Using a photonic quantum computer for boson sampling has demonstrated a tremendous advantage over classical supercomputers. It is highly desirable to develop boson sampling algorithms for realistic scientific problems. In this work, we propose a hybrid quantum-classical sampling (HQCS) algorithm to calculate the optical spectrum for complex molecules considering Duschinsky rotation effects and anharmonicity. The classical sum-over-states method for this problem has a computational complexity that exponentially increases with system size. The HQCS algorithm creates an intermediate harmonic potential energy surface (PES) to bridge the initial and final PESs. The magnitude and sign of the overlap between the initial and the intermediate state are estimated by boson sampling and classical algorithms, respectively. The overlap between the intermediate and the final state is efficiently evaluated by classical algorithms. The feasibility of HQCS is demonstrated in calculations of the emission spectrum of a Morse model as well as the pyridine molecule.
Using a photonic quantum computer for boson sampling has demonstrated a tremendous advantage over classical supercomputers. It is highly desirable to develop boson sampling algorithms for realistic scientific problems. In this work, we propose a hybrid quantum-classical sampling (HQCS) algorithm to calculate the optical spectrum for complex molecules considering Duschinsky rotation effects and anharmonicity. The classical sum-over-states method for this problem has a computational complexity that exponentially increases with system size. The HQCS algorithm creates an intermediate harmonic potential energy surface (PES) to bridge the initial and final PESs. The magnitude and sign of the overlap between the initial and the intermediate state are estimated by boson sampling and classical algorithms, respectively. The overlap between the intermediate and the final state is efficiently evaluated by classical algorithms. The feasibility of HQCS is demonstrated in calculations of the emission spectrum of a Morse model as well as the pyridine molecule.
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.
Abstract Electronic spectroscopy is today among the most powerful methods for studying chemical systems, and state-resolved (line-assigned) simulations are essential for attributing spectral features to specific vibrational excitations. The standard time-independent sum-over-states (SOS) route provides line assignments; while effective with truncation and prescreening, it can become computationally demanding as the number of modes increases. Vibronic boson sampling (VBS) offers an event-based alternative, but scaling photonic implementations remains challenging and the required vibronic inputs can be demanding for larger systems. Here we introduce coherent-state sampling (CSS), a sampling scheme for the Linear Coupling Model (LCM), where vibrational modes are independent. This enables a photonic architecture based on a single reconfigurable optical channel with essentially fixed hardware complexity; increasing system size is handled by additional measurement iterations rather than additional optical modes. Using pentacene as a test case, we demonstrate an end-to-end workflow—electronic-structure input, sampling strategy, hardware validation, and comparison to experiment—showing that both a laptop implementation and a superconducting-detector photonic implementation reproduce reference spectra with high fidelity and yield band shapes in good agreement with experiment. While not targeting quantum advantage, CSS provides a practically scalable, state-resolved tool for LCM vibronic spectroscopy and a controlled displacement-dominated complement to more general VBS schemes.
Molecular vibroic spectroscopy, where the transitions involve non-trivial Bosonic correlation due to the Duschinsky Rotation, is strongly believed to be in a similar complexity class as Boson Sampling. At finite temperature, the problem is represented as a Boson Sampling experiment with correlated Gaussian input states. This molecular problem with temperature effect is intimately related to the various versions of Boson Sampling sharing the similar computational complexity. Here we provide a full description to this relation in the context of Gaussian Boson Sampling. We find a hierarchical structure, which illustrates the relationship among various Boson Sampling schemes. Specifically, we show that every instance of Gaussian Boson Sampling with an initial correlation can be simulated by an instance of Gaussian Boson Sampling without initial correlation, with only a polynomial overhead. Since every Gaussian state is associated with a thermal state, our result implies that every sampling problem in molecular vibronic transitions, at any temperature, can be simulated by Gaussian Boson Sampling associated with a product of vacuum modes. We refer such a generalized Gaussian Boson Sampling motivated by the molecular sampling problem as Vibronic Boson Sampling.
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.
Developing efficient quantum computing algorithms is essential for tackling computationally challenging problems across various fields. This paper presents a novel quantum algorithm, XZ24, for efficiently computing the eigen-energy spectra of arbitrary quantum systems. Given a Hamiltonian H^ and an initial reference state ∣ψref⟩, the algorithm extracts information about ⟨ψref∣cos(H^t)∣ψref⟩ from an auxiliary qubit's state. By applying a Fourier transform, the algorithm resolves the energies of eigenstates of the Hamiltonian with significant overlap with the reference wavefunction. We provide a theoretical analysis and numerical simulations, showing XZ24's superior efficiency and accuracy compared to existing algorithms. XZ24 has three key advantages: 1. It removes the need for eigenstate preparation, requiring only a reference state with non-negligible overlap, improving upon methods like the Variational Quantum Eigensolver. 2. It reduces measurement overhead, measuring only one auxiliary qubit. For a system of size L with precision ε, the sampling complexity scales as O(L⋅ε−1). When relative precision ε is sufficient, the complexity scales as O(ε−1), making measurements independent of system size. 3. It enables simultaneous computation of multiple eigen-energies, depending on the reference state. We anticipate that XZ24 will advance quantum system simulations and enhance applications in quantum computing.
Quantum-centric workflows are a promising route to improving the accuracy of property predictions in computational chemistry and materials science. By integrating quantum sampling algorithms with classical solvers, electronic structure calculations have recently demonstrated their potential even on noisy intermediate-scale quantum devices. In principle, the method of Vibrational Configuration Interaction (VCI) is suitable for integration with quantum sampling algorithms as well. However, demonstrations of computational workflows for quantum-centric, vibrational property predictions are still lacking. Here, we introduce a methodology for performing anharmonic vibrational structure calculations that can be deployed in a hybrid, quantum-classical mode. Starting from a quartic force field, the approach combines a Vibrational Self-Consistent Field (VSCF) with VCI in either Full, Selected (S-VCI), or Symmetry-Adapted (SA-VCI) mode. In S-VCI, an Epstein-Nesbet perturbative screening significantly reduces the configuration space while retaining high predictive accuracy. A state-list input enables the integration of externally generated vibrational configurations as a seed space. As a proof-of-concept, we demonstrate a hybrid, quantum-classical computational workflow, in which a quantum sampling algorithm provides the seed. Our vibrational wave function analysis package ViBra, equipped with a graphical interface, is available at https://github.com/raphafe96/ViBra.