Near- and long-term quantum algorithmic approaches for vibrational spectroscopy

TL;DR

This paper proposes quantum algorithms tailored for vibrational spectroscopy, addressing unique challenges like multiple eigenstates and non-unitary operators, and suggests vibrational problems may be more feasible for quantum simulation than electronic ones.

Contribution

It introduces quantum algorithms specifically designed for vibrational structure problems, highlighting their potential advantages over electronic structure simulations.

Findings

Quantum algorithms can solve vibrational problems with fewer resources than electronic ones.

Vibrational problems may be simulatable on quantum computers before electronic problems.

Addressed challenges include multiple eigenstates and non-unitary operator calculations.

Abstract

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), and transition amplitudes with respect to a non-unitary Hermitian operator must be calculated. We address 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.