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arXiv:1812.10495 · The Journal of Physical Chemistry Letters

Quantum Algorithm for Calculating Molecular Vibronic Spectra

Nicolas P. D. Sawaya, Joonsuk Huh

Published Jun 11, 2019• 71 citations
arXivHTMLPDF

Abstract

We present a quantum algorithm for calculating the vibronic spectrum of a molecule, a useful but classically hard problem in chemistry. We show several advantages over previous quantum approaches: vibrational anharmonicity is naturally included; after measurement, some state information is preserved for further analysis; and there are potential error-related benefits. Considering four triatomic molecules, we numerically study truncation errors in the harmonic approximation. Further, in order to highlight the fact that our quantum algorithm's primary advantage over classical algorithms is in simulating anharmonic spectra, we consider the anharmonic vibronic spectrum of sulfur dioxide. In the future, our approach could aid in the design of materials with specific light-harvesting and energy transfer properties, and the general strategy is applicable to other spectral calculations in chemistry and condensed matter physics.

DOI
10.1021/acs.jpclett.9b01117

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We present a quantum algorithm for calculating the vibronic spectrum of a molecule, a useful but classically hard problem in chemistry. We show several advantages over previous quantum approaches: vibrational anharmonicity is naturally included; after measurement, some state information is preserved for further analysis; and there are potential error-related benefits. Considering four triatomic molecules, we numerically study truncation errors in the harmonic approximation. Further, in order to highlight the fact that our quantum algorithm's primary advantage over classical algorithms is in simulating anharmonic spectra, we consider the anharmonic vibronic spectrum of sulfur dioxide. In the future, our approach could aid in the design of materials with specific light-harvesting and energy transfer properties, and the general strategy is applicable to other spectral calculations in chemistry and condensed matter physics.
Molecular vibronic spectra can be used to derive the structural properties of molecules. Although there is no known efficient classical algorithm for calculating these spectra, it has recently been shown that an ideal quantum optics simulator can in principle be used to efficiently perform this calculation. In this work, we demonstrate that imperfect quantum simulators can also yield approximations of these spectra, and illustrate our findings using a proof of principle experimental simulation of the partial vibronic spectrum of tropolone. Specifically, we demonstrate a method for designing an experiment in the presence of imperfections, show that the error on the resulting estimations of vibronic spectra can be efficiently bounded, and show that such experiments can outperform a classicality criterion. Our findings provide a roadmap for future simulations of large molecules beyond the reach of current classical computers.
Molecular vibrations underpin important phenomena such as spectral properties, energy transfer, and molecular bonding. However, obtaining a detailed understanding of the vibrational structure of even small molecules is computationally expensive. While numerous algorithms exist for solving the electronic structure problem on a quantum computer, there has been comparatively little attention devoted to solving the vibrational structure problem with quantum hardware. In this work, we discuss the use of quantum algorithms for investigating both the static and dynamic vibrational properties of molecules. We introduce a physically motivated unitary vibrational coupled cluster ansatz, which also makes our method accessible to noisy, near-term quantum hardware. We numerically test our proposals for the water and sulfur dioxide molecules.
Molecular vibrations underpin important phenomena such as spectral properties, energy transfer, and molecular bonding. However, obtaining a detailed understanding of the vibrational structure of even small molecules is computationally expensive. While several algorithms exist for efficiently solving the electronic structure problem on a quantum computer, there has been comparatively little attention devoted to solving the vibrational structure problem with quantum hardware. In this work, we discuss the use of quantum algorithms for investigating both the static and dynamic vibrational properties of molecules. We introduce a physically motivated unitary vibrational coupled cluster ansatz, which also makes our method accessible to noisy, near-term quantum hardware. We numerically test our proposals for the water and sulfur dioxide molecules.
Determining the vibrational structure of a molecule is central to fundamental applications in several areas, from atmospheric science to catalysis, fuel combustion modeling, biochemical imaging, and astrochemistry. However, when significant anharmonicity and mode coupling are present, the problem is classically intractable for a molecule of just a few atoms. Here, we outline a set of quantum algorithms for solving the molecular vibrational structure problem for both near- and long-term quantum computers. There are previously unaddressed characteristics of this problem which require approaches distinct from most instances of the commonly studied quantum simulation of electronic structure: many eigenstates are often desired, states of interest are often far from the ground state (requiring methods for ``zooming in'' to some energy window), particle conservation is not required, and transition amplitudes with respect to a nonunitary Hermitian operator must be calculated. We address each of these hurdles and consider problem instances of four molecular vibrational Hamiltonians. Finally and most importantly, we give analytical and numerical results which suggest that, to a given energy precision, a vibrational problem instance will be simulatable on a quantum computer before an electronic structure problem instance. These results imply that more focus in the quantum information community ought to shift toward scientifically and industrially important quantum vibrational problems.
In this work, a direct quantum implementation of the Doktorov formulas for calculating the vibronic spectrum of molecules under the harmonic approximation is presented. It is applied to the three-atom molecules H 2 O, SO 2, ClO 2, HS 2, and ZnOH. The method solves the classically hard problem of estimating the Franck–Condon (FC) factors by using the Duschinsky matrices as the only input via the Doktorov quantum circuit. This has the advantage of avoiding basis changes, artificial squeezing parameters, and symmetry dependencies. In other words, it is a general method for three-atom molecules that can easily be generalized to bigger molecules. The results are compared with other quantum algorithms and classical anharmonic algorithms. Furthermore, the circuit requirements are studied in order to estimate its applicability on real superconducting quantum hardware.
We consider three distinct methods of calculating the vibronic levels and absorption spectra of molecular dimers coupled by dipole-dipole interactions. The first method is direct diagonalization of the vibronic Hamiltonian in a basis of monomer eigenstates. The second method is to use creation and annihilation operators leading in harmonic approximation to the Jaynes-Cummings Hamiltonian. The adiabatic approximation to this problem provides insight into spectral behavior in the weak and strong coupling limits. The third method, which serves as a check on the accuracy of the previous methods, is a numerically exact solution of the time-dependent Schrodinger equation. Using these methods, dimer spectra are calculated for three separate dye molecules and show good agreement with measured spectra.