Classical Simulations Research Articles

Classical Modeling of a Lossy Gaussian Bosonic Sampler.

Gaussian boson sampling (GBS) is considered a candidate problem for demonstrating quantum advantage. We propose an algorithm for the approximate classical simulation of a lossy GBS instance. The algorithm relies on the Taylor series expansion, and increasing the number of terms of the expansion that are used in the calculation yields greater accuracy. The complexity of the algorithm is polynomial in the number of modes given the number of terms is fixed. We describe conditions for the input state squeezing parameter and loss level that provide the best efficiency for this algorithm (by efficient, we mean that the Taylor series converges quickly). In recent experiments that claim to have demonstrated quantum advantage, these conditions are satisfied; thus, this algorithm can be used to classically simulate these experiments.

Dynamic Transitive Closure-based Static Analysis through the Lens of Quantum Search

Many existing static analysis algorithms suffer from cubic bottlenecks because of the need to compute a dynamic transitive closure (DTC). For the first time, this article studies the quantum speedups on searching subtasks in DTC-based static analysis algorithms using quantum search (e.g., Grover’s algorithm). We first introduce our oracle implementation in Grover’s algorithm for DTC-based static analysis and illustrate our quantum search subroutine. Then, we take two typical DTC-based analysis algorithms: context-free-language reachability and set constraint-based analysis, and show that our quantum approach can reduce the time complexity of these two algorithms to truly subcubic ( \(O(N^2\sqrt {N}{\it polylog}(N))\) ), yielding better results than the upper bound ( O ( N 3 /log N )) of existing classical algorithms. Finally, we conducted a classical simulation of Grover’s search to validate our theoretical approach, due to the current quantum hardware limitation of lacking a practical, large-scale, noise-free quantum machine. We evaluated the correctness and efficiency of our approach using IBM Qiskit on nine open-source projects and randomly generated edge-labeled graphs/constraints. The results demonstrate the effectiveness of our approach and shed light on the promising direction of applying quantum algorithms to address the general challenges in static analysis.

Experimental and numerical study of unsteady flows in a compound open channel

Unsteady flows are investigated in a compound open-channel flume, consisting of a Main Channel (MC) and an adjacent Flood Plain (FP). Two types of inflow hydrographs are studied, i.e., a discharge hydrograph with, at any time: a slightly unbalanced inflow partition between MC and FP (Case I); and a noticeably unbalanced inflow partition (Case II). Ensemble averages of the time-varying discharges, water depths and velocities are estimated based on 100 successive runs. The main focus of the experimental study is on assessing (i) the time-varying lateral discharge and depth-averaged Reynolds stress at the MC/FP interface, and (ii) the influence of the inflow partition on the downstream flow parameters. The experimental flows are then simulated using a 1D (one-dimensional) code that was adapted to implement the 1D+ Independent Sub-sections Model (ISM) (Proust et al. in Water Resour Res 45:1–16, 2009). The numerical study aims at validating the ISM under unsteady flow conditions, using classical 1D simulations as benchmark. It is experimentally found that 90 successive runs are required to get convergence of the ensemble averages of sub-section discharges and flow depth, while interfacial velocity is not fully converged after 100 runs. The influence of the inflow partition on the downstream parameters is felt along the whole flume. The ISM simulations are closer to the measurements than the classical 1D simulations. The ISM can accurately predict the time-varying flow depths and interfacial lateral discharge, and can approximate the interfacial Reynolds stresses.

On the solubility of azodicarbonamide in water/DMSO mixtures: an experimental and computational study.

This work aims at studying why azodicarbonamide (ADCA), a formally apolar compound with good hydrogen bond (HB) acceptors, is soluble only in polar aprotic solvents like dimethyl sulfoxide (DMSO) but not in water. Solubility measurements, as well as quantum mechanical and classical molecular dynamics simulations, were employed to tackle the problem. We found that in the liquid phase a polar conformer of ADCA (µ = 8.7 D), unreported to date, is favoured under the enthalpic drive provided by a highly polar solvent. At the same time, the very high hydrogen bond propensity of water with itself prevents this solvent from providing an effective hydrogen bond-mediated solvation. Solvents bearing good HB acceptors, while lacking strong HB donors, contribute to further stabilizing solute-solvent adducts through weak and fluxional HBs that involve the amide groups of ADCA. Implications for the solubility of ADCA down to µM concentrations were evaluated, also with the aid of classical simulations of solution nanodroplets.

Quantum simulation of discrete linear dynamical systems and simple iterative methods in linear algebra

Quantum simulation is capable of simulating certain dynamical systems in continuous time—Schrödinger’s equations being the most direct and well known—more efficiently than classical simulation. Any linear dynamical system can in fact be transformed into a system of Schrödinger’s equations via a method called Schrödingerisation (Jin et al. 2022. Quantum simulation of partial differential equations via Schrödingerisation. ( https://arxiv.org/abs/2212.13969 ) and Jin et al. 2023. Phys. Rev. A 108 , 032603. ( doi:10.1103/PhysRevA.108.032603 )). We show how Schrödingerisation allows quantum simulation to be directly used for the simulation of continuous-time versions of general (explicit) iterative schemes or discrete linear dynamical systems. In particular, we use this new method to solve linear systems of equations and for estimating the maximum eigenvector and eigenvalue of a matrix, respectively. This method is applicable using either discrete-variable quantum systems or on hybrid continuous-variable and discrete-variable quantum systems. This framework provides an interesting alternative to solve linear algebra problems using quantum simulation.

The rise and fall of the Standard-Model Higgs: electroweak vacuum stability during kination

In this paper we investigate the vacuum stability of the non-minimally coupled Standard-Model Higgs during a phase of kinetic domination following the end of inflation. The non-minimal coupling to curvature stabilises the Higgs fluctuations during inflation while driving them towards the instability scale during kination, when they can classically overcome the potential barrier separating the false electroweak vacuum from the true one at super-Planckian field values. Avoiding the instability of the Standard-Model vacuum sets an upper bound on the inflationary scale that depends both on the strength of the non-minimal interaction and on the top quark Yukawa coupling. Classical vacuum stability is guaranteed if the gravitationally-produced energy density is smaller than the height of barrier in the effective potential. Interestingly enough, thanks to the explosive particle production in the tachyonic phase, the Higgs itself can be also appointed to the role of reheaton field responsible for the onset of the hot Big Bang era, setting an additional lower bound on the inflationary scale Hinf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{H}}_{\ extrm{inf}} $$\\end{document} ≳ 105.5 GeV. Overall, these constraints favour lower masses for the top quark, in agreement with the current measurements of the top quark pole mass. We perform our analysis semi-analytically in terms of the one-loop and three-loop running of the Standard-Model Higgs self-coupling and make use of lattice-based parametric formulas for studying the (re)heating phase derived in arXiv:2307.03774. For a specific choice of mt = 171.3 GeV we perform also an extensive numerical scanning of the parameter space via classical lattice simulations, identifying stable/unstable regions and supporting the previous analytical arguments. For this fiducial value, the heating of the Universe is achieved at temperatures in the range 10−2–109 GeV.

Postselection-Free Learning of Measurement-Induced Quantum Dynamics

We address how one can empirically infer properties of quantum states generated by dynamics involving measurements. Our focus is on many-body settings where the number of measurements is extensive, making brute-force approaches based on postselection intractable due to their exponential sample complexity. We introduce a general-purpose scheme that can be used to infer any property of the postmeasurement ensemble of states (e.g., the average entanglement entropy, or frame potential) using a scalable number of experimental repetitions. We first identify a general class of “estimable properties” that can be directly extracted from experimental data. Then, based on empirical observations of such quantities, we show how one can indirectly infer information about any particular given nonestimable quantity of interest through classical postprocessing. Our approach is based on an optimization task, where one asks what are the minimum and maximum values that the desired quantity could possibly take, while ensuring consistency with observations. The true value of this quantity must then lie within a feasible range between these extrema, resulting in two-sided bounds. Narrow feasible ranges can be obtained by using a classical simulation of the device to determine which estimable properties one should measure. Even in cases where this simulation is inaccurate, unambiguous information about the true value of a given quantity realized on the quantum device can be learned. As an immediate application, we show that our method can be used to verify the emergence of quantum state designs in experiments. We identify some fundamental obstructions that in some cases prevent sharp knowledge of a given quantity from being inferred, and discuss what can be learned in cases where classical simulation is too computationally demanding to be feasible. In particular, we prove that any observer who cannot perform a classical simulation cannot distinguish the output states from those sampled from a maximally structureless ensemble. Published by the American Physical Society 2024

Invariant representations in abstract concept grounding - the physical world in grounded cognition.

Grounded cognition states that mental representations of concepts consist of experiential aspects. For example, the concept "cup" consists of the sensorimotor experiences from interactions with cups. Typical modalities in which concepts are grounded are: The sensorimotor system (including interoception), emotion, action, language, and social aspects. Here, we argue that this list should be expanded to include physical invariants (unchanging features of physical motion; e.g., gravity, momentum, friction). Research on physical reasoning consistently demonstrates that physical invariants are represented as fundamentally as other grounding substrates, and therefore should qualify. We assess several theories of concept representation (simulation, conceptual metaphor, conceptual spaces, predictive processing) and their positions on physical invariants. We find that the classic grounded cognition theories, simulation and conceptual metaphor theory, have not considered physical invariants, while conceptual spaces and predictive processing have. We conclude that physical invariants should be included into grounded cognition theories, and that the core mechanisms of simulation and conceptual metaphor theory are well suited to do this. Furthermore, conceptual spaces and predictive processing are very promising and should also be integrated with grounded cognition in the future.

A modified Lorentz force law for point-like charged particles in classical electrodynamics

In classical electrodynamics, the well-known Lorentz force law falls short of providing a satisfactory result for the trajectory of point-like charged particles when considering that particle’s own self-force. While there have been many historical attempts, Gralla, Harte and Wald developed a new model for classical charged particles that is free from pathologies while being consistent with Maxwell’s equations and conserves stress-energy. Expanding upon this approach, we derive a relativistically correct, modified Lorentz force law in vector form, which includes radiation reaction, and spin- and magnetic moment-dependent correction terms, suitable to be included in classical electrodynamics lectures and beam dynamics simulation tools. As by-products we obtain evolution equations for mass, spin angular momentum and the radiated power. We compare the new equations to the classical ones and use the new equations to conduct numerical simulations, showing that the results are free of any nonphysical artifacts, and which might be possible to test in future experiments at particle accelerators. The new equations foster improved insight into beam dynamics.

Sketching phase diagrams using low-depth variational quantum algorithms

Mapping out phase diagrams of quantum systems using classical simulations can be challenging or intractable due to the computational resources required to simulate even small quantum systems far away from the thermodynamic limit. We investigate using quantum computers and the variational quantum eigensolver (VQE) for this task. In contrast to the task of preparing the exact ground state using VQE, sketching phase diagrams might require less quantum resources and accuracy, because low fidelity approximations to the ground state may be enough to correctly identify different phases. We used classical numerical simulations of low-depth VQE circuits to compute order parameters for four well-studied spin and fermion models which represent a mix of 1D and 2D, and exactly-solvable and classically hard systems. We find that it is possible to predict the location of phase transitions up to reasonable accuracy using states produced by VQE even when their overlap with the true ground state is small. Further, we introduce a model-agnostic predictor of phase transitions based on the speed with which the VQE energy improves with respect to the circuit depth, and find that in some cases this is also able to predict phase transitions.

Isolation, Virtual Screening, and Evaluation of Hazelnut-Derived Immunoactive Peptides for the Inhibition of SARS-CoV-2 Main Protease.

The aim of this study is to validate the activity of hazelnut (Corylus avellana L.)-derived immunoactive peptides inhibiting the main protease (Mpro) of SARS-CoV-2 and further unveil their interaction mechanism using in vitro assays, molecular dynamics (MD) simulations, and binding free energy calculations. In general, the enzymatic hydrolysis components, especially molecular weight < 3 kDa, possess good immune activity as measured by the proliferation ability of mouse splenic lymphocytes and phagocytic activity of mouse peritoneal macrophages. Over 866 unique peptide sequences were isolated, purified, and then identified by nanohigh-performance liquid chromatography/tandem mass spectrometry (NANO-HPLC-MS/MS) from hazelnut protein hydrolysates, but Trp-Trp-Asn-Leu-Asn (WWNLN) and Trp-Ala-Val-Leu-Lys (WAVLK) in particular are found to increase the cell viability and phagocytic capacity of RAW264.7 macrophages as well as promote the secretion of the cytokines nitric oxide (NO), tumor necrosis factor-α (TNF-α), and interleukin-1β (IL-1β). Fluorescence resonance energy transfer assay elucidated that WWNLN and WAVLK exhibit excellent inhibitory potency against Mpro, with IC50 values of 6.695 and 16.750 μM, respectively. Classical all-atom MD simulations show that hydrogen bonds play a pivotal role in stabilizing the complex conformation and protein-peptide interaction. Molecular Mechanics/Generalized Born Surface Area (MM/GBSA) calculation indicates that WWNLN has a lower binding free energy with Mpro than WAVLK. Furthermore, adsorption, distribution, metabolism, excretion, and toxicity (ADMET) predictions illustrate favorable drug-likeness and pharmacokinetic properties of WWNLN compared to WAVLK. This study provides a new understanding of the immunomodulatory activity of hazelnut hydrolysates and sheds light on peptide inhibitors targeting Mpro.

Investigating the role of network former interactions on charge carrier diffusivity in glasses

Ionic transport is a critical property for the glass industry, since emerging applications such as sensors, batteries, and electric melting are based on the phenomenon. Short-range interactions (anion-charge carrier) have not been able to explain the total activation barrier observed experimentally, and, as such, it is critical to understand the larger role of all ions in a glass, not just the carrier and the ‘site’ ions. This research focuses on the role of network formers and their impact on diffusion in glasses, something that current models lack an explicit explanation of. Atomistic simulations with randomly generated parameters for the cation potentials and classical simulations were used to determine the diffusion coefficients and activation energies for synthetic network formers. Using this database, explainable machine learning algorithms were employed to explore network former interactions and determine which parameters are the most influential for ion diffusion. Results suggest that the bond length of the cations changes the geometry of the structure contributing the greatest to cation-modifier interactions.

Accuracy vs memory advantage in the quantum simulation of stochastic processes

Many inference scenarios rely on extracting relevant information from known data in order to make future predictions. When the underlying stochastic process satisfies certain assumptions, there is a direct mapping between its exact classical and quantum simulators, with the latter asymptotically using less memory. Here we focus on studying whether such quantum advantage persists when those assumptions are not satisfied, and the model is doomed to have imperfect accuracy. By studying the trade-off between accuracy and memory requirements, we show that quantum models can reach the same accuracy with less memory, or alternatively, better accuracy with the same memory. Finally, we discuss the implications of this result for learning tasks.

An atomic boson sampler.

A boson sampler implements a restricted model of quantum computing. It is defined by the ability to sample from the distribution resulting from the interference of identical bosons propagating according to programmable, non-interacting dynamics1. An efficient exact classical simulation of boson sampling is not believed to exist, which has motivated ground-breaking boson sampling experiments in photonics with increasingly many photons2-12. However, it is difficult to generate and reliably evolve specific numbers of photons with low loss, and thus probabilistic techniques for postselection7 or marked changes to standard boson sampling10-12 are generally used. Here, we address the above challenges by implementing boson sampling using ultracold atoms13,14 in a two-dimensional, tunnel-coupled optical lattice. This demonstration is enabled by a previously unrealized combination of tools involving high-fidelity optical cooling and imaging of atoms in a lattice, as well as programmable control of those atoms using optical tweezers. When extended to interacting systems, our work demonstrates the core abilities required to directly assemble ground and excited states in simulations of various Hubbard models15,16.

The Role of Momentum Partitioning in Covariance Ion Imaging Analysis.

We present results from a covariance ion imaging study, which employs extensive filtering, on the relationship between fragment momenta to gain deeper insight into photofragmentation dynamics. A new data analysis approach is introduced that considers the momentum partitioning between the fragments of the breakup of a molecular polycation to disentangle concurrent fragmentation channels, which yield the same ion species. We exploit this approach to examine the momentum exchange relationship between the products, which provides direct insight into the dynamics of molecular fragmentation. We apply these techniques to extensively characterize the dissociation of 1-iodopropane and 2-iodopropane dications prepared by site-selective ionization of the iodine atom using extreme ultraviolet intense femtosecond laser pulses with a photon energy of 95 eV. Our assignments are supported by classical simulations, using parameters largely obtained directly from the experimental data.

Quantum-Informed Recursive Optimization Algorithms

We propose and implement a family of quantum-informed recursive optimization (QIRO) algorithms for combinatorial optimization problems. Our approach leverages quantum resources to obtain information that is used in problem-specific classical reduction steps that recursively simplify the problem. These reduction steps address the limitations of the quantum component (e.g., locality) and ensure solution feasibility in constrained optimization problems. Additionally, we use backtracking techniques to further improve the performance of the algorithm without increasing the requirements on the quantum hardware. We showcase the capabilities of our approach by informing QIRO with correlations from classical simulations of shallow circuits of the quantum approximate optimization algorithm, solving instances of maximum independent set and maximum satisfiability problems with hundreds of variables. We also demonstrate how QIRO can be deployed on a neutral atom quantum processor to find large independent sets of graphs. In summary, our scheme achieves results comparable to classical heuristics even with relatively weak quantum resources. Furthermore, enhancing the quality of these quantum resources improves the performance of the algorithms. Notably, the modular nature of QIRO offers various avenues for modifications, positioning our work as a template for a broader class of hybrid quantum-classical algorithms for combinatorial optimization. Published by the American Physical Society 2024

Accelerating material property prediction using generically complete isometry invariants

Periodic material or crystal property prediction using machine learning has grown popular in recent years as it provides a computationally efficient replacement for classical simulation methods. A crucial first step for any of these algorithms is the representation used for a periodic crystal. While similar objects like molecules and proteins have a finite number of atoms and their representation can be built based upon a finite point cloud interpretation, periodic crystals are unbounded in size, making their representation more challenging. In the present work, we adapt the Pointwise Distance Distribution (PDD), a continuous and generically complete isometry invariant for periodic point sets, as a representation for our learning algorithm. The PDD distinguished all (more than 660 thousand) periodic crystals in the Cambridge Structural Database as purely periodic sets of points without atomic types. We develop a transformer model with a modified self-attention mechanism that combines PDD with compositional information via a spatial encoding method. This model is tested on the crystals of the Materials Project and Jarvis-DFT databases and shown to produce accuracy on par with state-of-the-art methods while being several times faster in both training and prediction time.

Theoretical and experimental study of molecular interactions between constituents of deep eutectic solvents

In this study, we aimed to elucidate the molecular interactions in deep eutectic solvents (DESs) and acquire additional experimental evidence to increase our understanding of the molecular mechanisms responsible for the preparation of DES. We investigated three N-methylthiourea (NMTU)-based DESs with choline chloride (ChCl), allyltrimethylammonium chloride (ATMAC), and benzyltriethylammonium chloride (BTEAC) as hydrogen bond acceptors (HBA). To accomplish this, we used both experimental techniques including isopiestic, differential scanning calorimetry (DSC), and FTIR measurements as well as molecular dynamics (MD) simulations. The thermal behaviors of the prepared DESs were investigated by DSC method. In order to study the interaction and hydrogen bonding between the DESs constituents, FT-IR analysis and isopiestic measurements were carried out. Constant solvent activity lines of ternary HBA + HBD + solvent mixtures were determined by the isopiestic technique. The large positive deviation of the isosolvent activity lines from the semi-ideal behavior indicates a strong interaction between HBA and HBD, which is much stronger than HBA-HBA and HBD-HBD interactions. Classical MD simulations were performed at 298.15 K to analyze the nanoscopic properties and structure of the DESs. To investigate the interaction between the components and visualize the three-dimensional structure of the DESs, radial distribution functions (RDFs), coordination numbers (CNs), and combined (CDFs), and spatial (SDFs) distribution functions were determined by MD simulations. The obtained theoretical results confirmed the importance of hydrogen bonds in the preparation of DESs and also showed that these systems exhibit different structural arrangements. MD simulations were also used to determine the density of the DESs and the results showed good agreement with the experimental density.

Effects of graphene and thermoplastic elastomer on tailoring the bulk properties of asphaltenes: an exploration from classical and quantum simulations

Effects of graphene and thermoplastic elastomer on tailoring the bulk properties of asphaltenes: an exploration from classical and quantum simulations

Hidden variable model for quantum computation with magic states on qudits of any dimension

It was recently shown that a hidden variable model can be constructed for universal quantum computation with magic states on qubits. Here we show that this result can be extended, and a hidden variable model can be defined for quantum computation with magic states on qudits with any Hilbert space dimension. This model leads to a classical simulation algorithm for universal quantum computation.