Molecular Quantum Dynamics: A Quantum Computing Perspective

Simulating Chemistry on Bosonic Quantum Devices

Bosonic quantum devices offer a novel approach to realize quantum computations, where the quantum two-level system (qubit) is replaced with the quantum (an)harmonic oscillator (qumode) as the fundamental building block of the quantum simulator. The simulation of chemical structure and dynamics can then be achieved by representing or mapping the system Hamiltonians in terms of bosonic operators. In this Perspective, we review recent progress and future potential of using bosonic quantum devices for addressing a wide range of challenging chemical problems, including the calculation of molecular vibronic spectra, the simulation of gas-phase and solution-phase adiabatic and nonadiabatic chemical dynamics, the efficient solution of molecular graph theory problems, and the calculations of electronic structure.

Reconfigurable quantum photonic circuits based on quantum dots

Quantum photonic integrated circuits, composed of linear-optical elements, offer an efficient way for encoding and processing quantum information on-chip. At their core, these circuits rely on reconfigurable phase shifters, typically constructed from classical components such as thermo- or electro-optical materials, while quantum solid-state emitters such as quantum dots are limited to acting as single-photon sources. Here, we demonstrate the potential of quantum dots as reconfigurable phase shifters. We use numerical models based on established literature parameters to show that circuits utilizing these emitters enable high-fidelity operation and are scalable. Despite the inherent imperfections associated with quantum dots, such as imperfect coupling, dephasing, or spectral diffusion, we show that circuits based on these emitters may be optimized such that these do not significantly impact the unitary infidelity. Specifically, they do not increase the infidelity by more than 0.001 in circuits with up to 10 modes, compared to those affected only by standard nanophotonic losses and routing errors. For example, we achieve fidelities of 0.9998 in quantum-dot-based circuits enacting controlled-phase and - not gates without any redundancies. These findings demonstrate the feasibility of quantum emitter-driven quantum information processing and pave the way for cryogenically-compatible, fast, and low-loss reconfigurable quantum photonic circuits.

Quantum circuit for high order perturbation theory corrections

Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which has led to a wide variety of applications. Over the past decades, advances in quantum computing provide opportunities for alternatives to classical methods. Recently, a general quantum circuit estimating the low order PT corrections has been proposed. In this article, we revisit the quantum circuits for PT calculations, and develop the methods for higher order PT corrections of eigenenergy, especially the 3rd and 4th order corrections. We present the feasible quantum circuit to estimate each term in these PT corrections. There are two the fundamental operations in the proposed circuit. One approximates the perturbation terms, the other approximates the inverse of unperturbed energy difference. The proposed method can be generalized to higher order PT corrections.

Efficient simulation of potential energy operators on quantum hardware: a study on sodium iodide (NaI)

This study introduces a conceptually novel polynomial encoding algorithm for simulating potential energy operators encoded in diagonal unitary forms in a quantum computing machine. The current trend in quantum computational chemistry is effective experimentation to achieve high-precision quantum computational advantage. However, high computational gate complexity and fidelity loss are some of the impediments to the realization of this advantage in a real quantum hardware. In this study, we address the challenges of building a diagonal Hamiltonian operator having exponential functional form, and its implementation in the context of the time evolution problem (Hamiltonian simulation and encoding). Potential energy operators when represented in the first quantization form is an example of such types of operators. Through systematic decomposition and construction, we demonstrate the efficacy of the proposed polynomial encoding method in reducing gate complexity from O ( 2 n ) to O ∑ i = 1 r n C r (for some r ≪ n ). This offers a solution with lower complexity in comparison to the conventional Hadamard basis encoding approach. The effectiveness of the proposed algorithm was validated with its implementation in the IBM quantum simulator and IBM quantum hardware. This study demonstrates the proposed approach by taking the example of the potential energy operator of the sodium iodide molecule (NaI) in the first quantization form. The numerical results demonstrate the potential applicability of the proposed method in quantum chemistry problems, while the analytical bound for error analysis and computational gate complexity discussed, throw light on issues regarding its implementation.

Quantum simulation of conical intersections

We explore the simulation of conical intersections (CIs) on quantum devices, setting the groundwork for potential applications in nonadiabatic quantum dynamics within molecular systems. The intersecting potential energy surfaces of H3+ are computed from a variance-based contracted quantum eigensolver. We show how the CIs can be correctly described on quantum devices using wavefunctions generated by the anti-Hermitian contracted Schrödinger equation ansatz, which is a unitary transformation of wavefunctions that preserves the topography of CIs. A hybrid quantum-classical procedure is used to locate the seam of CIs. Additionally, we discuss the quantum implementation of the adiabatic to diabatic transformation and its relation to the geometric phase effect. Results on noisy intermediate-scale quantum devices showcase the potential of quantum computers in dealing with problems in nonadiabatic chemistry.

Simulating chemical reaction dynamics on quantum computer

The electronic energies of molecules have been successfully evaluated on quantum computers. However, more attention is paid to the dynamics simulation of molecules in practical applications. Based on the variational quantum eigensolver (VQE) algorithm, Fedorov et al. proposed a correlated sampling (CS) method and demonstrated the vibrational dynamics of H2 molecules [J. Chem. Phys. 154, 164103 (2021)]. In this study, we have developed a quantum approach by extending the CS method based on the VQE algorithm (labeled eCS-VQE) for simulating chemical reaction dynamics. First, the CS method is extended to the three-dimensional cases for calculation of first-order energy gradients, and then, it is further generalized to calculate the second-order gradients of energies. By calculating atomic forces and vibrational frequencies for H2, LiH, H+ + H2, and Cl- + CH3Cl systems, we have seen that the approach has achieved the CCSD level of accuracy. Thus, we have simulated dynamics processes for two typical chemical reactions, hydrogen exchange and chlorine substitution, and obtained high-precision reaction dynamics trajectories consistent with the classical methods. Our eCS-VQE approach, as measurement expectations and ground-state wave functions can be reused, is less demanding in quantum computing resources and is, therefore, a feasible means for the dynamics simulation of chemical reactions on the current noisy intermediate-scale quantum-era quantum devices.

Harvesting Chemical Understanding with Machine Learning and Quantum Computers

It is tenable to argue that nobody can predict the future with certainty, yet one can learn from the past and make informed projections for the years ahead. In this Perspective, we overview the status of how theory and computation can be exploited to obtain chemical understanding from wave function theory and density functional theory, and then outlook the likely impact of machine learning (ML) and quantum computers (QC) to appreciate traditional chemical concepts in decades to come. It is maintained that the development and maturation of ML and QC methods in theoretical and computational chemistry represent two paradigm shifts about how the Schrödinger equation can be solved. New chemical understanding can be harnessed in these two new paradigms by making respective use of ML features and QC qubits. Before that happens, however, we still have hurdles to face and obstacles to overcome in both ML and QC arenas. Possible pathways to tackle these challenges are proposed. We anticipate that hierarchical modeling, in contrast to multiscale modeling, will emerge and thrive, becoming the workhorse of in silico simulations in the next few decades.

Implementation of the Projective Quantum Eigensolver on a Quantum Computer

We study the performance of our previously proposed projective quantum eigensolver (PQE) on IBM's quantum hardware in conjunction with error mitigation techniques. For a single qubit model of H2, we find that we are able to obtain energies within 4 millihartree (2.5 kcal/mol) of the exact energy along the entire potential energy curve, with the accuracy limited by both the stochastic error and the inconsistent performance of the IBM devices. We find that an optimization algorithm using direct inversion of the iterative subspace can converge swiftly, even to excited states, but stochastic noise can prompt large parameter updates. For the 4-site transverse-field Ising model at its critical point, PQE with an appropriate application of qubit tapering can recover 99% of the correlation energy, even after discarding several parameters. The large number of CNOT gates needed for the additional parameters introduces a concomitant error that, on the IBM devices, results in a loss of accuracy despite the increased expressivity of the trial state. Error extrapolation techniques and tapering or postselection are recommended to mitigate errors in PQE hardware experiments.

Improving potential energy surfaces using measured Feshbach resonance states

The structure and dynamics of a molecular system is governed by its potential energy surface (PES), representing the total energy as a function of the nuclear coordinates. Obtaining accurate potential energy surfaces is limited by the exponential scaling of Hilbert space, restricting quantitative predictions of experimental observables from first principles to small molecules with just a few electrons. Here, we present an explicitly physics-informed approach for improving and assessing the quality of families of PESs by modifying them through linear coordinate transformations based on experimental data. We demonstrate this "morphing" of the PES for the He - H2+ complex using recent comprehensive Feshbach resonance (FR) measurements for reference PESs at three different levels of quantum chemistry. In all cases, the positions and intensities of peaks in the energy distributions are improved. We find these observables to be mainly sensitive to the long-range part of the PES.

Data-Driven Protein Engineering for Improving Catalytic Activity and Selectivity

Protein engineering is essential for altering the substrate scope, catalytic activity and selectivity of enzymes for applications in biocatalysis. However, traditional approaches, such as directed evolution and rational design, encounter the challenge in dealing with the experimental screening process of a large protein mutation space. Machine learning methods allow the approximation of protein fitness landscapes and the identification of catalytic patterns using limited experimental data, thus providing a new avenue to guide protein engineering campaigns. In this concept article, we review machine learning models that have been developed to assess enzyme-substrate-catalysis performance relationships aiming to improve enzymes through data-driven protein engineering. Furthermore, we prospect the future development of this field to provide additional strategies and tools for achieving desired activities and selectivities.

Machine Learning-Guided Protein Engineering

Recent progress in engineering highly promising biocatalysts has increasingly involved machine learning methods. These methods leverage existing experimental and simulation data to aid in the discovery and annotation of promising enzymes, as well as in suggesting beneficial mutations for improving known targets. The field of machine learning for protein engineering is gathering steam, driven by recent success stories and notable progress in other areas. It already encompasses ambitious tasks such as understanding and predicting protein structure and function, catalytic efficiency, enantioselectivity, protein dynamics, stability, solubility, aggregation, and more. Nonetheless, the field is still evolving, with many challenges to overcome and questions to address. In this Perspective, we provide an overview of ongoing trends in this domain, highlight recent case studies, and examine the current limitations of machine learning-based methods. We emphasize the crucial importance of thorough experimental validation of emerging models before their use for rational protein design. We present our opinions on the fundamental problems and outline the potential directions for future research.

Mapping Molecular Hamiltonians into Hamiltonians of Modular cQED Processors

We introduce a general method based on the operators of the Dyson-Masleev transformation to map the Hamiltonian of an arbitrary model system into the Hamiltonian of a circuit Quantum Electrodynamics (cQED) processor. Furthermore, we introduce a modular approach to programming a cQED processor with components corresponding to the mapping Hamiltonian. The method is illustrated as applied to quantum dynamics simulations of the Fenna-Matthews-Olson (FMO) complex and the spin-boson model of charge transfer. Beyond applications to molecular Hamiltonians, the mapping provides a general approach to implement any unitary operator in terms of a sequence of unitary transformations corresponding to powers of creation and annihilation operators of a single bosonic mode in a cQED processor.

Interaction between hydrophobic chitosan derivative and asphaltene in heavy oil to reduce viscosity of heavy oil

The high viscosity of heavy oil made it difficult to exploit and transport heavy oil in pipeline. In this research, N-[(2-hydroxy-3-trimethylammonium) propyl] O-stearoyl chitosan tetraphenylboride (sc-CTS-st) was synthesized from chitosan, 2, 3-epoxy-propyl trimethyl ammonium chloride, sodium tetraphenylboron and stearyl chloride. sc-CTS-st contains long chain saturated aliphatic hydrocarbon, hydroxyl group and benzene ring, which could be dissolved in heavy oil fully and interacted with asphaltene. At 50 °C, the viscosity of heavy oil could be reduced to 13,800 mPa·s at most, with a viscosity reduction rate of 57.54 %. SEM and XRD showed that sc-CTS-st could affect the supramolecular accumulation structure of asphaltenes. Using FT-IR, sc-CTS-st could interact with asphaltene in the form of hydrogen bonds using the polar parts of the molecule, thereby weakening the self-association between asphaltene molecules. Molecular simulation was used to demonstrate the interaction mechanism between chitosan derivatives and asphaltenes. sc-CTS-st interacted with asphaltene through chemical bonding and influenced the self-association of asphaltene molecules. In addition, the non-polar portion of sc-CTS-st molecules could form a coating on the outside of the asphaltenes stacking structure, thus shielding or reducing the polarity of the stacking structure surface.

TenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era

TenCirChem is an open-source Python library for simulating variational quantum algorithms for quantum computational chemistry. TenCirChem shows high-performance in the simulation of unitary coupled-cluster circuits, using compact representations of quantum states and excitation operators. Additionally, TenCirChem supports noisy circuit simulation and provides algorithms for variational quantum dynamics. TenCirChem's capabilities are demonstrated through various examples, such as the calculation of the potential energy curve of H₂O with a 6-31G(d) basis set using a 34-qubit quantum circuit, the examination of the impact of quantum gate errors on the variational energy of the H₂ molecule, and the exploration of the Marcus inverted region for charge transfer rate based on variational quantum dynamics. Furthermore, TenCirChem is capable of running real quantum hardware experiments, making it a versatile tool for both simulation and experimentation in the field of quantum computational chemistry.

Quantum algorithms for quantum dynamics

Among the many computational challenges faced across different disciplines, quantum-mechanical systems pose some of the hardest ones and offer a natural playground for the growing field of quantum technologies. In this Perspective, we discuss quantum algorithmic solutions for quantum dynamics, reporting on the latest developments and offering a viewpoint on their potential and current limitations. We present some of the most promising areas of application and identify possible research directions for the coming years.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Quantum Algorithm for Numerical Energy Gradient Calculations at the Full Configuration Interaction Level of Theory

A Bayesian phase difference estimation (BPDE) algorithm allows us to compute the energy gap of two electronic states of a given Hamiltonian directly by utilizing the quantum superposition of their wave functions. Here we report an extension of the BPDE algorithm to the direct calculation of the energy difference of two molecular geometries. We apply the BPDE algorithm for the calculation of numerical energy gradients based on the two-point finite-difference method, enabling us to execute geometry optimization of one-dimensional molecules at the full-CI level on a quantum computer. Results of numerical quantum circuit simulations of the geometry optimization of the H₂ molecule with the STO-3G and 6-31G basis sets, the LiH and BeH₂ molecules at the full-CI/STO-3G level, and the N₂ molecule at the CASCI(6e,6o)/6-311G* level are given.

SP-A binding to the SARS-CoV-2 spike protein using hybrid quantum and classical in silico modeling and molecular pruning by Quantum Approximate Optimization Algorithm (QAOA) Based MaxCut with ZDOCK

The pulmonary surfactant protein A (SP-A) is a constitutively expressed immune-protective collagenous lectin (collectin) in the lung. It binds to the cell membrane of immune cells and opsonizes infectious agents such as bacteria, fungi, and viruses through glycoprotein binding. SARS-CoV-2 enters airway epithelial cells by ligating the Angiotensin Converting Enzyme 2 (ACE2) receptor on the cell surface using its Spike glycoprotein (S protein). We hypothesized that SP-A binds to the SARS-CoV-2 S protein and this binding interferes with ACE2 ligation. To study this hypothesis, we used a hybrid quantum and classical in silico modeling technique that utilized protein graph pruning. This graph pruning technique determines the best binding sites between amino acid chains by utilizing the Quantum Approximate Optimization Algorithm (QAOA)-based MaxCut (QAOA-MaxCut) program on a Near Intermediate Scale Quantum (NISQ) device. In this, the angles between every neighboring three atoms were Fourier-transformed into microwave frequencies and sent to a quantum chip that identified the chemically irrelevant atoms to eliminate based on their chemical topology. We confirmed that the remaining residues contained all the potential binding sites in the molecules by the Universal Protein Resource (UniProt) database. QAOA-MaxCut was compared with GROMACS with T-REMD using AMBER, OPLS, and CHARMM force fields to determine the differences in preparing a protein structure docking, as well as with Goemans-Williamson, the best classical algorithm for MaxCut. The relative binding affinity of potential interactions between the pruned protein chain residues of SP-A and SARS-CoV-2 S proteins was assessed by the ZDOCK program. Our data indicate that SP-A could ligate the S protein with a similar affinity to the ACE2-Spike binding. Interestingly, however, the results suggest that the most tightly-bound SP-A binding site is localized to the S2 chain, in the fusion region of the SARS-CoV-2 S protein, that is responsible for cell entry Based on these findings we speculate that SP-A may not directly compete with ACE2 for the binding site on the S protein, but interferes with viral entry to the cell by hindering necessary conformational changes or the fusion process.

Quantum embedding theories to simulate condensed systems on quantum computers

Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties that are more complex than tractable at present on classical architectures. Here, we discuss computational frameworks to carry out electronic structure calculations of solids on noisy intermediate-scale quantum computers using embedding theories, and we give examples for a specific class of materials, that is, solid materials hosting spin defects. These are promising systems to build future quantum technologies, such as quantum computers, quantum sensors and quantum communication devices. Although quantum simulations on quantum architectures are in their infancy, promising results for realistic systems appear to be within reach.

Molecular simulations of complex carbohydrates and glycoconjugates

Complex carbohydrates (glycans) are the most abundant and versatile biopolymers in nature. The broad diversity of biochemical functions that carbohydrates cover is a direct consequence of the variety of 3D architectures they can adopt, displaying branched or linear arrangements, widely ranging in sizes, and with the highest diversity of building blocks of any other natural biopolymer. Despite this unparalleled complexity, a common denominator can be found in the glycans' inherent flexibility, which hinders experimental characterization, but that can be addressed by high-performance computing (HPC)-based molecular simulations. In this short review, I present and discuss the state-of-the-art of molecular simulations of complex carbohydrates and glycoconjugates, highlighting methodological strengths and weaknesses, important insights through emblematic case studies, and suggesting perspectives for future developments.

Quantum Gaussian process model of potential energy surface for a polyatomic molecule

With gates of a quantum computer designed to encode multi-dimensional vectors, projections of quantum computer states onto specific qubit states can produce kernels of reproducing kernel Hilbert spaces. We show that quantum kernels obtained with a fixed ansatz implementable on current quantum computers can be used for accurate regression models of global potential energy surfaces (PESs) for polyatomic molecules. To obtain accurate regression models, we apply Bayesian optimization to maximize marginal likelihood by varying the parameters of the quantum gates. This yields Gaussian process models with quantum kernels. We illustrate the effect of qubit entanglement in the quantum kernels and explore the generalization performance of quantum Gaussian processes by extrapolating global six-dimensional PESs in the energy domain.