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DOE OSTI2024

Statistical Complexity of Quantum Learning

Abstract Learning problems involve settings in which an algorithm has to make decisions based on data, and possibly side information such as expert knowledge. This study has two main goals. First, it reviews and generalizes different results on the data and model complexity of quantum learning, where the data and/or the algorithm can be quantum, focusing on information‐theoretic techniques. Second, it introduces the notion of copy complexity, which quantifies the number of copies of a quantum state required to achieve a target accuracy level. Copy complexity arises from the destructive nature of quantum measurements, which irreversibly alter the state to be processed, limiting the information that can be extracted about quantum data. As a result, empirical risk minimization is generally inapplicable. The paper presents novel results on the copy complexity for both training and testing. To make the paper self‐contained and approachable by different research communities, an extensive background material is provided on classical results from statistical learning theory, as well as on the distinguishability of quantum states. Throughout, the differences between quantum and classical learning are highlighted by addressing both supervised and unsupervised learning, and extensive pointers are provided to the literature.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Efficient Parameterization of Density Functional Tight-Binding for 5 f -Elements: A Th–O Case Study

Density functional tight binding (DFTB) models for f-element species are challenging to parametrize owing to the large number of adjustable parameters. The explicit optimization of the terms entering the semiempirical DFTB Hamiltonian related to f orbitals is crucial to generating a reliable parametrization for f-block elements, because they play import roles in bonding interactions. However, since the number of parameters grows quadratically with the number of orbitals, the computational cost for parameter optimization is much more expensive for the f-elements than for the main group elements. In this work we present a set of efficient approaches for mitigating the hurdle imposed by the large size of the parameter space. A novel group-by-orbital correction functions for two-center bond integrals was developed. With this approach the number of parameters is reduced, and it grows linearly with the number of elements, maintaining the accuracy and the number of parameters, in the case of f elements, by more than 40%. The parameter optimization step was accelerated by means of the mini-batch BFGS method. This method allows parameter optimizations with much larger training sets than other single batch methods. A stochastic optimizer was employed that helped overcome shallow local minima in the objective function. The proposed algorithm was used to parametrize the DFTB Hamiltonian for the Th–O system, which was subsequently applied to the study of ThO 2 nanoparticles. The training set consisted of 6322 unique structures, which is barely feasible with conventional optimization methods. The optimized parameter set, LANL-ThO, displays good agreement with DFT-calculated properties such as energies, forces, and structures for both clusters and bulk ThO 2 . Benefiting from the fewer number of parameters and lower computational costs for objective function evaluations, this new approach shows its potential applications in DFTB parametrization for elements with high angular momentum, which present a challenge to conventional methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Combining dual domain material point method with molecular dynamics for thermodynamic nonequilibriums

The dual domain material point method (DDMP) combined with molecular dynamics (MD) is used to simulate a material undergoing a large deformation with a high strain rate. In the simulation, the continuum scale equation of motion is solved using DDMP, while the stresses required at the material points are obtained by performing MD simulations in small domains surrounding the material points following the entire history of the material deformation without reinitialization of the MD systems; therefore the history dependence, a common feature for thermodynamically nonequilibrium systems, can be tracked accurately. Two algorithms are introduced to avoid distortion of the MD domains and to ensure consistence in the energy density between the MD and macroscopic calculations. As an example, a hyper-velocity impact problem is simulated. The results of the combined DDMP-MD calculations are then compared to a pure MD simulation. The method of the combined simulation is applicable to macroscopic systems, although the size of the simulation domain is only a few hundred nanometers in this example because of the limitation of the pure MD simulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

QSpace - An open-source tensor library for Abelian and non-Abelian symmetries

This is the documentation for the tensor library QSpace (v4.0), a toolbox to exploit ‘quan tum symmetry spaces’ in tensor network states in the quantum many-body context. QSpace permits arbitrary combinations of symmetries including the abelian symmetries $\mathbb{Z}_n$ and U(1), as well as all non-abelian symmetries based on the semisimple classical Lie algebras: A n , B n , C n , and D n , or respectively, the special unitary group SU(n), the odd orthogonal group SO(2n+1), the symplectic group Sp(2n), and the even orthogonal group SO(2n). The code (C++ embedded via the MEX interface into Matlab) is available open source as of QSpace v4.0 on bitbucket under the Apache 2.0 license. QSpace is designed as a bottom-up approach for non-abelian symmetries. It starts from the defining representation and the respective Lie algebra. By explicitly comput ing and tabulating generalized Clebsch-Gordan coefficient tensors, QSpace is versatile in the type of operations that it can perform across all symmetries. At the level of an ap plication, much of the symmetry-related details are hidden within the QSpace C++ core libraries. Hence when developing tensor network algorithms with QSpace, these can be coded (nearly) as if there are no symmetries at all, despite being able to fully exploit general non-abelian symmetries.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Using a monomer potential energy surface to perform approximate path integral molecular dynamics simulation of ab initio water at near-zero added cost

It is now established that nuclear quantum motion plays an important role in determining water's hydrogen bonding, structure, and dynamics. Such effects are important to include in density functional theory (DFT) based molecular dynamics simulation of water. The standard way of treating nuclear quantum effects, path integral molecular dynamics (PIMD), multiplies the number of energy/force calculations by the number of beads required. In this work we introduce a method whereby PIMD can be incorporated into a DFT simulation with little extra cost and little loss in accuracy. The method is based on the many body expansion of the energy and has the benefit of including a monomer level correction to the DFT energy. Our method calculates intramolecular forces using the highly accurate monomer potential energy surface developed by Partridge–Schwenke, which is cheap to evaluate. Intermolecular forces and energies are calculated with DFT only once per timestep using the centroid positions. We show how our method may be used in conjunction with a multiple time step algorithm for an additional speedup and how it relates to ring polymer contraction and other schemes that have been introduced recently to speed up PIMD simulations. We show that our method, which we call “monomer PIMD”, correctly captures changes in the structure of water found in a full PIMD simulation but at much lower computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Massively parallel GPU enabled third-order cluster perturbation excitation energies for cost-effective large scale excitation energy calculations

We present here a massively parallel implementation of the recently developed CPS(D-3) excitation energy model that is based on cluster perturbation theory. The new algorithm extends the one developed in Baudin et al. [J. Chem. Phys., 150, 134110 (2019)] to leverage multiple nodes and utilize graphical processing units for the acceleration of heavy tensor contractions. Furthermore, we show that the extended algorithm scales efficiently with increasing amounts of computational resources and that the developed code enables CPS(D-3) excitation energy calculations on large molecular systems with a low time-to-solution. More specifically, calculations on systems with over 100 atoms and 1000 basis functions are possible in a few hours of wall clock time. This establishes CPS(D-3) excitation energies as a computationally efficient alternative to those obtained from the coupled-cluster singles and doubles model.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2019

Parallel general purpose multiobjective optimization framework with application to electron beam dynamics

Particle accelerators are invaluable tools for research in the basic and applied sciences, such as materials science, chemistry, the biosciences, particle physics, nuclear physics and medicine. The design, commissioning, and operation of accelerator facilities is a nontrivial task, due to the large number of control parameters and the complex interplay of several conflicting design goals. The Argonne Wakefield Accelerator facility has some unique challenges resulting from its purpose to carry out advanced accelerator R&D. Individual experiments often have challenging beam requirements, and the physical configuration of the beam lines is often changed to accommodate the variety of supported experiments. The need for rapid deployment of different operational settings further complicates the optimization work that must be done for multiple constraints and challenging operational regimes. One example of this is an independently staged two-beam acceleration experiment which requires the construction of an additional beam line (this is now in progress). The high charge drive beam, well into the space charge regime, must be threaded through small aperture (17.6 mm) decelerating structures. In addition, the bunch length must be sufficiently short to maximize power generation in the decelerator. We propose to tackle this problem by means of multiobjective optimization algorithms which also facilitate a parallel deployment. In order to compute solutions in a meaningful time frame, a fast and scalable software framework is required. In this paper, we present a general-purpose framework for simulation-based multiobjective optimization methods that allows the automatic investigation of optimal sets of machine parameters. Using evolutionary algorithms as the optimizer and opal as the forward solver, validation experiments and results of multiobjective optimization problems in the domain of beam dynamics are presented. Optimized solutions for the new high charge drive beam line found by the framework were used to finish the design of a two beam acceleration experiment. The selected solution along with the associated beam parameters is presented.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Expansion of Machine-Learning Method for Classifying Neutron Resonances

The understanding of astrophysics processes and the performance of nuclear reactors and other nuclear systems depend on a precise description of the neutron interaction cross sections for materials and nuclei present in these environments. At low neutron energies, these cross sections exhibit resonance structure represented by sharp enhancements when the neutron energy is sufficiently close to excited levels in a compound nucleus. Such resonances can be characterized by their quantum numbers relative to angular momenta, which are often deduced in an ad hoc and irreproducible manner from the shape of the cross sections. The correct assignment of the quantum numbers of neutron resonances is therefore of paramount importance. To address this we have developed a machine-learning method to automate the identification and correction of these spin assignments. The algorithm is trained from simulated data, generated from statistical properties of resonance data for a given nucleus, to mimic the errors found in real data. In this project we describe five independent approaches to further develop and expand the applicability of the machine-learning spin classifier: i) Feature impact; ii) Integration with the Atlas; iii) Training optimization; iv) Spacings systematics; and v) Validation with polarized data. The premises, methods, results, and future perspectives are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Entropic formation of a thermodynamically stable colloidal quasicrystal with negligible phason strain

Quasicrystals have been discovered in a variety of materials ranging from metals to polymers. Yet, why and how they form is incompletely understood. In situ transmission electron microscopy of alloy quasicrystal formation in metals suggests an error-and-repair mechanism, whereby quasiperiodic crystals grow imperfectly with phason strain present, and only perfect themselves later into a high-quality quasicrystal with negligible phason strain. The growth mechanism has not been investigated for other types of quasicrystals, such as dendrimeric, polymeric, or colloidal quasicrystals. Soft-matter quasicrystals typically result from entropic, rather than energetic, interactions, and are not usually grown (either in laboratories or in silico) into large-volume quasicrystals. Consequently, it is unknown whether soft-matter quasicrystals form with the high degree of structural quality found in metal alloy quasicrystals. Here, we investigate the entropically driven growth of colloidal dodecagonal quasicrystals (DQCs) via computer simulation of systems of hard tetrahedra, which are simple models for anisotropic colloidal particles that form a quasicrystal. Using a pattern recognition algorithm applied to particle trajectories during DQC growth, we analyze phason strain to follow the evolution of quasiperiodic order. As in alloys, we observe high structural quality; DQCs with low phason strain crystallize directly from the melt and only require minimal further reduction of phason strain. Finally, we also observe transformation from a denser approximant to the DQC via continuous phason strain relaxation. Our results demonstrate that soft-matter quasicrystals dominated by entropy can be thermodynamically stable and grown with high structural quality––just like their alloy quasicrystal counterparts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Approximating the linear response of physical chaos

Abstract Parametric derivatives of statistics are highly desired quantities in prediction, design optimization and uncertainty quantification. In the presence of chaos, the rigorous computation of these quantities is certainly possible, but mathematically complicated and computationally expensive. Based on Ruelle’s formalism, this paper shows that the sophisticated linear response algorithm can be dramatically simplified in higher-dimensional systems featuring statistical homogeneity in the physical space. We argue that the contribution of the SRB (Sinai–Ruelle–Bowen) measure gradient, which is an integral yet the most cumbersome part of the full algorithm, is negligible if the objective function is appropriately aligned with unstable manifolds. This abstract condition could potentially be satisfied by a vast family of real-world chaotic systems, regardless of the physical meaning and mathematical form of the objective function and perturbed parameter. We demonstrate several numerical examples that support these conclusions and that present the use and performance of a simplified linear response algorithm. In the numerical experiments, we consider physical models described by differential equations, including Lorenz 96 and Kuramoto–Sivashinsky.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Faster Tensor Network Decoding for Topological Quantum Codes

We present a fast and Bayes-optimal-approximating tensor network decoder for planar quantum LDPC codes based on the tensor renormalization group algorithm, originally proposed by Levin, and Nave. By precomputing the renormalization group flow for the null syndrome, we need only recompute tensor contractions in the causal cone of the measured syndrome at the time of decoding. This allows us to achieve an overall runtime complexity of ($pnχ^6$) where p is the depolarizing noise rate, and χ is the cutoff value used to control singular value decomposition approximations used in the algorithm. We apply our decoder to the surface code in the code capacity noise model and compare its performance to the original matrix product state (MPS) tensor network decoder introduced by Bravyi, Suchara, and Vargo. The MPS decoder has a p-independent runtime complexity of $\mathcal{O}(nχ^3)$ resulting in significantly slower decoding times compared to our algorithm in the low-p regime.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

2-Group global symmetries and anomalies in six-dimensional quantum field theories

We examine six-dimensional quantum field theories through the lens of higher-form global symmetries. Every Yang-Mills gauge theory in six dimensions, with field strength ƒ (2) , naturally gives rise to a continuous 1-form global symmetry associated with the 2-form instanton current J (2) ~ * Tr (ƒ (2) $\wedge$ ƒ (2) ). We show that suitable mixed anomalies involving the gauge field ƒ (2) and ordinary 0-form global symmetries, such as flavor or Poincaré symmetries, lead to continuous 2-group global symmetries, which allow two flavor currents or two stress tensors to fuse into the 2-form current J (2) . We discuss several features of 2-group symmetry in six dimensions, many of which parallel the four-dimensional case. The majority of six-dimensional supersymmetric conformal field theories (SCFTs) and little string theories have infrared phases with non-abelian gauge fields. We show that the mixed anomalies leading to 2-group symmetries can be present in little string theories, but that they are necessarily absent in SCFTs. This allows us to establish a previously conjectured algorithm for computing the ’t Hooft anomalies of most SCFTs from the spectrum of weakly-coupled massless particles on the tensor branch of these theories. We then apply this understanding to prove that the a -type Weyl anomaly of all SCFTs with a tensor branch must be positive, a > 0.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Promise of Graph Sparsification and Decomposition for Noise Reduction in QAOA: Analysis for Trapped-Ion Compilations

We develop new approximate compilation schemes that significantly reduce the expense of compiling the Quantum Approximate Optimization Algorithm (QAOA) for solving the Max-Cut problem. Our main focus is on compilation with trapped-ion simulators using Pauli-X operations and all-to-all Ising Hamiltonian HIsing evolution generated by Molmer-Sorensen or optical dipole force interactions, though some of our results also apply to standard gate-based compilations. Our results are based on principles of graph sparsification and decomposition; the former reduces the number of edges in a graph while maintaining its cut structure, while the latter breaks a weighted graph into a small number of unweighted graphs. Though these techniques have been used as heuristics in various hybrid quantum algorithms, there have been no guarantees on their performance, to the best of our knowledge. This work provides the first provable guarantees using sparsification and decomposition to improve quantum noise resilience and reduce quantum circuit complexity. For quantum hardware that uses edge-by-edge QAOA compilations, sparsification leads to a direct reduction in circuit complexity. For trapped-ion quantum simulators implementing all-to-all HIsing pulses, we show that for a (1−ϵ) factor loss in the Max-Cut approximation (ϵ>0), our compilations improve the (worst-case) number of HIsing pulses from O(n2) to O(nlog(n/ϵ)) and the (worst-case) number of Pauli-X bit flips from O(n2) to O(nlog(n/ϵ)ϵ2) for n-node graphs. This is an asymptotic improvement for any constant ϵ>0. We demonstrate that significant improvements to the approximation ratio are obtained using decomposition in simulated trapped-ion experiments with dephasing noise. We further present a generic argument showing that sparsification results in an exponentially improved circuit fidelity lower bound in digital computing schemes based on one- and two-qubit gates, which are relevant to a wide variety of hardwares such as superconducting qubits and certain neutral atom or trapped ion setups, and more sophisticated noise models. We anticipate these approximate compilation techniques will be useful tools in a variety of future quantum computing experiments.

Moondra, Jai [Georgia Institute of Technology]↗
DOE OSTI2017

Adaptive quantum/molecular mechanics: what have we learned, where are we, and where do we go from here?: Adaptive QM/MM

Adaptive quantum-mechanics/molecular-mechanics (QM/MM) methods feature on-the-fly reclassification of atoms as QM or MM during a molecular dynamics(MD) simulation, allowing the location and contents of the QM subsystem to be dynamically updated as needed. Such flexibility is a distinct advantage over conventional QM/MM, where a ‘static’ boundary is retained between the QM and MM subsystems. The ‘dynamic’ boundary in adaptive QM/MM allows a finite-size QM to sustain simulations with an arbitrary length of time. Here, to ensure smooth transitions between QM and MM, the energy or forces are interpolated.Special treatments are applied so that artifacts are eliminated or minimized.Recent developments have shed light on the relationship between the adaptive algorithms that describe Hamiltonian and non-Hamiltonian systems. Originally developed to model an ion solvated in bulk solvent, adaptive QM/MM has been enhanced in many aspects, including the treatment of molecular fragments in macromolecules, monitoring molecules entering/leaving binding sites, and tracking proton transfer via the Grotthuss mechanism. Because the size of the QM region can be set as small as possible in adaptive QM/MM, the computational costs can be kept low. Small QM subsystems also facilitate the utilization of high-level QM theory and long simulation time, which can potentially lead to new insights.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Quantum simulation of Lindbladian dynamics via repeated interactions

The Lindblad equation generalizes the Schrödinger equation to quantum systems that undergo dissipative dynamics. The quantum simulation of Lindbladian dynamics is therefore non-unitary, preventing a naive application of state-of-the-art quantum algorithms. Here, we make use of an approximate correspondence between Lindbladian dynamics and evolution based on repeated interaction (RI) CPTP maps to write down a Hamiltonian formulation of the Lindblad dynamics and derive a rigorous error bound on the master equation. Specifically, we show that the number of interactions needed to simulate the Liouvillian within error e scales in most physical scenarios as . This is significant because the error in the Lindbladian approximation to the dynamics is not explicitly bounded in existing quantum algorithms for open system simulations. We then provide quantum algorithms to simulate RI maps using an iterative qubitization approach and Trotter–Suzuki formulas, and specifically show that for iterative qubitization the number of operations needed to simulate the dynamics (for a fixed value of ?) scales as in the limit where a0 (the coefficient 1-norm for the system and bath Hamiltonians) asymptotically dominates over the corresponding factor for the interaction Hamiltonian, which is often the case in weak coupling. This scaling would appear to be optimal if the complexity of ? is not considered, which underscores the importance of considering the error in the Liouvillian that we reveal in this work.

Quantum Computing↗
DOE OSTI2020

Canonical Transformation of Potential Model Hamiltonian Mechanics to Geometrical Form I

Using the methods of symplectic geometry, we establish the existence of a canonical transformation from potential model Hamiltonians of standard form in a Euclidean space to an equivalent geometrical form on a manifold, where the corresponding motions are along geodesic curves. The advantage of this representation is that it admits the computation of geodesic deviation as a test for local stability, shown in recent previous studies to be a very effective criterion for the stability of the orbits generated by the potential model Hamiltonian. We describe here an algorithm for finding the generating function for the canonical transformation and describe some of the properties of this mapping under local diffeomorphisms. We give a convergence proof for this algorithm for the one-dimensional case, and provide a precise geometric formulation of geodesic deviation which relates the stability of the motion in the geometric form to that of the Hamiltonian standard form. We apply our methods to a simple one-dimensional harmonic oscillator and conclude with a discussion of the relation of bounded domains in the two representations for which Morse theory would be applicable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Energy stable discontinuous Galerkin methods for Maxwell's equations in nonlinear optical media

The propagation of electromagnetic waves in general media is modeled by the time-dependent Maxwell's partial differential equations (PDEs), coupled with constitutive laws that describe the response of the media. In this work, we focus on nonlinear optical media whose response is modeled by a system of first order nonlinear ordinary differential equations (ODEs), which include a single resonance linear Lorentz dispersion, and the nonlinearity comes from the instantaneous electronic Kerr response and the residual Raman molecular vibrational response. To design efficient, accurate, and stable computational methods, we apply high order discontinuous Galerkin discretizations in space to the hybrid PDE-ODE Maxwell system with several choices of numerical fluxes, and the resulting semi-discrete methods are shown to be energy stable. Under some restrictions on the strength of the nonlinearity, error estimates are also established. When we turn to fully discrete methods, the challenge to achieve provable stability lies in the temporal discretizations of the nonlinear terms. To overcome this, novel strategies are proposed to treat the nonlinearity in our model within the framework of the second-order leap-frog and implicit trapezoidal time integrators. The performance of the overall algorithms are demonstrated through numerical simulations of kink and antikink waves, and third-harmonic generation in soliton propagation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Direct Higgs-top CP-phase measurement with $t\overline{t}h$ at the 14 TeV LHC and 100 TeV FCC

The study of the Higgs boson’s properties is a cornerstone of the LHC and future collider programs. In this paper, we examine the potential to directly probe the Higgs-top interaction strength and CP-structure in the $t\overline{t}h$ channel with the Higgs boson decaying to bottom-quark pairs and top-quarks in the di-leptonic mode. We adopt the BDRS algorithm to tag the boosted Higgs and exploit the M 2 -assisted reconstruction to compute observables sensitive to the CP-phase at the $t\bar{t}$ rest frame, where the new physics sensitivity can be enhanced. Performing a side-band analysis at the LHC to control the continuum $t\bar{t}b\bar{b}$ background, we find that the Higgs-top strength and CP-phase can be probed up to δ κt ≲ 20% and |a| ≲ 36° at 95% CL, respectively. We also derive that a similar analysis at a 100 TeV future collider could further improve the precision to δ κt ≲ 1% and |a| ≲ 1.5° where the CP-odd observables play a crucial role, boosting the sensitivity on the CP-phase

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗