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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Almost strong zero modes at finite temperature

Interacting fermionic chains exhibit extended regions of topological degeneracy of their ground states as a result of the presence of Majorana or parafermionic zero modes localized at the edges. In the opposite limit of infinite temperature, the corresponding nonintegrable spin chains, obtained via generalized Jordan-Wigner mapping, are known to host so-called almost strong zero modes, which are long-lived with respect to any bulk excitations. Here we study the fairly unexplored territory that bridges these two extreme cases of zero and infinite temperature. We blend two established techniques for states, the Lanczos series expansion and a tensor network ansatz, uplifting them to the level of operator algebra. This allows us to efficiently simulate large system sizes for arbitrarily long timescales and to extract the temperature-dependent decay rates. We observe that for the Kitaev-Hubbard model, the decay rate of the edge mode depends exponentially on the inverse temperature 𝛽, and on an effective energy scale Δ eff that is greater than the thermodynamic gap of the system Δ.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Thermal nature of confining strings

We investigate the quantum statistical properties of the confining string connecting a static fermion-antifermion pair in the massive Schwinger model. By analyzing the reduced density matrix of the subsystem located in between the fermion and antifermion, we demonstrate that as the interfermion separation approaches the string-breaking distance, the overlap between the microscopic density matrix and an effective thermal density matrix exhibits a pronounced, narrow peak, approaching unity at the onset of string breaking. This behavior reveals that the confining flux tube evolves toward a genuinely thermal state as the separation between the charges grows, even in the absence of an external heat bath. In other words, one cannot tell whether a reduced state of the subsystem arises from a surrounding heat bath or from entanglement with the rest of the system. The entanglement spectrum near the critical string-breaking distance exhibits a rapid transition from the dominance of a single state describing the confining electric string towards a strongly entangled state containing virtual fermion-antifermion pairs. Our findings establish a quantitative link between confinement, entanglement, and emergent thermality, and suggest that string breaking corresponds to a microscopic thermalization transition within the flux tube.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Precision study of the massive Schwinger model near quantum criticality

We perform a numerical analysis of the massive Schwinger model in the presence of a background electric field. Using the Density Matrix Renormalization Group approach, we efficiently compute the spectrum of the Schwinger model on a staggered lattice with up to 3000 qubits. As a result, we achieve a precise computation of the critical mass of the massive Schwinger model to five digits using four different “criticality criteria,” observing perfect agreement among them Additionally, we discuss the effect of a four-fermion operator deformation of the Schwinger model and compute the critical mass for various values of the deformation parameter.

Critical phenomena↗
DOE OSTI2024

Accurate numerical simulations of open quantum systems using spectral tensor trains

Decoherence between qubits is a major bottleneck in quantum computations. Decoherence results from intrinsic quantum and thermal fluctuations as well as noise in the external fields that perform the measurement and preparation processes. With prescribed colored noise spectra for intrinsic and extrinsic noise, we present a numerical method, Quantum Accelerated Stochastic Propagator Evaluation (Q-ASPEN), to solve the time-dependent noise-averaged reduced density matrix in the presence of intrinsic and extrinsic noise. Q-ASPEN is arbitrarily accurate and can be applied to provide estimates for the resources needed to error-correct quantum computations. We employ spectral tensor trains, which combine the advantages of tensor networks and pseudospectral methods, as a variational ansatz to the quantum relaxation problem and optimize the ansatz using methods typically used to train neural networks. Here, the spectral tensor trains in Q-ASPEN make accurate calculations with tens of quantum levels feasible. We present benchmarks for Q-ASPEN on the spin-boson model in the presence of intrinsic noise and on a quantum chain of up to 32 sites in the presence of extrinsic noise. In our benchmark, the memory cost of Q-ASPEN scales as a low-order polynomial in the size of the system once the number of system states surpasses the number of basis functions used in the spectral expansion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM—rooted in bath correlation function decompositions—proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna–Matthews–Olson complex model highlight TTN-HEOM’s superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.

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

Ground state energy and magnetization curve of a frustrated magnetic system from real-time evolution on a digital quantum processor

Models of interacting many-body quantum systems that may realize new exotic phases of matter, notably quantum spin liquids, are challenging to study using even state-of-the-art classical methods such as tensor network simulations. Quantum computing provides a promising route for overcoming these difficulties to find ground states, dynamics, and more. In this paper, we argue that recently developed hybrid quantum-classical algorithms based on real-time evolution are promising methods for solving a particularly important model in the search for spin liquids, the antiferromagnetic Heisenberg model on the two-dimensional kagome lattice. We show how to construct efficient quantum circuits to implement time evolution for the model and to evaluate key observables on the quantum computer, and we argue that the method has favorable scaling with increasing system size. We then restrict to a 12-spin star plaquette from the kagome lattice and a related 8-spin system, and we give an empirical demonstration on these small systems that the hybrid algorithms can efficiently find the ground state energy and the magnetization curve. For these demonstrations, we use four levels of approximation: exact state vectors, exact state vectors with statistical noise from sampling, noisy classical emulators, and (for the 8-spin system only) real quantum hardware, specifically the Quantinuum H1-1 processor; for the noisy simulations and hardware demonstration, we also employ error mitigation strategies based on the symmetries of the Hamiltonian. Our results strongly suggest that these hybrid algorithms present a promising direction for studying quantum spin liquids and more generally for resolving important unsolved problems in condensed matter theory and beyond.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Beyond-classical computation in quantum simulation

Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. However, establishing this capability, especially for impactful and meaningful problems, remains a central challenge. Here, we show that superconducting quantum annealing processors can rapidly generate samples in close agreement with solutions of the Schrödinger equation. We demonstrate area-law scaling of entanglement in the model quench dynamics of two-, three-, and infinite-dimensional spin glasses, supporting the observed stretched-exponential scaling of effort for matrix-product-state approaches. We show that several leading approximate methods based on tensor networks and neural networks cannot achieve the same accuracy as the quantum annealer within a reasonable time frame. Thus, quantum annealers can answer questions of practical importance that may remain out of reach for classical computation.

King, Andrew D. [D-Wave Quantum Inc., Burnaby, BC ↗
DOE OSTI2026

A Tensor Network-Based Quantum Algorithm for the Nonlinear 1D Burgers' Equation

In this work, we implement a tensor network-based quantum algorithm to solve unsteady, nonlinear partial differential equations (PDEs). The challenge lies in how to effectively represent, encode, process, and evolve the nonlinear system of PDEs on quantum computers. We will discuss the new techniques using the compressible 1-dimensional (1D) Burgers' equation as an example, because it represents the fundamental nonlinear feature and yet removes certain complexity in physics, allowing us to focus on the design of quantum algorithms. Previous attempts to solve nonlinear PDEs in quantum computation have often involved storing multiple copies of solutions or employing linearizations. Neither is practical due to exponential scaling with evolution time or insufficient solution accuracy. Our framework is based on matrix product states (MPSs) and matrix product operators (MPOs). For example, the velocity field is represented by MPS, whereas the linear and nonlinear spatial differential terms of the velocity field are processed by MPOs. Our primary focus herein is to verify and validate the various tensor network components of the algorithm using solutions obtained by the classical algorithms on high performance computing (HPC) architectures. We use a classical time marching method to demonstrate the functionality of the tensor network operations to model the PDE and their robustness with the time evolution of the system. Our classical simulation results demonstrate the utility of tensor network-based operations in modeling nonlinear PDEs and highlight the necessity as well as potential advantages of using quantum simulations for these techniques.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗
DOE OSTI2025

Discrete generative diffusion models without stochastic differential equations: A tensor network approach

Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard DMs, this is done by learning a “score function” that reverses the effect of adding diffusive noise to the distribution of interest. Here we consider the generalisation of DMs to lattice systems with discrete degrees of freedom, and where noise is added via Markov chain jump dynamics. We show how to use tensor networks (TNs) to efficiently define and sample such “discrete diffusion models” (DDMs) without explicitly having to solve a stochastic differential equation. We show the following: (i) by parametrising the data and evolution operators as TNs, the denoising dynamics can be represented exactly; (ii) the auto-regressive nature of TNs allows to generate samples efficiently and without bias; (iii) for sampling Boltzmann-like distributions, TNs allow to construct an efficient learning scheme that integrates well with Monte Carlo. We illustrate this approach to study the equilibrium of two models with non-trivial thermodynamics, the d = 1 constrained Fredkin chain and the d = 2 Ising model. Published by the American Physical Society 2025

Causer, Luke (ORCID:0000000194243473)↗
DOE OSTI2025

Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments

In this work, we introduce an efficient method, TTN-HEOM, for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme with the bexcitonic generalization of the numerically exact hierarchical equations of motion (HEOM). The method yields a series of quantum master equations for all core tensors in the TTN that efficiently and accurately capture the open quantum dynamics for non-Markovian environments to all orders in the system–bath interaction. These master equations are constructed based on the time-dependent Dirac–Frenkel variational principle, which isolates the optimal dynamics for the core tensors given the TTN ansatz. The dynamics converges to the HEOM when increasing the rank of the core tensors, a limit in which the TTN ansatz becomes exact. We introduce TENSO, tensor equations for non-Markovian structured open systems, as a general-purpose Python code to propagate the TTN-HEOM dynamics. We implement three general propagators for the coupled master equations: two fixed-rank methods that require a constant memory footprint during the dynamics and one adaptive-rank method with a variable memory footprint controlled by the target level of computational error. We exemplify the utility of these methods by simulating a two-level system coupled to a structured bath containing one Drude–Lorentz component and eight Brownian oscillators, which is beyond what can presently be computed using the standard HEOM. Our results show that the TTN-HEOM is capable of simulating both dephasing and relaxation dynamics of driven quantum systems interacting with structured baths, even those of chemical complexity, with an affordable computational cost.

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

Graph neural networks for mechanical property prediction of 2D fiber composites

This work investigates the ability of graph neural networks (GNNs) to homogenize 2D fiber composite microstructures. We use different inhomogeneity and anisotropy indices to motivate and show that the Volume Elements (VEs) used in ML methods should ideally be far from their Representative Volume Element (RVE) size limit and, consequently, are notably anisotropic. Hence, training only the isotropic limit properties may not be acceptable. Another aspect is the need to normalize elastic stiffness values for ML, especially when high elastic contrast ratios are encountered between composite phases or in the material set. We introduce a normalization technique based on the mean-field method (MFM) to handle such high contrast ratios and train for the entire stiffness tensor. We show that the proposed GNN approaches exhibit high accuracy and efficiency compared to traditional methods and convolutional neural networks, utilizing unstructured graphs constructed from microstructure topology. Our model successfully predicts the stiffness tensor, peak strength under bulk damage, and brittle fracture initiation strength across diverse microstructure configurations while maintaining high accuracy even for extreme material contrasts and volume fractions. We also present a method to improve prediction accuracy for small dataset sizes using Voronoi partitioning.

Brittle strength↗
DOE OSTI2025

Thermal Radiation Transport with Tensor Trains

We present a novel tensor network algorithm to solve the time-dependent, gray thermal radiation transport equation. The method invokes a tensor train (TT) decomposition for the specific intensity. The efficiency of this approach is dictated by the rank of the decomposition. When the solution is “low rank,” the memory footprint of the specific intensity solution vector may be significantly compressed. The algorithm, following a step-then-truncate approach of a traditional discrete ordinates method, operates directly on the compressed state vector, thereby enabling large speedups for low-rank solutions. To achieve these speedups, we rely on a recently developed rounding approach based on the Gram-SVD. We detail how familiar S N algorithms for (gray) thermal transport can be mapped to this TT framework and present several numerical examples testing both the optically thick and thin regimes. The TT framework finds low-rank structure and supplies up to ≃60× speedups and ≃1000× compressions for problems demanding large angle counts, thereby enabling previously intractable SN calculations and supplying a promising avenue to mitigate ray effects.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Space-Time Finite Element Tensor Network Approach for the Time-Dependent Convection–Diffusion–Reaction Equation with Variable Coefficients

In this paper, we present a new space-time Galerkin-like method, where we treat the discretization of spatial and temporal domains simultaneously. This method utilizes a mixed formulation of the tensor-train (TT) and quantized tensor-train (QTT) (please see Section Tensor-Train Decomposition), designed for the finite element discretization (Q1-FEM) of the time-dependent convection–diffusion–reaction (CDR) equation. We reformulate the assembly process of the finite element discretized CDR to enhance its compatibility with tensor operations and introduce a low-rank tensor structure for the finite element operators. Recognizing the banded structure inherent in the finite element framework’s discrete operators, we further exploit the QTT format of the CDR to achieve greater speed and compression. Additionally, we present a comprehensive approach for integrating variable coefficients of CDR into the global discrete operators within the TT/QTT framework. The effectiveness of the proposed method, in terms of memory efficiency and computational complexity, is demonstrated through a series of numerical experiments, including a semi-linear example.

convection–diffusion–reaction equation↗
NASA NTRSDate not supplied

Exploring Quantum State Preparation Using Tensor Networks and Sparse Wavefunction Simulations

The variational quantum eigenvalue solver is a powerful hybrid quantum-classical approach that has been suggested as a candidate method to run on near-term quantum hardware for computing ground state electronic energies of molecular systems. However, even for small molecules, the number of variational parameters and qubits required to minimize the electronic energy is beyond the reach of current quantum computers except for small basis sets. We explore a new paradigm for state preparation where we test how much of the optimization can be approximately prepared with classical computers to reduce the number of optimization steps performed using a quantum device. By adapting a recent algorithm for the factorized form of the UCC ansatz, we can study molecular electronic structure problems with up to 64 qubits. In addition, we also test a related approach of using tensor networks to optimize quantum circuits in order to benchmark various lattice models. We present results using these approaches and discuss strategies for incorporating these ideas into variational algorithms involving near-term quantum computers. Our results help demonstrate the strength of the UCC ansatz and address pressing questions about optimal initial parameterizations and circuit construction.

quantum computing↗
DOE OSTI2025

Gradient flow based phase-field modeling using separable neural networks

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.

42 ENGINEERING↗
DOE OSTI2026

Locally purified maximally mixed states at scale: Entanglement pruning and symmetries

Locally Purified Density Operators (LPDOs) are state-of-the-art tensor network ansatze candidates that efficiently represent mixed quantum states at scale. However, given their non-uniqueness, their representational complexity is generally sub-optimal in practical computations. Here, in this work we perform a comprehensive numerical and analytical analysis and resolve this issue in the experimentally relevant limit where noise depolarizes the density operator into a maximally mixed state. To resolve the sub-optimality issue, we analyze two numerical tools, one analytic method, and detail the relations between them. The numerical tools used are fidelity-preserving truncations and isometric gauge transformations leveraging Riemannian optimizations over entropic objective functions. In addition, by invoking the injectivity and symmetry constraints of the maximally mixed LPDO, we also present analytical closed-form expressions for the disentangler and discuss their relation to numerical optimizers. Further, away from the maximally mixed state, our simulations highlight how the truncation threshold smoothly interpolate, as a function of depolarization, between established matrix product results and our new results. Our work shows how, by minimizing the resources required to represent key states of practical interest in experiment, the efficiency of tensor network algorithms can be substantially increased. This paves the path for uncovering tensor network’s fundamental scalability limits and latent potential in representing the wide locus of mixed quantum states that are accessible on near-term quantum devices.

Gangapuram, Amit Jamadagni [Oak Ridge National Lab↗
NASA NTRSDate not supplied

Ab initio ground states of strongly-correlated materials on quantum computers

The accurate first-principles description of strongly-correlated materials is an important and challenging problem in condensed matter physics. Ab initio downfolding has emerged as a way of deriving accurate many-body Hamiltonians including strong correlations, representing a subspace of interest of a material, using density functional theory calculations as a starting point. However, the solution of these material-specific models can scale exponentially on classical computers, constituting a challenge. Here we propose that utilizing quantum computers for obtaining the properties of downfolded Hamiltonians yields an accurate description of the ground state properties of strongly-correlated systems, while circumventing the exponential scaling problem. We benchmark the solution of Hubbard-like models obtained through downfolding by utilizing a classical tensor network implementation of variational quantum eigensolvers (VQE), and we reveal a strategy for driving the optimization through a hybrid minimization of the energy and maximization of the overlap with an approximate solution obtained through low-cost computational methods. This results in a reduction of the energy error by orders of magnitude compared to conventional VQE approaches, and allows us to reproduce long-range correlations for the first time. We demonstrate our first-principles approach for diverse strongly-correlated materials, correctly predicting the antiferromagnetic state of one-dimensional cuprate Ca 2 CuO 3 , the excitonic ground state of monolayer WTe2, and the charge-ordered state of correlated metal SrVO 3 . Our efficient computational implementation allows us to simulate large systems with up to 54 qubits and encompassing up to four correlated bands, which is indicative of the complexity that our framework can address.

Antonios M Alvertis↗