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DOE OSTI2025

Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach

Ground state energy estimation in physical, chemical, and materials sciences is one of the most promising applications of quantum computing. In this work, we introduce a new hybrid approach that finds the eigenenergies by collecting real-time measurements and post-processing them using the machinery of dynamic mode decomposition (DMD). From the perspective of quantum dynamics, we establish that our approach can be formally understood as a stable variational method on the function space of observables available from a quantum many-body system. We also provide strong theoretical and numerical evidence that our method converges rapidly even in the presence of a large degree of perturbative noise, and show that the method bears an isomorphism to robust matrix factorization methods developed independently across various scientific communities. Our numerical benchmarks on spin and molecular systems demonstrate an accelerated convergence and a favorable resource reduction over state-of-the-art algorithms. The DMD-centric strategy can systematically mitigate noise and stands out as a leading hybrid quantum-classical eigensolver.

Shen, Yizhi↗

DOE OSTI2026

Role of electron correlation on the adenine dimer interaction for non-equilibrium geometries: a benchmark Quantum Monte Carlo study

The accurate description of non-covalent interactions is critical for understanding the structure, dynamics, and eventual function of biomolecules. The adenine dimer serves as a benchmark system for computational methods due to its role in nucleic acid structures and its rich conformational landscape. In this study, we employ benchmark diffusion quantum Monte Carlo (DMC) methods to investigate the relative energies and role of electron correlation on a set of adenine dimer conformations generated via a search of the potential energy landscape using the global optimizer algorithm. Relative DMC energies are compared against a wide range of density functional theory (DFT) approximation results. We find that although most of the DFT functionals perform well for low-energy structures, their accuracy varies significantly for higher-energy conformations, including stacked and T-shaped structures. A large fraction of the variation is due to the treatment of the van der Waals interaction. BLYP, B3LYP, and PBE0 significantly improve with added D4 dispersion, while the recent r2SCAN-D4 and ωB97M-V functionals show the least scatter and closest agreement with the DMC. These findings highlight the delicate nature of these interactions in biomolecular systems and provide guidance for simulations of their structure and dynamics and for the development of machine learned interatomic potentials.

Washburn, Laurel [ORNL] (ORCID:0000000324179335)↗

DOE OSTI2022

Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers

The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1993

The quantum dynamics of electronically nonadiabatic chemical reactions

Considerable progress was achieved on the quantum mechanical treatment of electronically nonadiabatic collisions involving energy transfer and chemical reaction in the collision of an electronically excited atom with a molecule. In the first step, a new diabatic representation for the coupled potential energy surfaces was created. A two-state diabatic representation was developed which was designed to realistically reproduce the two lowest adiabatic states of the valence bond model and also to have the following three desirable features: (1) it is more economical to evaluate; (2) it is more portable; and (3) all spline fits are replaced by analytic functions. The new representation consists of a set of two coupled diabatic potential energy surfaces plus a coupling surface. It is suitable for dynamics calculations on both the electronic quenching and reaction processes in collisions of Na(3p2p) with H2. The new two-state representation was obtained by a three-step process from a modified eight-state diatomics-in-molecules (DIM) representation of Blais. The second step required the development of new dynamical methods. A formalism was developed for treating reactions with very general basis functions including electronically excited states. Our formalism is based on the generalized Newton, scattered wave, and outgoing wave variational principles that were used previously for reactive collisions on a single potential energy surface, and it incorporates three new features: (1) the basis functions include electronic degrees of freedom, as required to treat reactions involving electronic excitation and two or more coupled potential energy surfaces; (2) the primitive electronic basis is assumed to be diabatic, and it is not assumed that it diagonalizes the electronic Hamiltonian even asymptotically; and (3) contracted basis functions for vibrational-rotational-orbital degrees of freedom are included in a very general way, similar to previous prescriptions for locally adiabatic functions in various quantum scattering algorithms.

Truhlar, Donald G.↗

DOE OSTI2026

Sparse non-Markovian Noise Modeling of Transmon-Based Multi-Qubit Operations

The influence of noise on quantum dynamics is one of the main factors preventing current quantum processors from performing accurate quantum computations. Sufficient noise characterization and modeling can provide key insights into the effect of noise on quantum algorithms and inform the design of targeted error protection protocols. However, constructing effective noise models that are sparse in model parameters, yet predictive can be challenging. In this work, we present an approach for effective noise modeling of multi-qubit operations on transmon-based devices. Through a comprehensive characterization of seven devices offered by the IBM Quantum Platform, we show that the model can capture and predict a wide range of single- and two-qubit behaviors, including non-Markovian effects resulting from spatiotemporally correlated noise sources. The model’s predictive power is further highlighted through multi-qubit dynamical decoupling demonstrations and an implementation of the variational quantum eigensolver. As a training proxy for the hardware, we show that the model can predict expectation values within a relative error of 0.5%; this is a sevenfold improvement over default hardware noise models. Through these demonstrations, we highlight key error sources in superconducting qubits and illustrate the utility of reduced noise models for predicting hardware dynamics.

open quantum systems & decoherence↗

DOE OSTI2025

Towards a Quantum Algorithm for the Incompressible Nonlinear Navier-Stokes Equations

In this work, we present novel concepts for quantum algorithms to solve transient, 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 incompressible Navier-Stokes equations 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 solving 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. We propose a new framework based on matrix product states (MPSs) and matrix product operators (MPOs), in addition to the Krylov subspace methods. For example, the solution variables of the Navier-Stokes equations are represented by MPSs, and the linear and nonlinear terms are processed by MPOs. The time evolution of the operators is attained by a fast-forwarding algorithm using Krylov subspace methods. Furthermore, we discuss various techniques for efficient encoding of MPSs, measurement reduction for MPOs, and use of tensor operations to treat multi-variate, multi-physics characteristics of Navier-Stokes.

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

DOE OSTI2025

Counterdiabatic Driving with Performance Guarantees

Counterdiabatic (CD) driving has the potential to speed up adiabatic quantum state preparation by suppressing unwanted excitations. However, existing approaches either require intractable classical computations or are based on approximations that do not have performance guarantees. We propose and analyze a nonvariational, system-agnostic CD expansion method and analytically show that it converges exponentially quickly in the expansion order. In finite systems, the required resources scale inversely with the spectral gap, which we argue is asymptotically optimal. To extend our method to the thermodynamic limit and suppress errors stemming from high-frequency transitions, we leverage finite-time adiabatic protocols. In particular, we show that a time determined by the quantum speed limit is sufficient to prepare the desired ground state, without the need to optimize the adiabatic trajectory. Numerical tests of our method on the quantum Ising chain show that our method can outperform state-of-the-art variational CD approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

An improved guess for the variational calculation of charge-transfer excitations in large systems

Ab initio quantum-chemical methods that perform well for computing the electronic ground state are not straightforwardly transferable to electronically excited states, particularly in large molecular systems. Wave function theory offers high accuracy, but is often prohibitively expensive. Methods based on time-dependent density functional theory (TD-DFT) are crucially sensitive to the chosen exchange-correlation functional (XCF) parameterization, and system-specific tuning protocols were therefore proposed to address the method's robustness. Methods based on the variational relaxation of the excited-state electron density showcased promising results for the calculation of charge-transfer excitations, but the complex shape of the electronic hypersurface makes convergence to a specific excited state much more difficult than for the ground state when standard variational techniques are applied. We address the latter aspect by providing suitable initial guesses, which we obtain by two separate constrained algorithms. Combined with the squared-gradient minimization algorithm for all-electrons relaxation in a freeze-and-release scheme (FRZ-SGM), we demonstrate that orbital-optimized density functional theory (OO-DFT) calculations can reliably converge to the charge-transfer states of interest even for large molecular systems. We test the FRZ-SGM method on a phenothiazine-anthraquinone CT excitation in a supramolecular Pd(II) coordination cage complex as a function of the cage conformation. This compound has been studied experimentally prior to our work. We compare this freeze-and-release scheme to two XCF reparameterizations, which were recently proposed as low-cost TD-DFT-based alternatives to variational methods. Two dye-semiconductor complexes, which were previously investigated in the context of photovoltaic applications, serve as a second example to investigate the convergence and stability of the FRZ-SGM approach. Our results demonstrate that FRZ-SGM provides reliable convergence for charge-transfer excited states and avoids variational collapse to lower-lying electronic states, whereas time-dependent DFT calculations with an adequate tuning procedure for the range-separation parameter provide a computationally efficient initial estimate of the corresponding energies, with a computational cost comparable to that of configuration-interaction singles (CIS) calculations.

Bogo, Nicola↗

DOE OSTI2025

Alternating and Gaussian Fermionic Isometric Tensor Network States

Isometric tensor networks in two dimensions enable efficient and accurate study of quantum many-body states, yet the effect of the isometric restriction on the represented quantum states is not fully understood. We address this question in two main contributions. First, we introduce an improved variant of isometric tensor network states (isoTNS) in two dimensions, where the isometric arrows on the columns of the network alternate between pointing upward and downward; hence the name alternating isometric tensor network states. Second, we introduce a numerical tool—the isometric Gaussian fermionic TNS (isoGfTNS)—that incorporates isometric constraints into the framework of Gaussian fermionic tensor network states. We demonstrate in numerous ways that alternating isoTNSs represent many-body ground states of two-dimensional quantum systems significantly better than the original isoTNSs. First, we show that the entanglement in an isoTNS is mediated along the isometric arrows and that alternating isoTNSs mediate entanglement more efficiently than conventional isoTNSs. Second, alternating isoTNSs correspond to a deeper, and thus more representative, sequential-circuit construction of depth 𝒪⁢(𝐿𝑥 ⋅𝐿𝑦) compared to the original isoTNSs of depth 𝒪⁢(𝐿𝑥 +𝐿𝑦). Third, using the Gaussian framework and gradient-based energy minimization, we provide numerical evidence of better bond-dimension scaling and variational energy of alternating isoGfTNSs for ground states of various free-fermionic models, including the Fermi surface, the band insulator, and the 𝑝𝑥 +𝑖⁢𝑝𝑦 mean-field superconductor. Finally, benchmarking on the transverse-field Ising model, we demonstrate that an alternating isoTNS provides substantially improved performance and stability relative to the original isoTNS for the ground-state search algorithm in interacting systems.

Wu, Yantao [Chinese Academy of Sciences, Beijing (↗

DOE OSTI2025

Electronic structure theory with molecular point group symmetries on quantum annealers

Quantum computation has the potential to revolutionize quantum chemistry through major speedups in computation times and an exponential reduction in computational resources. Here, we combine the symmetry-adapted Jordan–Wigner encoding based on the full Boolean symmetry group $\mathbb{Z}$$^{k}_{2}$ with our new implementation of the Xia–Bian–Kais (XBK) method for improving the efficiency of electronic structure theory calculations on quantum annealers, particularly by reducing the number of qubits needed to achieve the same accuracy. By providing a more extensive symmetry-adapted encoding (SAE) than previous work, we are able to simulate molecules larger than those previously reported that have been studied using methods developed for quantum annealers and without using an active space. We calculated the potential energy surfaces of H 2 , LiH, He 2 , H 2 O, O 2 , N 2 , Li 2 , F 2 , CO, BH 3 , NH 3 , and CH 4 , with the largest molecule in the STO-6G basis set requiring 16 qubits with our SAE, and compared them with full configuration interaction results. The application of SAE to the XBK method provides an exponential reduction in the size of the Hilbert space and scales well with the size of the problem. It does not introduce significant additional errors for even or large values of a key variational parameter that determines the number of ancilla qubits used in the XBK method’s Hamiltonian embedding, or for certain molecules such as He 2 and H 2 O. Here, we provide an explanation for this behavior and a recommendation on the usage of our method. In addition, we briefly discuss the potential of extracting electronic excited states from our method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1996

Scaling Properties of Algorithms in Nanotechnology

At the present time, several technologies are pressing the limits of microminiature manufacturing. In semiconductor technology, for example, the Intel Pentium Pro (which is used in the Department of Energy's ASCI 'red' parallel supercomputer system) and the DEC Alpha 21164 (which is used in the CRAY T3E) both are fabricated using 0.35 micron process technology. Recently Texas Instruments (TI) announced the availability of 0.25 micron technology chips by the end of 1996 and plans to have 0.18 micron devices in production within two years. However, some significant challenges lie down the road. These include the skyrocketing cost of manufacturing plants, the 0.1 micron foreseeable limit of the photolithography process, quantum effects, data communication bandwidth limitations, heat dissipation, and others. Some related microminiature technologies include micro-electromechanical systems (MEMS), opto-electronic devices, quantum computing, biological computing, and others. All of these technologies require the fabrication of devices whose sizes are approaching the nanometer level. As such they are often collectively referred to with the name 'nanotechnology'. Clearly nanotechnology in this general sense is destined to be a very important technology of the 21st century. The ultimate dream in this arena is 'molecular nanotechnology', in other words the fabrication of devices and materials with most or all atoms and molecules in a pre-programmed position, possibly placed there by 'nano-robots'. This futuristic capability will probably not be achieved for at least two decades. However, it appears that somewhat less ambitious variations of molecular nanotechnology, such as devices and materials based on 'buckyballs' and 'nanotubes' may be realized significantly sooner, possibly within ten years or so. Even at the present time, semiconductor devices are approaching the regime where quantum chemical effects must be considered in design.

Saini, Subhash↗

DOE OSTI2025

Thermal Weight Determination and Interstate Coupling in State-Averaged ADAPT-VQE

Characterizing electronic thermal states at low temperatures is an important but challenging task in quantum chemistry and condensed matter physics, making it a prime candidate for a useful application in quantum computing. One of the most successful methods for state preparation on quantum computers is the Adaptive, Problem-Tailored (ADAPT) Variational Quantum Eigensolver (VQE), which has recently been generalized to treat excited states within a state-averaged framework as well as Gibbs states. In this work, we introduce Helmholtz-Optimized Thermal (HOT) ADAPT-VQE, an ancilla-free strategy for preparing Gibbs states that directly minimizes the Helmholtz free energy by targeting the dominant eigenstates of the thermal ensemble. We demonstrate the usefulness of HOT-ADAPT-VQE by predicting the free energy of two model systems with strongly correlated ground states: (1) the Fe 2+ cation in a magnetic field and (2) a [Cu 2 O 7 ] 10– fragment of the Mott insulator La 2 CuO 4 . Our results demonstrate that HOT-ADAPT-VQE significantly improves upon Gibbs-state estimates from multistate variants of ADAPT-VQE, often with substantially shallower quantum circuits, making it a promising candidate for thermal-state calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Lie-algebraic classical simulations for quantum computing

The classical simulation of quantum dynamics plays an important role in our understanding of quantum complexity and in the development of quantum technologies. Efficient techniques such as those based on the Gottesman-Knill theorem for Clifford circuits, tensor networks for low entanglement-generating circuits, or Wick's theorem for fermionic Gaussian states have become central tools in quantum computing. In this work, we contribute to this body of knowledge by presenting a framework for classical simulations, dubbed “𝔤-sim”, which is based on the underlying Lie algebraic structure of the dynamical process. When the dimension of the algebra grows at most polynomially in the system size, there exist observables for which the simulation is efficient. Indeed, we show that 𝔤-sim enables new regimes for classical simulations, is able to deal with certain forms of noise in the evolution, as well as can be used to tackle several paradigmatic variational and nonvariational quantum computing tasks. For the former, we perform Lie-algebraic simulations to train and optimize parametrized quantum circuits (thus effectively showing that some variational models can be dequantized), design enhanced parameter initialization strategies, solve tasks of quantum circuit synthesis, and train a quantum-phase classifier. For the latter, we report large-scale noiseless and noisy simulations on benchmark problems. By comparing the limitations of 𝔤-sim and certain Wick's theorem-based simulations, we find that the two methods become inefficient for different types of states or observables, hinting at the existence of distinct, nonequivalent resources for classical simulation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Cheaper and more noise-resilient quantum state preparation using eigenvector continuation

Subspace methods are powerful, noise-resilient methods that can effectively prepare ground states on quantum computers. The challenge is to get a subspace with a small condition number that spans the states of interest using minimal quantum resources. In this work, we will use eigenvector continuation to build a subspace from the low-lying states of a set of Hamiltonians. The basis vectors are prepared using truncated versions of standard state preparation methods such as imaginary-time evolution (ITE), adiabatic state preparation (ASP), and variational quantum eigensolver. By using these truncated methods combined with eigenvector continuation, we can directly improve upon them, obtaining more accurate ground-state energies at a reduced cost. We use several spin systems to demonstrate convergence even when methods like ITE and ASP fail, such as ASP in the presence of level crossings and ITE with vanishing energy gaps. We also showcase the noise resilience of this approach beyond the gains already made by having shallower quantum circuits. Furthermore, our findings suggest that eigenvector continuation can be used to improve existing state preparation methods in the near term.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Neuralized fermionic tensor networks for quantum many-body systems

In this work, we describe a class of neuralized fermionic tensor network states (NN-fTNSs) that introduce nonlinearity into fermionic tensor networks through configuration-dependent neural network transformations of the local tensors. The construction uses the fTNS algebra to implement a natural fermionic sign structure and is compatible with standard tensor network algorithms but gains enhanced expressivity through the neural network parametrization. Using the 1D and 2D Fermi-Hubbard models as benchmarks, we demonstrate that NN-fTNSs achieve order of magnitude improvements in the ground-state energy compared to pure fTNSs with the same bond dimension and can be systematically improved through both the tensor network bond dimension and the neural network parametrization. Compared to existing fermionic neural quantum states based on Slater determinants and Pfaffians, NN-fTNSs offer a physically motivated alternative fermionic structure. Furthermore, compared to such states, NN-fTNSs naturally exhibit improved computational scaling and we demonstrate a construction that achieves linear scaling with the lattice size.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1998

[MODIS Investigation]

The objective of the last six months were: (1) Continue analysis of Hawaii Ocean Time-series (HOT) bio-optical mooring data, and Southern Ocean bio-optical drifter data; (2) Complete development of documentation of MOCEAN algorithms and software for use by MOCEAN team and GLI team; (3) Deploy instrumentation during JGOFS cruises in the Southern Ocean; (4) Participate in test cruise for Fast Repetition Rate (FRR) fluorometer; (5) Continue chemostat experiments on the relationship of fluorescence quantum yield to environmental factors; and (6) Continue to develop and expand browser-based information system for in situ bio-optical data. We are continuing to analyze bio-optical data collected at the Hawaii Ocean Time Series mooring as well as data from bio-optical drifters that were deployed in the Southern Ocean. A draft manuscript has now been prepared and is being revised. A second manuscript is also in preparation that explores the vector wind fields derived from NSCAT measurements. The HOT bio-optical mooring was recovered in December 1997. After retrieving the data, the sensor package was serviced and redeployed. We have begun preliminary analysis of these data, but we have only had the data for 3 weeks. However, all of the data were recovered, and there were no obvious anomalies. We will add second sensor package to the mooring when it is serviced next spring. In addition, Ricardo Letelier is funded as part of the SeaWiFS calibration/validation effort (through a subcontract from the University of Hawaii, Dr. John Porter), and he will be collecting bio-optical and fluorescence data as part of the HOT activity. This will provide additional in situ measurements for MODIS validation. As noted in the previous quarterly report, we have been analyzing data from three bio-optical drifters that were deployed in the Southern Ocean in September 1996. We presented results on chlorophyll and drifter speed. For the 1998 Ocean Sciences meeting, a paper will be presented on this data set, focusing on the diel variations in fluorescence quantum yield. Briefly, there are systematic patterns in the apparent quantum yield of fluorescence (defined as the slope of the line relating fluorescence/chlorophyll and incoming solar radiation). These systematic variations appear to be related to changes in the circulation of the Antarctic Polar Front which force nutrients into the upper ocean. A more complete analysis will be provided in the next Quarterly report.

Abbott, Mark R.↗

DOE OSTI2025

Dynamic, symmetry-preserving, and hardware-adaptable circuits for quantum computing many-body states and correlators of the Anderson impurity model

We present a hardware-reconfigurable ansatz on N q -qubits for the variational preparation of many-body states of the Anderson impurity model (AIM) with N imp + N bath = N q /2 sites, which conserves total charge and spin z component within each variational search subspace. The many-body ground state of the AIM is determined as the minimum over all minima of O(N$^2_ q$) distinct charge-spin sectors. Hamiltonian expectation values are shown to require ω(N q ) < N meas. $\leqslant$ O(N imp N bath ) symmetry-preserving, parallelizable measurement circuits, each amenable to postselection. To obtain the one-particle impurity Green’s function we show how initial Krylov vectors can be computed via midcircuit measurement and how Lanczos iterations can be computed using the symmetry-preserving ansatz. For a single-impurity Anderson model with a number of bath sites increasing from one to seven, we show using numerical emulation that the ease of variational ground-state preparation is suggestive of linear scaling in circuit depth and subquartic scaling in optimizer complexity. We therefore expect that, combined with time-dependent methods for Green’s function computation, our ansatz provides a useful tool to account for electronic correlations on early fault-tolerant processors. Finally, with a view towards computing real materials properties of interest like magnetic susceptibilities and electron-hole propagators, we provide a straightforward method to compute many-body, time-dependent correlation functions using a combination of time evolution, midcircuit measurement-conditioned operations, and the Hadamard test.

36 MATERIALS SCIENCE↗