arXiv subjects

Timothy N. Georges

Publications and source records attributed to Timothy N. Georges.

4 recordsLinked to original sources

arXiv2025

A Vibronic Coupling Model to Study the Nonadiabatic Dynamics of Polyenes

We develop a linear vibronic coupling (LVC) model for polyenes described by the extended Hubbard-Peierls Hamiltonian. This model is applied to trans-hexatriene to benchmark quantum-classical dynamics methods against fully quantum simulations. We find that surface-hopping methods describe short times more accurately than multi-trajectory Ehrenfest. None of the quantum-classical methods studied obtain the long-time population oscillations found in fully quantum simulations. Varying the parameters of the LVC Hamiltonian, we find that surface hopping reproduces the correct trends in the long-time dynamics across a wide range of parameters, but generally overestimates the degree of internal conversion. On the other hand, multi-trajectory Ehrenfest gives more accurate long-time populations in proximity to the hexatriene parameter set.

physics.chem-ph↗

arXiv2024

Pauli Decomposition via the Fast Walsh-Hadamard Transform

The decomposition of a square matrix into a sum of Pauli strings is a classical pre-processing step required to realize many quantum algorithms. Such a decomposition requires significant computational resources for large matrices. We present an exact and explicit formula for the Pauli string coefficients which inspires an efficient algorithm to compute them. More specifically, we show that up to a permutation of the matrix elements, the decomposition coefficients are related to the original matrix by a multiplication of a generalised Hadamard matrix. This allows one to use the Fast Walsh-Hadamard transform and calculate all Pauli decomposition coefficients in $\mathcal{O}(N^2\log N)$ time and using $\mathcal{O}(1)$ additional memory, for an $N\times N$ matrix. A numerical implementation of our equation outperforms currently available solutions.

quant-ph↗

arXiv2024

Quantum Simulations of Chemistry in First Quantization with any Basis Set

Quantum computation of the energy of molecules and materials is one of the most promising applications of fault-tolerant quantum computers. Practical applications require development of quantum algorithms with reduced resource requirements. Previous work has mainly focused on quantum algorithms where the Hamiltonian is represented in second quantization with compact basis sets while existing methods in first quantization are limited to a grid-based basis. In this work, we present a new method to solve the generic ground-state chemistry problem in first quantization using any basis set. We achieve asymptotic speedup in Toffoli count for molecular orbitals, and orders of magnitude improvement using dual plane waves as compared to the second quantization counterparts. In some instances, our approach provides similar or even lower resources compared to previous first quantization plane wave algorithms that, unlike our approach, avoids the loading of the classical data. The developed methodology can be applied to variety of applications, where the matrix elements of a first quantized Hamiltonian lack simple circuit representation.

quant-ph↗

arXiv2022

Photoexcited state dynamics and singlet fission in carotenoids

We describe our dynamical simulations of the excited states of the carotenoid, neurosporene, following its photoexcitation into the 'bright' (nominally $1^1B_u^+$) state. We employ the adaptive tDMRG method on the UV model of $π$-conjugated electrons and use the Ehrenfest equations of motion to simulate the coupled nuclei dynamics. To account for the experimental and theoretical uncertainty in the relative energetic ordering of the nominal $1^1B_u^+$ and $2^1A_g^-$ states at the Franck-Condon point, we consider two parameter sets. In both cases there is ultrafast internal conversion from the 'bright' state to a 'dark' singlet triplet-pair state. We make a direct connection from our predictions to experimental observables by calculating the transient absorption. For the case of direct $1^1B_u^+$ to $2^1A_g^-$ internal conversion, we show that the dominant transition at ca. 2 eV, being close to but lower in energy than the $T_1$ to $T_1^*$ transition, can be attributed to the $2^1A_g^-$ component of $S_1$. Moreover, we show that it is the charge-transfer exciton component of the $2^1A_g^-$ state that is responsible for this transition, and not its triplet-pair component. We next discuss the microscopic mechanism of 'bright' to 'dark' state internal conversion, emphasising that this occurs via the exciton components of both states. Finally, we describe a mechanism whereby the strongly bound intrachain triplet-pairs of the 'dark' state may undergo interchain exothermic dissociation. We predict that this is only possible if the molecules are twisted in their ground states. The computational methodology underlying the calculations described here is explained in our companion paper, $\textit{Dynamical simulations of carotenoid photoexcited states using density matrix renormalization group techniques}$, D. Manawadu, D. J. Valentine, and W. Barford, $\textit{J. Chem. Theo. Comp.}$ (2023).

physics.chem-ph↗