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DOE OSTI2026

Noise-Directed Adaptive Remapping for Integer Optimization: from qubits to (encoded) qudits

We extend Noise-Directed Adaptive Remapping (NDAR), a recently proposed heuristic meta-algorithm that leverages device noise as a computational resource, to optimization problems over discrete (integer) domains. While originally introduced for unconstrained binary optimization, the proposed generalization introduces additional gauge degrees of freedom at the logical level, such that the gauge transformation applied at each iteration is no longer unique, allowing tailoring to particular encodings or quantum hardware. We identify encoding-dependent requirements for NDAR beyond binary domains: feasibility of the noise attractor, existence of compatible gauge transformations that preserve an efficiently implementable circuit family, and a systematic way to select the transform to apply at each step. We analyze these criteria for qudit-native and for binary, one-hot, and domain-wall qubit encodings, using the Max-k-colorable subgraph problem as a running example. We demonstrate that these encodings can exhibit distinct advantages and tradeoffs when integrated within the NDAR framework, particularly in how noise-induced dynamics interact with the solution landscape and choice of encoding. Our results indicate that NDAR-guided noise considerations provide a new criterion for comparing device-level encoding choices for quantum optimization. Finally, we outline directions toward experimental realization in superconducting qudit devices and further algorithmic improvements.

Hadfield, Stuart [RIACS, Mtn. View] (ORCID:0000000↗

DOE OSTI2024

Evaluating a quantum-classical quantum Monte Carlo algorithm with Matchgate shadows

Solving the electronic structure problem of molecules and solids to high accuracy is a major challenge in quantum chemistry and condensed matter physics. The rapid emergence and development of quantum computers offer a promising route to systematically tackle this problem. Recent work by [Huggins et al ., Nature (London) 603 , 416 (2022)] proposed a hybrid quantum-classical quantum Monte Carlo (QC-QMC) algorithm using Clifford shadows to determine the ground state of a Fermionic Hamiltonian. This approach displayed inherent noise resilience and the potential for improved accuracy compared to its purely classical counterpart. Nevertheless, the use of Clifford shadows introduces an exponentially scaling postprocessing cost. In this work, we investigate an improved QC-QMC scheme utilizing the recently developed Matchgate shadows technique [Commun. Math. Phys. 404 , 629 (2023)], which removes the aforementioned exponential bottleneck. We observe from experiments on quantum hardware that the use of Matchgate shadows in QC-QMC is inherently noise robust. We show that this noise resilience has a more subtle origin than in the case of Clifford shadows. Nevertheless, we find that classical postprocessing, while asymptotically efficient, requires hours of runtime on thousands of classical CPUs for even the smallest chemical systems, presenting a major challenge to the scalability of the algorithm.

Monte Carlo methods↗

DOE OSTI2024

Quantum tensor network algorithms for evaluation of spectral functions on quantum computers

We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we call a quantum tensor network (QTN), we demonstrate algorithms to prepare ground and excited states on a quantum computer and apply them to molecular nanomagnets (MNMs) as a paradigmatic example. In this setting, we develop two approaches for extracting the spectral correlation functions measured in neutron-scattering experiments: (a) a generalization of the SWAP test for computing wave function overlaps and, (b) a generalization of the notion of matrix product operators to the QTN setting which generates a linear combination of unitaries. The latter method is discussed in detail for translationally invariant spin-half systems, where it is shown to reduce the qubit resource requirements compared with the SWAP method and may be generalized to other systems. We demonstrate the versatility of our approaches by simulating spin-1/2 and spin-3/2 MNMs, with the latter being an experimentally relevant model of a Cr$^{3+}_{8}$ ring. Here, our approach has qubit requirements that are independent of the number of constituents of the many-body system and scale only logarithmically with the bond dimension of the MPS representation, making them appealing for implementation on near-term quantum hardware with mid-circuit measurement and reset.

Neutron scattering↗

DOE OSTI2025

Systematic many-fermion Hamiltonian input scheme and spectral calculations on quantum computers

We present a novel input scheme for general second-quantized Hamiltonians of relativistic or non-relativistic many-fermion systems. This input scheme incorporates the fermionic anticommutation relations, particle number variations, and respects the symmetries of the Hamiltonian. Based on our input scheme, we propose a hybrid quantum-classical framework for spectral calculations on future quantum hardwares. We provide explicit circuit designs and the associated gate cost. We demonstrate our hybrid framework by solving the low-lying spectra of 42 Ca and 46 Ca. Our input scheme provides new pathways to solving the spectra and dynamics of the relativistic and nonrelativistic many-fermion systems via first-principles approaches.

Hybrid spectral calculation framework↗

DOE OSTI2024

Artificial-intelligence-driven shot reduction in quantum measurement

Variational Quantum Eigensolver (VQE) provides a powerful solution for approximating molecular ground state energies by combining quantum circuits and classical computers. However, estimating probabilistic outcomes on quantum hardware requires repeated measurements (shots), incurring significant costs as accuracy increases. Optimizing shot allocation is thus critical for improving the efficiency of VQE. Current strategies rely heavily on hand-crafted heuristics requiring extensive expert knowledge. This paper proposes a reinforcement learning (RL)-based approach that automatically learns shot assignment policies to minimize total measurement shots while achieving convergence to the minimum of the energy expectation in VQE. The RL agent assigns measurement shots across VQE optimization iterations based on the progress of the optimization. This approach reduces VQE's dependence on static heuristics and human expertise. When the RL-enabled VQE is applied to a small molecule, a shot reduction policy is learned. The policy demonstrates transferability across systems and compatibility with other wavefunction Ansätze. In addition to these specific findings, this work highlights the potential of RL for automatically discovering efficient and scalable quantum optimization strategies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Exact block encoding of imaginary time evolution with universal quantum neural networks

We develop a constructive approach to generate quantum neural networks capable of representing the exact thermal states of all many-body qubit Hamiltonians. The Trotter expansion of the imaginary time propagator is implemented through an exact block encoding by means of a unitary, restricted Boltzmann machine architecture. Marginalization over the hidden-layer neurons (auxiliary qubits) creates the nonunitary action on the visible layer. Then, we introduce a unitary deep Boltzmann machine architecture in which the hidden-layer qubits are allowed to couple laterally to other hidden qubits. We prove that this wave-function is closed under the action of the imaginary time propagator and, more generally, can represent the action of a universal set of quantum gate operations. We provide analytic expressions for the coefficients for both architectures, thus enabling exact network representations of thermal states without stochastic optimization of the network parameters. In the limit of large imaginary time, the yields the ground state of the system. The number of qubits grows linearly with the number of interactions and total imaginary time for a fixed interaction order. Both networks can be readily implemented on quantum hardware via midcircuit measurements of auxiliary qubits. If only one auxiliary qubit is measured and reset, the circuit depth scales linearly with imaginary time and number of interactions, while the width is constant. Alternatively, one can employ a number of auxiliary qubits linearly proportional to the number of interactions, and circuit depth grows linearly with imaginary time only. Every midcircuit measurement has a postselection success probability, and the overall success probability is equal to the product of the probabilities of the midcircuit measurements.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Chemical applications of variational quantum eigenvalue-based quantum algorithms: Perspective and survey

Exploring many-body chemical systems on classical computers often involves solving the Schrödinger equation. However, this approach is frequently limited by the exponential increase in the dimensionality of the Hamiltonian as the number of degrees of freedom increases. In contrast, quantum computing, specifically through the variational quantum eigensolver (VQE) framework, shows promise in overcoming this exponential cost. VQE can utilize the collective properties of quantum states to model the wavefunction in polynomial time. Despite the current limitations of quantum hardware, significant advances have been made in the development of VQE-based algorithms. Here, in this review, we provide an overview of emerging protocols, focusing on their applications in simulating the ground state, excited state, and vibrational properties of chemical systems. By examining notable algorithmic advancements and applications, this review aims to shed light on the challenges and potential of VQE-based algorithms in addressing relevant chemical problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Problem-tailored Simulation of Energy Transport on Noisy Quantum Computers

The transport of conserved quantities like spin and charge is fundamental to characterizing the behavior of quantum many-body systems. Numerically simulating such dynamics is generically challenging, which motivates the consideration of quantum computing strategies. However, the relatively high gate errors and limited coherence times of today's quantum computers pose their own challenge, highlighting the need to be frugal with quantum resources. In this work we report simulations on quantum hardware of infinite-temperature energy transport in the mixed-field Ising chain, a paradigmatic many-body system that can exhibit a range of transport behaviors at intermediate times. We consider a chain with L = 12 sites and find results broadly consistent with those from ideal circuit simulators over 90 Trotter steps, containing up to 990 entangling gates. To obtain these results, we use two key problem-tailored insights. First, we identify a convenient basis – the Pauli Y basis – in which to sample the infinite-temperature trace and provide theoretical and numerical justifications for its efficiency relative to, e.g., the computational basis. Second, in addition to a variety of problem-agnostic error mitigation strategies, we employ a renormalization strategy that compensates for global nonconservation of energy due to device noise. We discuss the applicability of the proposed sampling approach beyond the mixed-field Ising chain and formulate a variational method to search for a sampling basis with small sample-to-sample fluctuations for an arbitrary Hamiltonian. This opens the door to applying these techniques in more general models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Solution of the Schrödinger equation for quasi-one-dimensional materials using helical waves

We formulate and implement a spectral method for solving the Schrödinger equation, as it applies to quasi-one-dimensional materials and structures. This allows for computation of the electronic structure of important technological materials such as nanotubes (of arbitrary chirality), nanowires, nanoribbons, chiral nanoassemblies, nanosprings and nanocoils, in an accurate, efficient and systematic manner. Our work is motivated by the observation that one of the most successful methods for carrying out electronic structure calculations of bulk/crystalline systems — the plane-wave method — is a spectral method based on eigenfunction expansion. Our scheme avoids computationally onerous approximations involving periodic supercells often employed in conventional plane-wave calculations of quasi-one-dimensional materials, and also overcomes several limitations of other discretization strategies, e.g., those based on finite differences and atomic orbitals. The basis functions in our method — called helical waves (or twisted waves) — are eigenfunctions of the Laplacian with symmetry adapted boundary conditions, and are expressible in terms of plane waves and Bessel functions in helical coordinates. We describe the setup of fast transforms to carry out discretization of the governing equations using our basis set, and the use of matrix-free iterative diagonalization to obtain the electronic eigenstates. Miscellaneous computational details, including the choice of eigensolvers, use of a preconditioning scheme, evaluation of oscillatory radial integrals and the imposition of a kinetic energy cutoff are discussed. We have implemented these strategies into a computational package called HelicES (Helical Electronic Structure). We demonstrate the utility of our method in carrying out systematic electronic structure calculations of various quasi-one-dimensional materials through numerous examples involving nanotubes, nanoribbons and nanowires. We also explore the convergence properties of our method, and assess its accuracy and computational efficiency by comparison against reference finite difference, transfer matrix method and plane-wave results. We anticipate that our method will find applications in computational nanomechanics and multiscale modeling, for carrying out transport calculations of interest to the field of semiconductor devices, and for the discovery of novel chiral phases of matter that are of relevance to the burgeoning quantum hardware industry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Dirac Fermions and Flat Bands in Phosphorus Carbide Nanotubes: Structural and Quantum Phase Transitions in a Quasi-One-Dimensional Material

Chemically realistic quasi-one-dimensional (1D) materials in which Dirac Fermions and highly degenerate flat bands coexist intrinsically at the Fermi level are exceedingly rare, while representing a highly desirable platform for correlated and topological quantum phenomena. Here, in this work, using specialized symmetry-adapted first-principles calculations we predict a new class of nanomaterials─phosphorus carbide nanotubes (P 2 C 3 NTs)─obtained by rolling monolayer P 2 C 3 , a two-dimensional material shown in a previous letter to host “double Kagome bands”. Both armchair and zigzag P 2 C 3 NTs are stable at room temperature and feature the rare coexistence of Dirac crossings and multiple flat bands at the Fermi level inherited from the underlying honeycomb–Kagome lattice, with the flat bands resilient to elastic deformations. Under large strain, the structure transforms from honeycomb–Kagome to “brick-wall”, accompanied by multiple coupled structural and quantum phase transitions. We also uncover localized edge states, spin splitting from vacancies and dopants, and strain-tunable magnetism. Together, these results establish P 2 C 3 NTs as a chemically specific and mechanically tunable 1D material platform with potential applications in quantum hardware and spintronics.

carbon nanotubes↗

DOE OSTI2025

Classical and quantum simulations of 1+1-dimensional ${\mathbb{Z}}_{2}$ gauge theory at finite temperature and density

Simulating strongly coupled gauge theories at finite temperature and density is a longstanding challenge in nuclear and high-energy physics with fundamental implications for condensed matter physics. Here, we simulate such systems using minimally entangled typical thermal state (METTS) approaches, which combine classical random sampling with imaginary-time evolution, implementable on either classical or quantum computers, to estimate thermal averages of observables. We study 1+1-dimensional ${\mathbb{Z}}_{2}$ gauge theory coupled to spinless fermionic matter, which maps onto a local quantum spin chain. We benchmark both a classical matrix-product-state implementation of METTS and a recently proposed adaptive variational approach for near-term quantum devices, focusing on the equation of state and measures of fermion confinement. Of particular importance is the choice of basis for METTS sampling, which impacts both the sampling overhead and quantum circuit complexity. Our work sets the stage for future studies of strongly coupled gauge theories using classical and quantum hardware.

Chen, I-Chi [Iowa State Univ., Ames, IA (United St↗

DOE OSTI2024

Reducing measurement costs by recycling the Hessian in adaptive variational quantum algorithms

Abstract Adaptive protocols enable the construction of more efficient state preparation circuits in variational quantum algorithms (VQAs) by utilizing data obtained from the quantum processor during the execution of the algorithm. This idea originated with Adaptive Derivative-Assembled Problem-Tailored variational quantum eigensolver (ADAPT-VQE), an algorithm that iteratively grows the state preparation circuit operator by operator, with each new operator accompanied by a new variational parameter, and where all parameters acquired thus far are optimized in each iteration. In ADAPT-VQE and other adaptive VQAs that followed it, it has been shown that initializing parameters to their optimal values from the previous iteration speeds up convergence and avoids shallow local traps in the parameter landscape. However, no other data from the optimization performed at one iteration is carried over to the next. In this work, we propose an improved quasi-Newton optimization protocol specifically tailored to adaptive VQAs. The distinctive feature in our proposal is that approximate second derivatives of the cost function are recycled across iterations in addition to optimal parameter values. We implement a quasi-Newton optimizer where an approximation to the inverse Hessian matrix is continuously built and grown across the iterations of an adaptive VQA. The resulting algorithm has the flavor of a continuous optimization where the dimension of the search space is augmented when the gradient norm falls below a given threshold. We show that this inter-optimization exchange of second-order information leads the approximate Hessian in the state of the optimizer to be consistently closer to the exact Hessian. As a result, our method achieves a superlinear convergence rate even in situations where the typical implementation of a quasi-Newton optimizer converges only linearly. Our protocol decreases the measurement costs in implementing adaptive VQAs on quantum hardware as well as the runtime of their classical simulation.

Ramôa, Mafalda (ORCID:0000000302187801)↗

DOE OSTI2025

Quantum algorithm for polaritonic chemistry based on an exact ansatz

Abstract Cavity-modified chemistry uses strong light-matter interactions to modify the electronic properties of molecules in order to enable new physical phenomena such as novel reaction pathways. As cavity chemistry often involves critical regions where configurations become nearly degenerate, the ability to treat multireference problems is crucial to understanding polaritonic systems. In this Letter, we show through the use of a unitary ansatz derived from the anti-Hermitian contracted Schrödinger equation that cavity-modified systems with strong correlation, such as the deformation of rectangular H 4 coupled to a cavity mode, can be solved efficiently and accurately on a quantum device. In contrast, while our quantum algorithm can be made formally exact, classical-computing methods as well as other quantum-computing algorithms often yield answers that are both quantitatively and qualitatively incorrect. Additionally, we demonstrate the current feasibility of the algorithm on near intermediate-scale quantum hardware by computing the dissociation curve of H 2 strongly coupled to a bosonic bath.

Warren, Samuel (ORCID:0000000157134454)↗

DOE OSTI2026

Superdiffusion resilience in Heisenberg chains with two-dimensional interactions on a quantum processor

Superdiffusive spin transport in the one-dimensional (1D) Heisenberg model is a key theoretical discovery in nonequilibrium quantum many-body physics. Although extensively studied in 1D systems, the breakdown and sustenance of superdiffusion in two-dimensional (2D) lattices with integrability-breaking terms, as found in real materials, remains an open question. To address this, we develop a toy model that extends the 1D Heisenberg model with a representative set of 2D interaction types and tunable strengths. Our model exhibits varying degrees of superdiffusion breakdown depending on the interaction type, spanning ballistic to diffusive regimes. We establish and justify a hierarchy of 2D interactions based on their resilience against superdiffusion breakdown: Heisenberg >𝑋⁢𝑋 > Ising. This precise control over the superdiffusive behavior also enables rigorous benchmarking of quantum hardware, and our simulations on IBM's Heron devices confirm the hardware's ability to accurately capture these many-body nonequilibrium phenomena. Overall, our results are relevant not only to simulating superdiffusion in real materials, such as the 1D Heisenberg compound KCuF3, which contains modest nonintegrable 2D terms, but also to extending superdiffusive behavior to larger 2D qubit lattices and other 2D materials.

Alagarsamy Manikandan, Keerthi Kumaran [ORNL]↗

DOE OSTI2025

TRIM: AI Guided Random Number Generation for Resource-Constrained IoT Systems

Random numbers often serve as the backbone for many security solutions in diverse domains such as cryptography, side channel leakage prevention, and moving target defense. However, generating true random numbers requires a physical source of entropy (e.g. hardware, quantum, environmental phenomenon) making it difficult to realize at a large scale and at a low cost. On the flip side, pseudorandom number generators (easy to implement) following a specific distribution (e.g. Gaussian) can be easily compromised given a sufficient amount of traces. In this work, we have developed a machine learning-guided generative approach that can be used to create portable, resource-efficient, and cost-effective random number generators with high throughput and true randomness characteristics. We implement the proposed approach as a highly parameterized framework and perform extensive evaluation for different settings. The framework was able to learn from true random sources such as irrational numbers and environmental audio noise and imitate those sources towards generating new good quality random numbers on demand. We have generated more than 1 billion bits and observed robust performance in terms of true randomness metrics obtained from NIST SP 800-22 and FIPS 140-1 randomness test suites achieving a throughput of up to 142.85 Mbps. Compared to the state-of-the-art (SOTA) technique, the iso-cost setup of our framework can achieve more than 500 Mbps in a distributed setting. We have evaluated the efficacy of running the true randomness imitation AI models on target edge devices such as Raspberry Pi 4 (Model B), Nvidia Jetson Nano, Nvidia Jetson Orin Nano and Nvidia Jetson Xavier. We have also looked at the security of the TRIM framework itself against different adversarial threat models.

Cybersecurity↗

DOE OSTI2025

Attention to quantum complexity

The imminent era of error-corrected quantum computing demands robust methods to characterize quantum state complexity from limited, noisy measurements. We introduce the Quantum Attention Network (QuAN), a classical artificial intelligence (AI) framework leveraging attention mechanisms tailored for learning quantum complexity. Inspired by large language models, QuAN treats measurement snapshots as tokens while respecting permutation invariance. Combined with our parameter-efficient miniset self-attention block, this enables QuAN to access high-order moments of bit-string distributions and preferentially attend to less noisy snapshots. We test QuAN across three quantum simulation settings: driven hard-core Bose-Hubbard model, random quantum circuits, and toric code under coherent and incoherent noise. QuAN directly learns entanglement and state complexity growth from experimental computational basis measurements, including complexity growth in random circuits from noisy data. In regimes inaccessible to existing theory, QuAN unveils the complete phase diagram for noisy toric code data as a function of both noise types, highlighting AI’s transformative potential for assisting quantum hardware.

Kim, Hyejin [Cornell Univ., Ithaca, NY (United Sta↗

DOE OSTI2024

Quantum Computing for Energy-Related Applications

Growing interest in quantum computing and simulations have created opportunities for its deployment to improve processes pertaining to energy production, distribution, and consumption. While quantum computing is considered as a paradigm shift in our basic understanding of physical computation, effective implementation of quantum computing in energy applications also depends on progress and development in the dimensions of both quantum computing hardware and quantum computing algorithms. To fully address the status and future challenges of quantum information science (QIS) applied within the energy sector, in this presentation, we firstly summarize recent advancements on the applications of quantum computing to energy infrastructure and materials, complex energy system processes, advanced manufacturing, and energy system security. Then, we will demonstrate the results of quantum computing both on a simulator and a quantum device accessing from OLCF. Our first example is to use the variational quantum eigensolver (VQE) with a unitary coupled cluster with singles and doubles (UCCSD) ansatz to simulate a series of LixHyq molecules (q=-1, 0, +1). The obtained results showed that the quantum computing VQE-UCCSD is comparable to classical CCSD for small systems like LiH with respect to full configuration interaction (FCI). Targeting on CO2 capture application, our second example is to use VQE to quantify molecular vibrational energies and reaction pathways between CO2 and a simplified amine-based solvent model—NH3 to form H2NCOOH. This research showcases quantum computing applications in the study of CO2 capture reactions.

Duan, Yuhua↗

DOE OSTI2024

Investigation of cosmic ray impact on transmon qubits with different materials through fast decay detection at Fermilab’s SQMS laboratory

Noise sources affecting superconducting qubits, such as cosmic rays and ambient gamma radiation, have garnered attention for their potential impact. These radiations deposit energy in the qubit's substrate, generating high-energy phonons that break Cooper pairs, leading to the formation of quasi-particles. When these quasi-particles tunnel across Josephson junctions, they induce qubit de-excitation, causing relaxation errors. In this study, we employ a fast feedback mechanism for performing qubit reset to detect decay events with high time resolution. This capability along with frequency multiplexed readout allows us to explore error correlations across time and space. Transmon qubits, manufactured within the Superconducting Quantum Materials and Systems (SQMS) center [1], are investigated at the above-ground lab. We study the impact of cosmic rays on qubits with different encapsulations, geometries, and locations on the same or different chips. We present preliminary findings and discuss the implications for the performance of contemporary quantum hardware.

Roy, Tanay↗