Chemical Problems Research Articles

Lineup polytopes of products of simplices

Consider a real point configuration \bm{A} of size n and an integer r \leq n . The vertices of the r -lineup polytope of \bm{A} correspond to the possible orderings of the top r points of the configuration obtained by maximizing a linear functional. The motivation behind the study of lineup polytopes comes from the representability problem in quantum chemistry. In that context, the relevant point configurations are the vertices of hypersimplices and the integer points contained in an inflated regular simplex. The central problem consists in providing an inequality representation of lineup polytopes as efficiently as possible. In this article, we adapt the developed techniques to the quantum information theory setup. The appropriate point configurations become the vertices of products of simplices. A particular case is that of lineup polytopes of cubes, which form a type B analog of hypersimplices, where the symmetric group of type A naturally acts. To obtain the inequalities, we center our attention on the combinatorics and the symmetry of products of simplices to obtain an algorithmic solution. Along the way, we establish relationships between lineup polytopes of products of simplices with the Gale order, standard Young tableaux, and the resonance arrangement.

KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Search

AbstractQuantum architecture Search (QAS) is a promising direction for optimization and automated design of quantum circuits towards quantum advantage. Recent techniques in QAS emphasize Multi-Layer Perceptron (MLP)-based deep Q-networks. However, their interpretability remains challenging due to the large number of learnable parameters and the complexities involved in selecting appropriate activation functions. In this work, to overcome these challenges, we utilize the Kolmogorov-Arnold Network (KAN) in the QAS algorithm, analyzing their efficiency in the task of quantum state preparation and quantum chemistry. In quantum state preparation, our results show that in a noiseless scenario, the probability of success is 2× to 5× higher than MLPs. In noisy environments, KAN outperforms MLPs in fidelity when approximating these states, showcasing its robustness against noise. In tackling quantum chemistry problems, we enhance the recently proposed QAS algorithm by integrating curriculum reinforcement learning with a KAN structure. This facilitates a more efficient design of parameterized quantum circuits by reducing the number of required 2-qubit gates and circuit depth. Further investigation reveals that KAN requires a significantly smaller number of learnable parameters compared to MLPs; however, the average time of executing each episode for KAN is higher.

Ultrastrong coupling limit to quantum mean force Gibbs state for anharmonic environment.

The equilibrium state of a quantum system can deviate from the Gibbs state if the system-environment (SE) coupling is not weak. An analytical expression for this mean force Gibbs state (MFGS) is known in the ultrastrong coupling (USC) regime for the Caldeira-Leggett (CL) model that assumes a harmonic environment. Here, we derive analytical expressions for the MFGS in the USC regime for more general SEmodels. For all the generalized models considered here, we find the USC state to be diagonal in the basis set by the SEinteraction, just like in the CL case. While for the generic model considered, the corresponding USC-MFGS is found to alter from the CL result, we do identify a class of models more general than the CL model for which the CL-USC result remains unchanged. We also provide numerical verification for our results. These results provide key tools for the study of strong coupling quantum thermodynamics and several quantum chemistry and biology problems under more realistic SEmodels, going beyond the CL model.

A circuit-generated quantum subspace algorithm for the variational quantum eigensolver.

Recent research has shown that wavefunction evolution in real and imaginary time can generate quantum subspaces with significant utility for obtaining accurate ground state energies. Inspired by these methods, we propose combining quantum subspace techniques with the variational quantum eigensolver (VQE). In our approach, the parameterized quantum circuit is divided into a series of smaller subcircuits. The sequential application of these subcircuits to an initial state generates a set of wavefunctions that we use as a quantum subspace to obtain high-accuracy groundstate energies. We call this technique the circuit subspace variational quantum eigensolver (CSVQE) algorithm. By benchmarking CSVQE on a range of quantum chemistry problems, we show that it can achieve significant error reduction in the best case compared to conventional VQE, particularly for poorly optimized circuits, greatly improving convergence rates. Furthermore, we demonstrate that when applied to circuits trapped at local minima, CSVQE can produce energies close to the global minimum of the energy landscape, making it a potentially powerful tool for diagnosing local minima.

Arithmetic Proficiency of Pre-Service Science Teachers: An Empirical Study

Mastery of arithmetic operations is fundamental for students pursuing science education, as these skills are essential in solving complex problems in physics, chemistry, and biology. However, gaps in students' arithmetic proficiency can hinder their academic and professional development. This study aims to examine the arithmetic skills of pre-service science teachers in solving mathematical problems across six domains: addition, subtraction, multiplication, division, exponentiation, and mixed operations. A total of 37 short-answer questions were administered, and the results were analyzed by domain. The findings indicate that students demonstrate proficiency in basic operations involving whole numbers, particularly in addition and subtraction. However, challenges persist in the areas of fractions, decimals, and mixed operations, where accuracy rates were notably lower. These gaps in understanding may affect students' ability to apply mathematical concepts in their science courses and future teaching roles. The study's limitations include a focus on quantitative results without exploring the cognitive processes behind student errors. Future research should investigate intervention strategies to address these weaknesses, potentially through targeted instructional approaches or the use of technology to enhance learning outcomes

Qudit-based variational quantum eigensolver using photonic orbital angular momentum states.

Solving the electronic structure problem is a notorious challenge in quantum chemistry and material science. Variational quantum eigensolver (VQE) is a promising hybrid classical-quantum algorithm for finding the lowest-energy configuration of a molecular system. However, it typically requires many qubits and quantum gates with substantial quantum circuit depth to accurately represent the electronic wave function of complex structures. Here, we propose an alternative approach to solve the electronic structure problem using VQE with a single qudit. Our approach exploits a high-dimensional orbital angular momentum state of a heralded single photon and notably reduces the required quantum resources compared to conventional multi-qubit-based VQE. We experimentally demonstrate that our single-qudit-based VQE can efficiently estimate the ground state energy of hydrogen (H2) and lithium hydride (LiH) molecular systems corresponding to two- and four-qubit systems, respectively. We believe that our scheme opens a pathway to perform a large-scale quantum simulation for solving more complex problems in quantum chemistry and material science.

Variational quantum imaginary time evolution for matrix product state Ansatz with tests on transcorrelated Hamiltonians.

The matrix product state (MPS) Ansatz offers a promising approach for finding the ground state of molecular Hamiltonians and solving quantum chemistry problems. Building on this concept, the proposed technique of quantum circuit MPS (QCMPS) enables the simulation of chemical systems using a relatively small number of qubits. In this study, we enhance the optimization performance of the QCMPS Ansatz by employing the variational quantum imaginary time evolution (VarQITE) approach. Guided by McLachlan's variational principle, the VarQITE method provides analytical metrics and gradients, resulting in improved convergence efficiency and robustness of the QCMPS. We validate these improvements numerically through simulations of H2, H4, and LiH molecules. In addition, given that VarQITE is applicable to non-Hermitian Hamiltonians, we evaluate its effectiveness in preparing the ground state of transcorrelated Hamiltonians. This approach yields energy estimates comparable to the complete basis set (CBS) limit while using even fewer qubits. In particular, we perform simulations of the beryllium atom and LiH molecule using only three qubits, maintaining high fidelity with the CBS ground state energy of these systems. This qubit reduction is achieved through the combined advantages of both the QCMPS Ansatz and transcorrelation. Our findings demonstrate the potential practicality of this quantum chemistry algorithm on near-term quantum devices.

Parallel Implementation of the Density Matrix Renormalization Group Method Achieving a Quarter petaFLOPS Performance on a Single DGX-H100 GPU Node.

We report cutting edge performance results on a single node hybrid CPU-multi-GPU implementation of the spin adapted ab initio Density Matrix Renormalization Group (DMRG) method on current state-of-the-art NVIDIA DGX-H100 architectures. We evaluate the performance of the DMRG electronic structure calculations for the active compounds of the FeMoco, the primary cofactor of nitrogenase, and cytochrome P450 (CYP) enzymes with complete active space (CAS) sizes of up to 113 electrons in 76 orbitals [CAS(113, 76)] and 63 electrons in 58 orbitals [CAS(63, 58)], respectively. We achieve 246 teraFLOPS of sustained performance, an improvement of more than 2.5× compared to the performance achieved on the DGX-A100 architectures and an 80× acceleration compared to an OpenMP parallelized implementation on a 128-core CPU architecture. Our work highlights the ability of tensor network algorithms to efficiently utilize high-performance multi-GPU hardware and shows that the combination of tensor networks with modern large-scale GPU accelerators can pave the way toward solving some of the most challenging problems in quantum chemistry and beyond.

Spectral Map for Slow Collective Variables, Markovian Dynamics, and Transition State Ensembles.

Understanding the behavior of complex molecular systems is a fundamental problem in physical chemistry. To describe the long-time dynamics of such systems, which is responsible for their most informative characteristics, we can identify a few slow collective variables (CVs) while treating the remaining fast variables as thermal noise. This enables us to simplify the dynamics and treat it as diffusion in a free-energy landscape spanned by slow CVs, effectively rendering the dynamics Markovian. Our recent statistical learning technique, spectral map [Rydzewski, J. J. Phys. Chem. Lett. 2023, 14(22), 5216-5220], explores this strategy to learn slow CVs by maximizing a spectral gap of a transition matrix. In this work, we introduce several advancements into our framework, using a high-dimensional reversible folding process of a protein as an example. We implement an algorithm for coarse-graining Markov transition matrices to partition the reduced space of slow CVs kinetically and use it to define a transition state ensemble. We show that slow CVs learned by spectral map closely approach the Markovian limit for an overdamped diffusion. We demonstrate that coordinate-dependent diffusion coefficients only slightly affect the constructed free-energy landscapes. Finally, we present how spectral maps can be used to quantify the importance of features and compare slow CVs with structural descriptors commonly used in protein folding. Overall, we demonstrate that a single slow CV learned by spectral map can be used as a physical reaction coordinate to capture essential characteristics of protein folding.

Spiers Memorial Lecture: Quantum chemistry, classical heuristics, and quantum advantage.

We describe the problems of quantum chemistry, the intuition behind classical heuristic methods used to solve them, a conjectured form of the classical complexity of quantum chemistry problems, and the subsequent opportunities for quantum advantage. This article is written for both quantum chemists and quantum information theorists. In particular, we attempt to summarize the domain of quantum chemistry problems as well as the chemical intuition that is applied to solve them within concrete statements (such as a classical heuristic cost conjecture) in the hope that this may stimulate future analysis.

Solving quantum chemistry problems on quantum computers

One of the earliest applications that the new era of computing may be used for is the simulation of the quantum effects that drive chemical reactions.

ROBERT: Bridging the Gap Between Machine Learning and Chemistry

ABSTRACTBeyond addressing technological demands, the integration of machine learning (ML) into human societies has also promoted sustainability through the adoption of digitalized protocols. Despite these advantages and the abundance of available toolkits, a substantial implementation gap is preventing the widespread incorporation of ML protocols into the computational and experimental chemistry communities. In this work, we introduce ROBERT, a software carefully crafted to make ML more accessible to chemists of all programming skill levels, while achieving results comparable to those of field experts. We conducted benchmarking using six recent ML studies in chemistry containing from 18 to 4149 entries. Furthermore, we demonstrated the program's ability to initiate workflows directly from SMILES strings, which simplifies the generation of ML predictors for common chemistry problems. To assess ROBERT's practicality in real‐life scenarios, we employed it to discover new luminescent Pd complexes with a modest dataset of 23 points, a frequently encountered scenario in experimental studies.

Low depth virtual distillation of quantum circuits by deterministic circuit decomposition

Virtual distillation using measurements of multiple copies of a quantum circuit have recently been proposed as a method of noise mitigation of expectation values. Circuit decompositions known as B gates were found only for 1-local Hamiltonians, however practical problems for chemistry require n-local Hamiltonians, which cannot be corrected with B gates. We discover low depth circuit decompositions for expectation values for n-local Pauli strings by combining multiple projections to recover the correct measurement statistics or expectation values. Our method adds linear entangling gates with the number of qubits, but it requires extra measurements. Furthermore, in applications to find ground states such as the variational quantum eigensolver (VQE) algorithm, the variational principle is required which states that the energy cannot go below the ground-state energy. We find that the variational principle is violated when using B gates and is preserved if we use our low depth decomposition on all expectation values. We perform a demonstration on real devices, and we show that our decomposition can mitigate real experimental noise in VQE for the H2 molecule with a two-qubit tapered mapping, H3 with three qubits, and H2 with four qubits. Our decomposition provides a way to perform duplicate circuit virtual distillation on real devices at significantly lower depth and for arbitrary observables. Published by the American Physical Society 2024

Examining the Importance of Hydrogen Bonding and Proton Transfer in Iron Porphyrin-Mediated Carbon Dioxide Upconversion.

ConspectusThe title should give a sense of the "big picture" of this Account, but what is it really about? An unexpected change in research direction? A series of courageous and creative students? A team taking on challenging problems in chemistry? The answer is a definite "yes" to all of the above. More specifically, the problem in which we are interested is the upconversion or valorization of carbon dioxide. This problem has captured the attention of a great many chemists in earnest following the gas crisis of the 1970s and more recently galvanized due to climate concerns arising from the ongoing release of anthropogenic carbon. Addressing the problem of atmospheric carbon accumulation requires effort in two very broad areas: capture and conversion. Storage is an alternative to conversion, but this eliminates the opportunity to use what might be otherwise a waste product. Our group has investigated a series of modified versions of iron(III)-5,10,15,20-tetraphenylporphyrin (FeTPP) that can convert CO2 to carbon monoxide, which is a versatile and useful precursor for other syntheses. Following pioneering work from Savéant and his colleagues in the 1990s and thereafter, we started with a simple question: how many pendent ancillary groups that can donate H-bonds or protons are needed to support efficient CO2-to-CO conversion? Using a molecule with only one 2-hydroxylphenyl group, we demonstrated that the single prepositioned -OH group gave rise to efficient turnover, but only when experiments were carried out in a weakly H-bond-accepting solvent system. In other words, the ability of a solvent to accept H-bonds can impede CO2 reduction. We followed up with a deeper investigation of the influence of H-bonding interactions with external acids in FeTPP-mediated CO2 reduction. Savéant's framework mechanism appears to be independent of solvent, and rate differences can be approximated by considering H-bonding equilibria. Following that work, we sought to better understand the minimum catalyst design requirements with respect to internal H-bond/proton donors. To that end, we produced all possible isomers of tetraarylpoprhyrins with 2,6-dihydroxyphenyl + phenyl groups. All else being equal, the complexes with a formally trans orientation of the 2,6-dihydroxyphenyl groups performed the best. Most recently, we surveyed the roles of internal and external Brønsted acids with different pKa values. Surprisingly, the best-performing catalysts have more weakly acidic internal groups. Overall, our work has demonstrated that CO2 reduction mediated by porphyrin catalysts can be improved by considering solvent H-bonding, the orientation of internal H-bonding groups, and the balance of the pKa values of internal and external acids. The future for molecular electrocatalysts is promising as more ideas emerge about how to design molecules and conditions for CO2 reduction.

Manipulation of facet zincophilicity of protective coatings for long lifetime zinc anodes

Aqueous zinc-ion batteries are considered to be a promising technology for large scale energy storage deployment due to their advantages of low cost and high security. However, the zinc anodes suffer long-standing problems of uncontrollable dendrite growth and unstable interfacial chemistry that hinder their industrial applications. In this work, we manage to manipulate the facet zincophilicity of commercial titanium oxide (TiO2) by nitrogen implanting as a protective coating to realize long-term zinc plating/stripping. The nitrogen-implanting significantly increases the habitual facet zincophilicity of TiO2 layer to enable uniform and fast zinc deposition kinetics. Impressively, the as-protected Zn anode could be operated for a long lifespan of 2400 h accompanying with a high cumulative capacity of 4.1 Ah cm-2 and a stable Coulombic efficiency of 99.53 % over 900 cycles. This work will shed new insight on the importance of manipulating the facet zincophicility of protective coatings for dendrite-free metal anodes beyond zinc chemistry.

Underwater surface discharge characteristics and multi-physical effects with conductive coating load under fast electric pulse

Abstract Underwater pulsed discharges, where intense reactions between ionized gas and condensed-state water exist, can be a joint problem of both physics and chemistry. The study tries to build a comprehensive visualization of nanosecond-risetime discharge initiated by a conductive coating and its successive multi-physical effects. The scenario is established via a pair of thin-plate electrodes positioned on both sides of the coating, and diagnosed using high-speed backlight photography synchronized with electrical and optical measurements. For the sprayed Cu/Ag composite coating, the current density can achieve 20 A/mm2 which is high enough to induce the surface “electrical explosion” and breakup the conductive matrix within 500 ns. By increasing the discharge energy from 0.5 to 10 J, the explosion of coating can exhibit different discharge types as exploding wires. Adopting a thicker carbon foil or cermet sheet can reduce the current density and energy deposition rate, which converts the global explosion to partial ones, significantly increasing the lifetime. With the aid of the conductive coating, the breakdown delay diminishes, and hot plasma spots form in 100 ns due to non-uniform Joule heating of the pulsed current, which gradually evolve to a plasma bubble cluster above the lower-conductive coating (bypassing branch). Once the high-conductive plasma channel bridges two electrodes, it will be intensively heated (MW-level energy deposition rate) and rapidly expand, accompanied by underwater shock wave (102 kPa @30 cm) and bubble/cavity generation (20 mm maximum). Finally, microscopic characterization has been made, and the erosion morphology suggests typical arc erosion features (pits, cracks, etc.) and nanoparticles condensation from evaporated materials.

A square-root speedup for finding the smallest eigenvalue

We describe a quantum algorithm for finding the smallest eigenvalue of a Hermitian matrix. This algorithm combines quantum phase estimation and quantum amplitude estimation to achieve a quadratic speedup with respect to the best classical algorithm in terms of matrix dimensionality, i.e. O~(N/ε) 9 9In this work O~ ignores terms that are polylogarithmic in N or 1/ε . black-box queries to an oracle encoding the matrix, where N is the matrix dimension and ɛ is the desired precision. In contrast, the best classical algorithm for the same task requires Ω(N)polylog(1/ε) queries. In addition, this algorithm allows the user to select any constant success probability. We also provide a similar algorithm with the same runtime that allows us to prepare a quantum state lying mostly in the matrix’s low-energy subspace. We implement simulations of both algorithms and demonstrate their application to problems in quantum chemistry and materials science.

Пространственная сетка водородных связей в жидкостях и растворах

A review of the author's studies of the problem of a three-dimensional network of hydrogen bonds in liquids and solutions is presented. The main properties of the spatial network are revealed: stability, lability, elasticity and correlation of different types of motion of particles forming the network. Methods and results of description and study of three-dimensional networks are presented. The determining role of spatial networks of hydrogen bonds in a wide range of liquid problems of biology, physics and chemistry in applied and fundamental science is shown. It is proposed to distinguish liquids with a spatial network of hydrogen bonds into a separate class of solvents, headed by water.

Going beyond gadgets: the importance of scalability for analogue quantum simulators

Quantum hardware has the potential to efficiently solve computationally difficult problems in physics and chemistry to reap enormous practical rewards. Analogue quantum simulation accomplishes this by using the dynamics of a controlled many-body system to mimic those of another system; such a method is feasible on near-term devices. We show that previous theoretical approaches to analogue quantum simulation suffer from fundamental barriers which prohibit scalable experimental implementation. By introducing a new mathematical framework and going beyond the usual toolbox of Hamiltonian complexity theory with an additional resource of engineered dissipation, we show that these barriers can be overcome. This provides a powerful new perspective for the rigorous study of analogue quantum simulators.

How Well Can Quantum Embedding Method Predict the Reaction Profiles for Hydrogenation of Small Li Clusters?

Quantum computing leverages the principles of quantum mechanics in novel ways to tackle complex chemistry problems that cannot be accurately addressed using traditional quantum chemistry methods. However, the high computational cost and available number of physical qubits with high fidelity limit its application to small chemical systems. This work employed a quantum-classical framework which features a quantum active space-embedding approach to perform simulations of chemical reactions that require up to 14 qubits. This framework was applied to prototypical example metal hydrogenation reactions: the coupling between hydrogen and Li2, Li3, and Li4 clusters. Particular attention was paid to the computation of barriers and reaction energies. The predicted reaction profiles compare well with advanced classical quantum chemistry methods, demonstrating the potential of the quantum embedding algorithm to map out reaction profiles of realistic gas-phase chemical reactions to ascertain qualitative energetic trends. Additionally, the predicted potential energy curves provide a benchmark to compare against both current and future quantum embedding approaches.