On-the-fly ab initio semiclassical evaluation of time-resolved electronic spectra

We present a methodology for computing vibrationally and time-resolved pump-probe spectra, which takes into account all vibrational degrees of freedom and is based on the combination of the thawed Gaussian approximation with on-the-fly ab initio evaluation of the electronic structure. The method is applied to the phenyl radical and compared with two more approximate approaches based on the global harmonic approximation - the global harmonic method expands both the ground- and excited-state potential energy surfaces to the second order about the corresponding minima, while the combined global harmonic/on-the-fly method retains the on-the-fly scheme for the excited-state wavepacket propagation. We also compare the spectra by considering their means and widths, and show analytically how these measures are related to the properties of the semiclassical wavepacket. We find that the combined approach is better than the global harmonic one in describing the vibrational structure, while the global harmonic approximation estimates better the overall means and widths of the spectra due to a partial cancellation of errors. Although the full-dimensional on-the-fly ab initio result seems to reflect the dynamics of only one mode, we show, by performing exact quantum calculations, that this simple structure cannot be recovered using a one-dimensional model. Yet, the agreement between the quantum and semiclassical spectra in this simple, but anharmonic model lends additional support for the full-dimensional ab initio thawed Gaussian calculation of the phenyl radical spectra. We conclude that the thawed Gaussian approximation provides a viable alternative to the expensive or unfeasible exact quantum calculations in cases, where low-dimensional models are not sufficiently accurate to represent the full system.Comment: Last 6 pages contain the Supplementary Materia

On-the-fly ab initio semiclassical evaluation of absorption spectra of polyatomic molecules beyond the Condon approximation

To evaluate vibronic spectra beyond the Condon approximation, we extend the on-the-fly ab initio thawed Gaussian approximation by considering the Herzberg-Teller contribution due to the dependence of the electronic transition dipole moment on nuclear coordinates. The extended thawed Gaussian approximation is tested on electronic absorption spectra of phenyl radical and benzene: Calculated spectra reproduce experimental data and are much more accurate than standard global harmonic approaches, confirming the significance of anharmonicity. Moreover, the extended method provides a tool to quantify the Herzberg-Teller contribution: we show that in phenyl radical, anharmonicity outweighs the Herzberg-Teller contribution, whereas in benzene, the Herzberg-Teller contribution is essential, since the transition is electronically forbidden and Condon approximation yields a zero spectrum. Surprisingly, both adiabatic harmonic spectra outperform those of the vertical harmonic model, which describes the Franck-Condon region better. Finally, we provide a simple recipe for orientationally averaging spectra, valid beyond Condon approximation, and a relation among the transition dipole, its gradient, and nonadiabatic coupling vectors.Comment: Final form available via open access in J. Phys. Chem. Lett.: https://pubs.acs.org/doi/10.1021/acs.jpclett.8b00827. Last 11 pages contain the Supporting Informatio

On-the-fly ab initio semiclassical evaluation of third-order response functions for two-dimensional electronic spectroscopy

Ab initio computation of two-dimensional electronic spectra is an expanding field, whose goal is improving upon simple, few-dimensional models often employed to explain experiments. Here, we propose an accurate and computationally affordable approach, based on the single-trajectory semiclassical thawed Gaussian approximation, to evaluate two-dimensional electronic spectra. Importantly, the method is exact for arbitrary harmonic potentials with mode displacement, changes in the mode frequencies, and inter-mode coupling (Duschinsky effect), but can also account partially for the anharmonicity of the involved potential energy surfaces. We test its accuracy on a set of model Morse potentials and use it to study anharmonicity and Duschinsky effects on the linear and two-dimensional electronic spectra of phenol. We find that in this molecule, the anharmonicity effects are weak, whereas the Duschinsky rotation and the changes in the mode frequencies must be included in accurate simulations. In contrast, the widely used displaced harmonic oscillator model captures only the basic physics of the problem but fails to reproduce the correct vibronic lineshape.Comment: v3: Minor improvements in the main tex

Fast classical simulation of evidence for the utility of quantum computing before fault tolerance

We show that a classical algorithm based on sparse Pauli dynamics can efficiently simulate quantum circuits studied in a recent experiment on 127 qubits of IBM's Eagle processor [Nature 618, 500 (2023)]. Our classical simulations on a single core of a laptop are orders of magnitude faster than the reported walltime of the quantum simulations, as well as faster than the estimated quantum hardware runtime without classical processing, and are in good agreement with the zero-noise extrapolated experimental results

Simulating quantum circuit expectation values by Clifford perturbation theory

The classical simulation of quantum circuits is of central importance for benchmarking near-term quantum devices. The fact that gates belonging to the Clifford group can be simulated efficiently on classical computers has motivated a range of methods that scale exponentially only in the number of non-Clifford gates. Here, we consider the expectation value problem for circuits composed of Clifford gates and non-Clifford Pauli rotations, and introduce a heuristic perturbative approach based on the truncation of the exponentially growing sum of Pauli terms in the Heisenberg picture. Numerical results are shown on a Quantum Approximate Optimization Algorithm (QAOA) benchmark for the E3LIN2 problem and we also demonstrate how this method can be used to quantify coherent and incoherent errors of local observables in Clifford circuits. Our results indicate that this systematically improvable perturbative method offers a viable alternative to exact methods for approximating expectation values of large near-Clifford circuits

Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance

A recent quantum simulation of observables of the kicked Ising model on 127 qubits [Nature 618, 500 (2023)] implemented circuits that exceed the capabilities of exact classical simulation. We show that several approximate classical methods, based on sparse Pauli dynamics and tensor network algorithms, can simulate these observables orders of magnitude faster than the quantum experiment, and can also be systematically converged beyond the experimental accuracy. Our most accurate technique combines a mixed Schr\"odinger and Heisenberg tensor network representation with the Bethe free entropy relation of belief propagation to compute expectation values with an effective wavefunction-operator sandwich bond dimension ${>}16,000,000$, achieving an absolute accuracy, without extrapolation, in the observables of ${<}0.01$, which is converged for many practical purposes. We thereby identify inaccuracies in the experimental extrapolations and suggest how future experiments can be implemented to increase the classical hardness.Comment: This can be regarded as the full version of the preliminary note in arXiv:2306.1637