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.
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.
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.
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, we present a comprehensive comparative study between two different Ansatz quantum circuits , specifically the Unitary Vibrational Coupled Cluster (UVCC) and the Compact Heuristic Circuit (CHC) with use in computational chemistry . By incorporating these circuits into the Variational Quantum Eigensolver (VQE), we aim to find the vibrational ground state energy of small molecules. Our results, obtained using both the UVCC and CHC ansatzes with and without quantum hardware noise, are benchmarked against classical computational methods for energy state determination. We emphasize the efficiency and accuracy of the CHC Ansatz , which significantly reduces circuit complexity without sacrificing the fidelity of the results. This characteristic demonstrates the potential of the CHC Ansatz for scalable quantum chemistry applications, particularly in the Noisy Intermediate-Scale Quantum (NISQ) era. Furthermore, we employ the CHC Ansatz in conjunction with the Variational Quantum Deflation (VQD) algorithm to determine the excited vibrational state energies, which is compared against the reliable method of quantum Equation of Motion(qEOM). Through this comparative study, we aim to provide valuable insights into the practical applications of these Ansatz in quantum simulations of molecular systems, highlighting their respective advantages and potential for future quantum chemistry research.
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.
Multidimensional optical spectroscopies are powerful techniques to investigate energy transfer pathways in natural and artificial systems. Because of the high information content of the spectra, numerical simulations of the optical response are of primary importance to assist the interpretation of spectral features. However, the increasing complexity of the investigated systems and their quantum dynamics call for the development of novel simulation strategies. In this work, we consider using digital quantum computers. By combining quantum dynamical simulation and nonlinear response theory, we present a quantum algorithm for computing the optical response of molecular systems. The quantum advantage stems from the efficient quantum simulation of the dynamics governed by the molecular Hamiltonian, and it is demonstrated by explicitly considering exciton-vibrational coupling. The protocol is tested on a near-term quantum device, providing the digital quantum simulation of the linear and nonlinear response of simple molecular models.
Abstract Digital quantum computers provide a computational framework for solving the Schrödinger equation for a variety of many‐particle systems. Quantum computing algorithms for the quantum simulation of these systems have recently witnessed remarkable growth, notwithstanding the limitations of existing quantum hardware, especially as a tool for electronic structure computations in molecules. In this review, we provide a self‐contained introduction to emerging algorithms for the simulation of Hamiltonian dynamics and eigenstates, with emphasis on their applications to the electronic structure in molecular systems. Theoretical foundations and implementation details of the method are discussed, and their strengths, limitations, and recent advances are presented. This article is categorized under: Quantum Computing > Algorithms Electronic Structure Theory > Ab Initio Electronic Structure Methods Quantum Computing > Theory Development