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DOE OSTI2026

Quantum-Inspired Bayesian Sampling for Uncertainty Quantification and Machine Learning (Final Technical Report)

With increasing simulation and measurement data, machine learning and artificial intelligence have been widely used in computational decision-making of complex engineering systems. The resulting tools, such as uncertainty quantification solvers, reinforcement learning, and physics-informed machine learning, have achieved great success in critical DOE tasks such as material discovery and design, energy system modeling and control, and numerical weather and climate prediction. A core topic in scientific machine learning and artificial intelligence is Bayesian inference: given an observed data set, people want to estimate the posterior distribution of a (possibly large) number of hidden parameters. Due to the flexibility and weak assumptions, Bayesian sampling has been the mainstream Bayesian inference solvers despite the rapid progress of approximate Bayesian inference. Classical Bayesian sampling methods such as Markov-chain Monte Carlo suffer from a low-acceptance rate due to the random walk nature, therefore state-of-the-art techniques use Hamiltonian Monte Carlo and its variants to efficiently draw posterior samples in a high dimension. The key idea of Hamiltonian Monte Carlo and its variants is to simulate the Hamiltonian dynamics of a classical particle with a fixed mass, and their performance significantly degrades when the posterior distribution is highly spiky or has multiple modes. Leveraging the idea of quantum physics, this project has investigated new theory, algorithms and applications of Bayesian inference (especially Bayesian sampling). The main results include: (1) novel quantum-inspired Bayesian sampling methods that can lead to better accuracy for challenging multi-modal or spiky distributions, (2) more scalable machine learning framework leveraging tensor-compressed Bayesian inference, and (3) Bayesian and sampling approaches for verifying the robustness of continuous and binary neural networks.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Influence of disorder on antidot vortex Majorana states in three-dimensional topological insulators

Topological insulator/superconductor two-dimensional heterostructures are promising candidates for realizing topological superconductivity and Majorana modes. In these systems, a vortex pinned by a prefabricated antidot in the superconductor can host Majorana zero-energy modes (MZMs), which are exotic quasiparticles that may enable quantum information processing. However, a major challenge is to design devices that can manipulate the information encoded in these MZMs. One of the key factors is to create small and clean antidots, so the MZMs, localized in the vortex core, have a large gap to other excitations. If the antidot is too large or too disordered, the level spacing for the subgap vortex states may become smaller than temperature. In this paper, we numerically investigate the effects of disorder, chemical potential, and antidot size on the subgap vortex spectrum, using a two-dimensional effective model of the topological insulator surface. Our model allows us to simulate large system sizes with vortices up to 1.8 µ⁢m in diameter (with a 6 nm lattice constant). We also compare our disorder model with the transport data from existing experiments. As a result, we find that the spectral gap can exhibit a nonmonotonic behavior as a function of disorder strength, and that it can be tuned by applying a gate voltage.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Collective neutrino oscillations in three flavors on qubit and qutrit processors

Collective neutrino flavor oscillations are of primary importance in understanding the dynamic evolution of core-collapse supernovae and subsequent terrestrial detection, but also among the most challenging aspects of numerical simulations. This situation is complicated by the quantum many-body nature of the problem due to neutrino-neutrino interactions, which demands a quantum treatment. An additional complication is the presence of three flavors, which often is approximated by the electron flavor and a heavy lepton flavor. In this work, we provide both qubit and qutrit encodings for all three flavors, and develop optimized quantum circuits for the time evolution and analyze the Trotter error. We conclude our study with a hardware experiment of a system of two neutrinos with superconducting hardware: the IBM Torino device for qubits and Advanced Quantum Testbed device at the Lawrence Berkeley National Laboratory for qutrits. We find that error mitigation greatly helps in obtaining a signal consistent with simulations. Finally, while hardware results are comparable at this stage, we expect the qutrit setup to be more convenient for large-scale simulations since it does not suffer from probability leakage into nonphysical qubit space, unlike the qubit setup.

Neutrino oscillations↗

DOE OSTI2024

Memcomputing the Spectrum of Correlated Quantum Systems

The goals and objectives of the grant DE‐SC0020892 were to apply a new computing paradigm, MemComputing, to efficiently simulate properties of correlated quantum systems. The method has been applied to a wide set of problems ranging from quantum state tomography to finding the ground state of correlated systems. In all cases, substantial advantages compared to state-of-the-art approaches have been obtained. The project has also led to the suggestion of the transformer architecture (used nowadays in large-language models) as an efficient quantum state representation, and a better understanding of the role of memory in the generation of long-range order in neural networks. This grant has supported the work of a PhD student, inspired a new class on unconventional computing taught at the University of California, San Diego and has generated several peer-reviewed papers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Floquet Engineering of Interactions and Entanglement in Periodically Driven Rydberg Chains

Neutral atom arrays driven into Rydberg states constitute a promising approach for realizing programmable quantum systems. Enabled by strong interactions associated with Rydberg blockade, they allow for simulation of complex spin models and quantum dynamics. We introduce a new Floquet engineering technique for systems in the blockade regime that provides control over novel forms of interactions and entanglement dynamics in such systems. Our approach is based on time-dependent control of Rydberg laser detuning and leverages perturbations around periodic many-body trajectories as resources for operator spreading. These time-evolved operators are utilized as a basis for engineering interactions in the effective Hamiltonian describing the stroboscopic evolution. As an example, we show how our method can be used to engineer strong spin exchange, consistent with the blockade, in a one-dimensional chain, enabling the exploration of gapless Luttinger liquid phases. In addition, we demonstrate that combining gapless excitations with Rydberg blockade can lead to dynamic generation of large-scale multipartite entanglement. Experimental feasibility and possible generalizations are discussed.

Floquet systems↗

DOE OSTI2022

Eigenstate entanglement scaling for critical interacting spin chains

With increasing subsystem size and energy, bipartite entanglement entropies of energy eigenstates cross over from the groundstate scaling to a volume law. In previous work, we pointed out that, when strong or weak eigenstate thermalization (ETH) applies, the entanglement entropies of all or, respectively, almost all eigenstates follow a single crossover function. The crossover functions are determined by the subsystem entropy of thermal states and assume universal scaling forms in quantum-critical regimes. This was demonstrated by field-theoretical arguments and the analysis of large systems of non-interacting fermions and bosons. Here, we substantiate such scaling properties for integrable and non-integrable interacting spin-1/2 chains at criticality using exact diagonalization. In particular, we analyze XXZ and transverse-field Ising models with and without next-nearest-neighbor interactions. Indeed, the crossover of thermal subsystem entropies can be described by a universal scaling function following from conformal field theory. Furthermore, we analyze the validity of ETH for entanglement in these models. Even for the relatively small system sizes that can be simulated, the distributions of eigenstate entanglement entropies are sharply peaked around the subsystem entropies of the corresponding thermal ensembles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Unorthodox parallelization for Bayesian quantum state estimation

Quantum state tomography (QST) allows for the reconstruction of quantum states through measurements and some inference technique under the assumption of repeated state preparations. Bayesian inference provides a promising platform to achieve both efficient QST and accurate uncertainty quantification, yet is generally plagued by the computational limitations associated with long Markov chains. In this work, we present a novel Bayesian QST approach that leverages modern distributed parallel computer architectures to efficiently sample a D-dimensional Hilbert space. Using a parallelized preconditioned Crank–Nicholson Metropolis–Hastings algorithm, we demonstrate our approach on simulated data and experimental results from IBM Quantum systems up to four qubits, showing significant speedups through parallelization. Although highly unorthodox in pooling independent Markov chains, our method proves remarkably practical, with validation ex post facto via diagnostics like the intrachain autocorrelation time. We conclude by discussing scalability to higher-dimensional systems, offering a path toward efficient and accurate Bayesian characterization of large quantum systems.

Bayesian inference↗

DOE OSTI2021

Quantum simulation: From spin models to gauge-gravity correspondence

Quantum many-body systems with coherent and controllable interactions enable the realization of novel quantum materials, the quantum simulation of problems that cannot be simulated on classical computers, computational systems that are exponentially faster than existing classical algorithms, and the direct investigation of the conjectured duality between gravitational theories and quantum field theories. This project focusses on quantum phase transitions in strongly interacting many-body spin systems, and in particular on the dynamical evolution near the critical point and across the phase transition. The dynamics of a large quantum system containing more than 50 qubits is investigated in various critical regimes. In particular, the Kibble-Zurek transition has been characterized and critical exponents have been measured. Furthermore, quantum many-body scars have been observed and characterized for the first time. We are investigating the Kibble-Zurek mechanism in the quantum phase transition in one dimension from a disordered system to a system with ordering induced by Rydberg interactions between neighboring atoms. The Kibble-Zurek mechanism describes the formation of topological defects as a system evolves across a phase transitions, and is expected to apply to a large number of problems, including cosmology, where it should describe the structure of domain formation in the early universe.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2020

NESSi : The N on- E quilibrium S ystems S imulation package

The nonequilibrium dynamics of correlated many-particle systems is of interest in connection with pump–probe experiments on molecular systems and solids, as well as theoretical investigations of transport properties and relaxation processes. Nonequilibrium Green’s functions are a powerful tool to study interaction effects in quantum many-particle systems out of equilibrium, and to extract physically relevant information for the interpretation of experiments. Here, we present the open-source software package NESSi (The Non-Equilibrium Systems Simulation package) which allows to perform many-body dynamics simulations based on Green’s functions on the L-shaped Kadanoff–Baym contour. NESSi contains the library libcntr which implements tools for basic operations on these nonequilibrium Green’s functions, for constructing Feynman diagrams, and for the solution of integral and integro-differential equations involving contour Green’s functions. The library employs a discretization of the Kadanoff–Baym contour into time points and a high-order implementation of integration routines. The total integrated error scales up to $\mathcal{O}(N^{-7})$, which is important since the numerical effort increases at least cubically with the simulation time. A distributed-memory parallelization over reciprocal space allows large-scale simulations of lattice systems. We provide a collection of example programs ranging from dynamics in simple two-level systems to problems relevant in contemporary condensed matter physics, including Hubbard clusters and Hubbard or Holstein lattice models. The libcntr library is the basis of a follow-up software package for nonequilibrium dynamical mean-field theory calculations based on strong-coupling perturbative impurity solvers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Scalable Circuits for Preparing Ground States on Digital Quantum Computers: The Schwinger Model Vacuum on 100 Qubits

The vacuum of the lattice Schwinger model is prepared on up to 100 qubits of IBM’s Eagle-processor quantum computers. A new algorithm to prepare the ground state of a gapped translationally invariant system on a quantum computer is presented, which we call “scalable circuits ADAPT-VQE” (SC-ADAPT-VQE). This algorithm uses the exponential decay of correlations between distant regions of the ground state, together with ADAPT-VQE, to construct quantum circuits for state preparation that can be scaled to arbitrarily large systems. These scalable circuits can be determined with use of classical computers, avoiding the challenging task of optimizing parameterized circuits on a quantum computer. SC-ADAPT-VQE is applied to the Schwinger model, and is shown to be systematically improvable, with an accuracy that converges exponentially with circuit depth. Both the structure of the circuits and the deviations of prepared wave functions are found to become independent of the number of spatial sites, L . This allows a controlled extrapolation of the circuits, determined with use of small or modest-sized systems, to arbitrarily large L . The circuits for the Schwinger model are determined on lattices up to L = 14 (28 qubits) with the Qiskit classical simulator, and are subsequently scaled up to prepare the L = 50 (100 qubits) vacuum on IBM’s 127-superconducting-qubit quantum computers ibm_brisbane and ibm_cusco. After introduction of an improved error-mitigation technique, which we call “operator decoherence renormalization”, the chiral condensate and charge-charge correlators obtained from the quantum computers are found to be in good agreement with classical matrix product state simulations. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Quantum utility in simulating the real-time dynamics of the Fermi–Hubbard model using superconducting quantum computers

The Fermi–Hubbard model is a fundamental model in condensed matter physics that describes strongly correlated electrons. On the other hand, quantum computers are emerging as powerful tools for exploring the complex dynamics of these quantum many-body systems. In this work, we demonstrate the quantum simulation of the one-dimensional Fermi–Hubbard model using IBM's superconducting quantum computers, employing over 100 qubits. We introduce a first-order Trotterization scheme and extend it to an optimized second-order Trotterization for the time evolution in the Fermi–Hubbard model, specifically tailored for the limited qubit connectivity of quantum architectures, such as IBM's platforms. Notably, both Trotterization approaches are scalable and maintain a constant circuit depth at each Trotter step, regardless of the qubit count, enabling us to precisely investigate the relaxation dynamics in the Fermi–Hubbard model by measuring the expectation value of the Néel observable (staggered magnetization) for time-evolved quantum states. Lastly, our successful measurement of expectation values in such large-scale quantum many-body systems, especially at longer time scales with larger entanglement, highlights the quantum utility of superconducting quantum platforms over conventional classical approximation methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Feasibility of the LAMMPS SPH Package for Simulating Bubble Motion in Vibrating Containers

The Smoothed Particle Hydrodynamics (SPH) package within LAMMPS is explored as a possible tool for simulating the motion of bubbles in a vibrating liquid-filled container. As an initial test case, the unphysical but computationally less intense situation of a two-dimensional single bubble rising in a quiescent liquid under the influence of gravity is considered herein. Although physically plausible behavior was obtained under certain conditions, this behavior depends strongly on the system parameters. Moreover, the large density ratio between the liquid and bubble requires extremely small timesteps, which make the simulations undesirably computationally expensive. Ultimately, it was determined that this method is not feasible for providing quantitatively accurate results for the desired application.

42 ENGINEERING↗

DOE OSTI2025

Potential quantum advantage for simulation of fluid dynamics

Numerical simulation of turbulent fluid dynamics needs to either parametrize turbulence—which introduces large uncertainties—or explicitly resolve the smallest scales—which is prohibitively expensive. Here, we provide evidence through analytic bounds and numerical studies that a potential quantum speedup can be achieved to simulate fluid dynamics using quantum computing. Specifically, we provide a lattice Boltzmann formulation of fluid dynamics for which we give evidence that low-order Carleman linearization is much more accurate than previously believed for these systems. This is achieved via a combination of reformulating the Navier-Stokes nonlinearity (u·$\triangledown$u) to lattice-Boltzmann nonlinearity (u 2 ) and accurately linearizing the dynamical equations, which effectively trades nonlinearity for additional degrees of freedom that add negligible expense in the quantum solver. Based on this, we apply a quantum algorithm for simulating the Carleman-linearized lattice Boltzmann equation and provide evidence that its cost scales logarithmically with system size compared with polynomial scaling in the best known classical algorithms. In this paper, we suggest that a quantum advantage may exist for simulating fluid dynamics, paving the way for simulating nonlinear multiscale transport phenomena in a wide range of disciplines using quantum computing.

42 ENGINEERING↗

DOE OSTI2023

Preparations for quantum simulations of quantum chromodynamics in 1+1 dimensions. I. Axial gauge

Here, tools necessary for quantum simulations of 1+1 dimensional quantum chromodynamics are developed. When formulated in axial gauge and with two flavors of quarks, this system requires 12 qubits per spatial site with the gauge fields included via nonlocal interactions. Classical computations and D-wave’s quantum annealer advantage are used to determine the hadronic spectrum, enabling a decomposition of the masses and a study of quark entanglement. Color “edge” states confined within a screening length of the end of the lattice are found. IBM’s seven-qubit quantum computers, ibmq_jakarta and ibm_perth, are used to compute dynamics from the trivial vacuum in one-flavor QCD with one spatial site. More generally, the Hamiltonian and quantum circuits for time evolution of 1+1 dimensional SU(N c ) gauge theory with Nf flavors of quarks are developed, and the resource requirements for large-scale quantum simulations are estimated.

1+1 dimensions↗

DOE OSTI2025

Analysis and Validation of PMT s Waveforms in ICARUS LArTPC Using Monte Carlo Simulations

ICARUS (Imaging Cosmic and Rare Underground Signals) serves as the Far Detector in the Short Baseline Neutrino (SBN) program at Fermilab, playing a central role in investigating the potential existence of sterile neutrinos in the eV squared mass range. The detector consists of two large Liquid Argon Time Projection Chambers (LArTPCs) with a total capacity of 760 tons of liquid Argon. A key component of the system is its array of 360 Photo-Multiplier Tubes (PMTs), which detect the scintillation light produced by charged particles in liquid Argon; the fast scintillation signal enables accurate event timing, triggering, and reconstruction. Together with the TPC and CRT systems, the PMTs ensure precise interaction time measurements, which are crucial for distinguishing neutrino interactions from cosmic-ray backgrounds. ICARUS uses Hamamatsu R5912-MOD PMTs, optimized for cryogenic temperatures, with high quantum efficiency, excellent timing resolution, low dark current (around 10 nA at 1500 V), and broad spectral sensitivity (300–650 nm). These characteristics are crucial for the efficient detection of scintillation light. Analyzing the waveforms of PMT signals allows for a detailed comparison between experimental data and Monte Carlo simulations. This analysis is fundamental for improving the accuracy of neutrino event reconstruction, enhancing detector calibration, and optimizing the detector's performance for current and future operations.

Brio, V. [Catania U.] (ORCID:0009000088807391)↗

DOE OSTI2024

Random insights into the complexity of two-dimensional tensor network calculations

Projected entangled pair states (PEPS) offer memory-efficient representations of some quantum many-body states that obey an entanglement area law and are the basis for classical simulations of ground states in two-dimensional (2d) condensed matter systems. However, rigorous results show that exactly computing observables from a 2d PEPS state is generically a computationally hard problem. Yet approximation schemes for computing properties of 2d PEPS are regularly used, and empirically seen to succeed, for a large subclass of (“not too entangled”) condensed matter ground states. Adopting the philosophy of random matrix theory, in this work, we analyze the complexity of approximately contracting a 2d random PEPS by exploiting an analytic mapping to an effective replicated statistical mechanics model that permits a controlled analysis at a large bond dimension. Through this statistical-mechanics lens, we argue that (i) although approximately sampling wave-function amplitudes of random PEPS faces a computational-complexity phase transition above a critical bond dimension, and (ii) one can generically efficiently estimate the norm and correlation functions for any finite bond dimension. Furthermore, these results are supported numerically for various bond-dimension regimes. It is an important open question whether the above results for random PEPS apply more generally also to PEPS representing physically relevant ground states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Reaching the equilibrium state of the frustrated triangular Ising magnet Ca 3 Co 2 O 6

Ca 3 Co 2 O 6 is a frustrated magnet consisting of a triangular arrangement of chains of Ising spins. It shows regular magnetization steps versus magnetic field every 1.2 T that are metastable with very slow dynamics. This has puzzled the community for many years and given rise to numerous potential theories. Here we approach the problem by seeking the elusive magnetic equilibrium state at T=2 K. To this end, we explore two approaches: (1) bypassing the slow dynamics produced by changing fields by instead field-cooling directly to the target temperature and (2) quantum annealing in transverse magnetic fields. While we observe no measurable effect of the quantum annealing in fields up to 7 T, which is likely due to the large Ising anisotropy of Co spins in this material, we find that for the field cooling in longitudinal fields we achieve the predicted equilibrium 1/3 magnetization. We perform Monte Carlo simulations of the ground state phase diagram and we also simulate the quantum annealing process and find good agreement between experiment and theory. Thus we present an investigation of the elusive ground state properties of the canonical frustrated triangular system Ca 3 Co 2 O 6 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Transport, correlations, and chaos in a classical disordered anharmonic chain

Here, we explore transport properties in a disordered nonlinear chain of classical harmonic oscillators, and thereby identify a regime exhibiting behavior analogous to that seen in quantum many-body-localized systems. Through extensive numerical simulations of this system connected at its ends to heat baths at different temperatures, we computed the heat current and the temperature profile in the nonequilibrium steady state as a function of system size $\textit{N}$, disorder strength Δ, and temperature $\textit{T}$. The conductivity $κ_N$, obtained for finite length ($\textit{N}$), saturates to a value $κ_∞$ > 0 in the large $\textit{N}$ limit, for all values of disorder strength Δ and temperature $\textit{T}$ > 0. We show evidence that for any Δ > 0 the conductivity goes to zero faster than any power of $\textit{T}$ in the ($\textit{T}$/Δ) → 0 limit, and find that the form $κ_∞$ ~ $e^{{–B|\text{ln}(CΔ/T)|}^{3}}$ fits our data. This form has earlier been suggested by a theory based on the dynamics of multioscillator chaotic islands. The finite-size effect can be $κ_N < κ_∞$ due to boundary resistance when the bulk conductivity is high (the weak disorder case), or $κ_N > κ_∞$ due to direct bath-to-bath coupling through bulk localized modes when the bulk is weakly conducting (the strong disorder case). We also present results on equilibrium dynamical correlation functions and on the role of chaos on transport properties. Finally, we explore the differences in the growth and propagation of chaos in the weak and strong chaos regimes by studying the classical version of the out-of-time-ordered commutator.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗