Quantum Circuit and Mapping Algorithms for Wavepacket Dynamics: Case Study of Anharmonic Hydrogen Bonds in Protonated and Hydroxide Water Clusters.

The accurate computational study of wavepacket nuclear dynamics is considered to be a classically intractable problem, particularly with increasing dimensions. Here, we present two algorithms that, in conjunction with other methods developed by us, may result in one set of contributions for performing quantum nuclear dynamics in arbitrary dimensions. For one of the two algorithms discussed here, we present a direct map between the Born-Oppenheimer Hamiltonian describing the nuclear wavepacket time evolution and the control parameters of a spin-lattice Hamiltonian that describes the dynamics of qubit states in an ion-trap quantum computer.

Quantum Nuclear Dynamics on a Distributed Set of Ion-Trap Quantum Computing Systems.

Quantum nuclear dynamics with wavepacket time evolution is classically intractable and viewed as a promising avenue for quantum information processing. Here, we use IonQ, Inc.'s 11-qubit trapped-ion quantum computer, Harmony, to study the quantum wavepacket dynamics of a shared-proton within a short-strong hydrogen-bonded system.

Resource Optimization for Quantum Dynamics with Tensor Networks: Quantum and Classical Algorithms.

The exponential scaling of the quantum degrees of freedom with the size of the system is one of the biggest challenges in computational chemistry and particularly in quantum dynamics. We present a tensor network approach for the time-evolution of the nuclear degrees of freedom of multiconfigurational chemical systems at a reduced storage and computational complexity. We also present quantum algorithms for the resultant dynamics.

Rare Events Sampling Methods for Quantum and Classical Ab Initio Molecular Dynamics.

We provide an approach to sample rare events during classical ab initio molecular dynamics and quantum wavepacket dynamics. For classical AIMD, a set of fictitious degrees of freedom are introduced that may harmonically interact with the electronic and nuclear degrees of freedom to steer the dynamics in a conservative fashion toward energetically forbidden regions. A similar approach when introduced for quantum wavepacket dynamics has the effect of biasing the trajectory of the wavepacket centroid toward the regions of the potential surface that are difficult to sample.

Reformulation of All ONIOM-Type Molecular Fragmentation Approaches and Many-Body Theories Using Graph-Theory-Based Projection Operators: Applications to Dynamics, Molecular Potential Surfaces, Machine Learning, and Quantum Computing.

We present a graph-theory-based reformulation of all ONIOM-based molecular fragmentation methods. We discuss applications to (a) accurate post-Hartree-Fock AIMD that can be conducted at DFT cost for medium-sized systems, (b) hybrid DFT condensed-phase studies at the cost of pure density functionals, (c) reduced cost on-the-fly large basis gas-phase AIMD and condensed-phase studies, (d) post-Hartree-Fock-level potential surfaces at DFT cost to obtain quantum nuclear effects, and (e) novel transfer machine learning protocols derived from these measures. Additionally, in previous work, the unifying strategy discussed here has been used to construct new quantum computing algorithms.

Capturing Weak Interactions in Surface Adsorbate Systems at Coupled Cluster Accuracy: A Graph-Theoretic Molecular Fragmentation Approach Improved through Machine Learning.

The accurate and efficient study of the interactions of organic matter with the surface of water is critical to a wide range of applications. For example, environmental studies have found that acidic polyfluorinated alkyl substances, especially perfluorooctanoic acid (PFOA), have spread throughout the environment and bioaccumulate into human populations residing near contaminated watersheds, leading to many systemic maladies. Thus, the study of the interactions of PFOA with water surfaces became important for the mitigation of their activity as pollutants and threats to public health.

Graph-|⟩⟨|: A Quantum Algorithm with Reduced Quantum Circuit Depth for Electronic Structure.

The accurate determination of chemical properties is known to have a critical impact on multiple fundamental chemical problems but is deeply hindered by the steep algebraic scaling of electron correlation calculations and the exponential scaling of quantum nuclear dynamics. With the advent of new quantum computing hardware and associated developments in creating new paradigms for quantum software, this avenue has been recognized as perhaps one way to address exponentially complex challenges in quantum chemistry and molecular dynamics. In this paper, we discuss a new approach to drastically reduce the quantum circuit depth (by several orders of magnitude) and help improve the accuracy in the quantum computation of electron correlation energies for large molecular systems.

Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics.

We describe a general formalism for quantum dynamics and show how this formalism subsumes several quantum algorithms, including the Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, Simon, and Shor algorithms as well as the conventional approach to quantum dynamics based on tensor networks. The common framework exposes similarities among quantum algorithms and natural quantum phenomena: we illustrate this connection by showing how the correlated behavior of protons in water wire systems that are common in many biological and materials systems parallels the structure of Shor's algorithm.

Quantum Computing with Dartboards.

We present a physically appealing and elegant picture for quantum computing, using rules constructed for a game of darts. A dartboard is used to represent the state space in quantum mechanics, and the act of throwing the dart is shown to have close similarities to the concept of measurement or collapse of the wave function in quantum mechanics. The analogy is constructed in arbitrary dimensional spaces, that is, using arbitrary dimensional dartboards, and for such arbitrary spaces this also provides us a "visual" description of uncertainty.

Quantum Computation of Hydrogen Bond Dynamics and Vibrational Spectra.

Calculating observable properties of chemical systems is often classically intractable and widely viewed as a promising application of quantum information processing. Here, we introduce a new framework for solving generic quantum chemical dynamics problems using quantum logic. We experimentally demonstrate a proof-of-principle instance of our method using the QSCOUT ion-trap quantum computer, where we experimentally drive the ion-trap system to emulate the quantum wavepacket dynamics corresponding to the shared-proton within an anharmonic hydrogen bonded system.

Analogy between Boltzmann Machines and Feynman Path Integrals.

Machine learning has had a significant impact on multiple areas of science, technology, health, and computer and information sciences. Through the advent of quantum computing, quantum machine learning has developed as a new and important avenue for the study of complex learning problems. Yet there is substantial debate and uncertainty in regard to the foundations of machine learning.

Graph-Theoretic Molecular Fragmentation for Potential Surfaces Leads Naturally to a Tensor Network Form and Allows Accurate and Efficient Quantum Nuclear Dynamics.

Molecular fragmentation methods have revolutionized quantum chemistry. Here, we use a graph-theoretically generated molecular fragmentation method, to obtain accurate and efficient representations for multidimensional potential energy surfaces and the quantum time-evolution operator, which plays a critical role in quantum chemical dynamics. In doing so, we find that the graph-theoretic fragmentation approach naturally reduces the potential portion of the time-evolution operator into a tensor network that contains a stream of coupled lower-dimensional propagation steps to potentially achieve quantum dynamics with reduced complexity.

Graph Theoretic Molecular Fragmentation for Multidimensional Potential Energy Surfaces Yield an Adaptive and General Transfer Machine Learning Protocol.

Over a series of publications we have introduced a graph-theoretic description for molecular fragmentation. Here, a system is divided into a set of nodes, or vertices, that are then connected through edges, faces, and higher-order simplexes to represent a collection of spatially overlapping and locally interacting subsystems. Each such subsystem is treated at two levels of electronic structure theory, and the result is used to construct many-body expansions that are then embedded within an ONIOM-scheme.

Graph-|⟩⟨|, a Graph-Based Quantum/Classical Algorithm for Efficient Electronic Structure on Hybrid Quantum/Classical Hardware Systems: Improved Quantum Circuit Depth Performance.

We present a procedure to reduce the depth of quantum circuits and improve the accuracy of results in computing post-Hartree-Fock electronic structure energies in large molecular systems. The method is based on molecular fragmentation where a molecular system is divided into overlapping fragments through a graph-theoretic procedure. This allows us to create a set of projection operators that decompose the unitary evolution of the full system into separate sets of processes, some of which can be treated on quantum hardware and others on classical hardware.

Mapping Quantum Chemical Dynamics Problems to Spin-Lattice Simulators.

The accurate computational determination of chemical, materials, biological, and atmospheric properties has a critical impact on a wide range of health and environmental problems, but is deeply limited by the computational scaling of quantum mechanical methods. The complexity of quantum chemical studies arises from the steep algebraic scaling of electron correlation methods and the exponential scaling in studying nuclear dynamics and molecular flexibility. To date, efforts to apply quantum hardware to such quantum chemistry problems have focused primarily on electron correlation.

Weighted-Graph-Theoretic Methods for Many-Body Corrections within ONIOM: Smooth AIMD and the Role of High-Order Many-Body Terms.

We present a weighted-graph-theoretic approach to adaptively compute contributions from many-body approximations for smooth and accurate post-Hartree-Fock (pHF) molecular dynamics (AIMD) of highly fluxional chemical systems. This approach is ONIOM-like, where the full system is treated at a computationally feasible quality of treatment (density functional theory (DFT) for the size of systems considered in this publication), which is then improved through a perturbative correction that captures local many-body interactions up to a certain order within a higher level of theory (post-Hartree-Fock in this publication) described through graph-theoretic techniques. Due to the fluxional and dynamical nature of the systems studied here, these graphical representations evolve during dynamics.

Efficient and Accurate Approach To Estimate Hybrid Functional and Large Basis-Set Contributions to Condensed-Phase Systems and Molecule-Surface Interactions.

We present a graph theoretic approach to adaptively compute contributions from many-body approximations in an efficient manner and perform accurate hybrid density functional theory (DFT) electronic structure calculations for condensed-phase systems. The salient features of the approach are ONIOM-like. (a) The full-system calculation is performed at a lower level of theory (pure DFT) by enforcing periodic boundary conditions.

Challenges in constructing accurate methods for hydrogen transfer reactions in large biological assemblies: rare events sampling for mechanistic discovery and tensor networks for quantum nuclear effects.

We present two methods that address the computational complexities arising in hydrogen transfer reactions in enzyme active sites. To address the challenge of reactive rare events, we begin with an ab initio molecular dynamics adaptation of the Caldeira-Leggett system-bath Hamiltonian and apply this approach to the study of the hydrogen transfer rate-determining step in soybean lipoxygenase-1. Through direct application of this method to compute an ensemble of classical trajectories, we discuss the critical role of isoleucine-839 in modulating the primary hydrogen transfer event in SLO-1.

Fragment-Based Electronic Structure for Potential Energy Surfaces Using a Superposition of Fragmentation Topologies.

We present a new approach for adaptive molecular fragmentation. Here multiple fragmentation protocols, or fragmentation topologies, are combined to efficiently and accurately construct potential energy surfaces that are in agreement with post-Hartree-Fock levels of electronic structure theories at density functional theory (DFT) cost. We benchmark the method through evaluation of quantum nuclear effects in a set of protonated water clusters that are known to display significant quantum effects.

Photoelectrons Are Not Always Quite Free.

The photoelectron spectra of SmO obtained over a range of photon energies exhibit anomalous changes in relative excited-state band intensities. Specifically, the excited-state transition intensities increase relative to the transition to the neutral ground state with decreasing photon energy, the opposite of what is expected from threshold effects. This phenomenon was previously observed in studies on several Sm-rich homo- and heterolanthanide oxides collected with two different harmonic outputs of a Nd:YAG (2.

Efficiently Capturing Weak Interactions in ab Initio Molecular Dynamics with on-the-Fly Basis Set Extrapolation.

Weak interactions have a critical role in accurately portraying conformational change. However, the computational study of these often requires large basis electronic structure calculations that are generally cost-prohibitive within ab initio molecular dynamics. Here, we present a new approach to efficiently obtain AIMD trajectories in agreement with large, triple-ζ, polarized valence basis functions, at much reduced computational cost.

Exotic electronic structures of SmCeO (x = 0-3; y = 2-4) clusters and the effect of high neutral density of low-lying states on photodetachment transition intensities.

Lanthanide (Ln) oxide clusters have complex electronic structures arising from the partially occupied Ln 4f subshell. New anion photoelectron (PE) spectra of SmCeO (x = 0-3; y = 2-4) along with supporting results of density functional theory (DFT) calculations suggest interesting x and y-dependent Sm 4f subshell occupancy with implications for Sm-doped ionic conductivity of ceria, as well as the overall electronic structure of the heterometallic oxides. Specifically, the Sm centers in the heterometallic species have higher 4f subshell occupancy than the homonuclear SmO/SmO clusters.

Adaptive, Geometric Networks for Efficient Coarse-Grained Ab Initio Molecular Dynamics with Post-Hartree-Fock Accuracy.

We introduce a new coarse-graining technique for ab initio molecular dynamics that is based on the adaptive generation of connected geometric networks or graphs specific to a given molecular geometry. The coarse-grained nodes depict a local chemical environment and are networked to create edges, triangles, tetrahedrons, and higher order simplexes based on (a) a Delaunay triangulation procedure and (b) a method that is based on molecular, bonded and nonbonded, local interactions. The geometric subentities thus created, that is nodes, edges, triangles, and tetrahedrons, each represent an energetic measure for a specific portion of the molecular system, capturing a specific set of interactions.