamiltonian. Both corrections are compatible with compact quantum encodings, and their representation in truncated Fourier or Walsh series offers an additional reduction in circuit depth. Collectively, these studies advance the grid-based SO-QFT scheme from a promising construct to a systematically assessed framework, establishing methodological guidance, algorithmic variants and quantitative resource benchmarks for future fault-tolerant quantum applications.
Accurate time-dependent quantum dynamics of Coulombic systems on grid-based representations remains computationally demanding due to the singularity of the Coulomb potential, which necessitates extremely fine spatial grids to mitigate discretisation errors. We propose two complementary correction schemes that, under identical resource budgets, consistently outperform the uncorrected counterparts. The first scheme modifies the potential operator to incorporate grid-basis structure into its representation, while the second introduces a corrected initial wavefunction inspired by analytical solutions of softened Coulomb potentials. Applied to hydrogenic systems, these corrections deliver improved energy accuracy and time fidelity across long evolutions. Beyond classical simulations, the proposed framework aligns naturally with quantum computing architectures, where the corrected operators and states can be encoded through truncated Walsh and Fourier series expansions. A resource analysis for the representative 2D hydrogen system yields a circuit depth of 1.5×108 gates over 6,000 Trotter steps. This study thus establishes practical strategies toward high-accuracy Coulombic dynamics on both classical and emerging quantum platforms.
We establish and analyse the performance and resource requirements of an end-to-end fault-tolerant quantum algorithm for computing the absorption spectrum and population dynamics of photoexcited pyrazine. The quantum circuit construction consists of initial state preparation using uniformly controlled rotations, the time-dependent Hamiltonian propagation based on the grid-based Split Operator Quantum Fourier Transform (SO-QFT) method, and cost-effective measurements including statistical and canonical phase estimation. We use classical emulations to validate the quantum resources required for the task, and propose generalised formulae for the qubit count and gate depth calculation. Simulating the vibronic dynamics of pyrazine in a low-dimensional abstraction requires 17-qubit circuits with a gate depth of O(105), whereas a full-dimensional simulation of pyrazine in 24 modes requires at least 97-qubit circuits with a gate depth of O(106). Our work provides a foundational framework for understanding high-dimensional wavepacket-based quantum simulations of photo-induced dynamics and vibronic spectra, anticipating future applications in the simulation of even larger molecular systems on fault-tolerant quantum computers.
Theoretical quantum dynamics calculations scale deeply with system size, rendering classical calculations intractable for complex systems. While quantum computing offers a natural solution, its application to nuclear quantum dynamics remains scarce. Here, we present a quantum algorithm to study photodissociation dynamics on quantum computers, benchmarked on the NOCl molecule. The wavefunction is propagated via a split-operator method, utilizing the Quantum Fourier Transform and unitary transformation matrix to switch representations. To impose outgoing boundary conditions on a truncated grid, we use a non-unitary absorbing potential propagator, implemented through a dilation scheme. The photodissociation cross section is calculated from the auto-correlation function, which is extracted using the Hadamard test. Our quantum computing results agree well with benchmarks under ideal conditions, and we further demonstrate that the algorithm is robust to noise and statistical sampling errors, indicating the promising application of noisy devices to quantum dynamics studies.
Near-infrared (NIR) spectroscopy is a non-invasive, low-cost, reagent-less, and rapid technique to measure chemical concentrations in a wide variety of sample types. However, extracting concentration information from the NIR spectrum requires training a statistical model on a large collection of measurements, which can be impractical, expensive, or dangerous. In this work, we propose a method for simulating NIR spectra on a quantum computer, as part of a larger workflow to improve NIR-based chemical detection. The quantum algorithm is highly optimized, exhibiting a cost reduction of many orders of magnitude relative to prior approaches. The main optimizations include the localization of vibrational modes, an efficient real-space-based representation of the Hamiltonian with a quantum arithmetic-based implementation of the time-evolution, optimal Trotter step size determination, and specific targeting of the NIR region. Overall, our algorithm achieves a O(M^2) scaling, compared with the O(M^12) coming from equivalent high-accuracy classical methods. As a concrete application, we show that simulating the spectrum of azidoacetylene (HC2N3), a highly explosive molecule with strong anharmonicities consisting of M = 12 vibrational modes, requires circuits with a maximum 8.47 x 10^8 T gates and 173 logical qubits. By enhancing the training datasets of detection models, the full potential of vibrational spectroscopy for chemical detection could be unlocked across a range of applications, including pharmaceuticals, agriculture, environmental monitoring, and medical sensing.
Quantum dynamics calculations scale steeply with system size, rendering calculations on a classical computer intractable for complex systems. While quantum computing offers a natural solution, its application to nuclear quantum dynamics has been scarce. Here, we present a quantum algorithm to study photodissociation dynamics on quantum computers, benchmarked on the NOCl molecule. The wave function is propagated via a split-operator method, utilizing the quantum Fourier transform and unitary transformation matrix to switch representations. To impose outgoing boundary conditions on a truncated grid, we use a nonunitary absorbing potential propagator, implemented through a dilation scheme. The photodissociation cross section is calculated from the autocorrelation function, which is extracted using the Hadamard test. Our quantum computing results agree well with benchmarks under ideal conditions, and we further demonstrate that the algorithm is robust to noise and statistical sampling errors, indicating its promise for application of noisy devices for quantum dynamics studies.