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DOE OSTI2025

Quantum Simulators and Applications on Quantum Framework

Simulating quantum circuits is essential for validating quantum algorithms. However, no single simulator consistently performs best - efficiency depends on circuit structure, entanglement, and depth. In this work, we integrate Qiskit-Aer (state-vector and matrix product state) and QTensor, a tree-tensor-network based simulator, into the Quantum Framework (QFw), a modular platform that supports multiple quantum backends via a unified interface. We also enable distributed quantum approximate optimization algorithm (DQAOA) application compatibility with QFw, allowing sub-problems to be solved in parallel at scale. We then benchmark DQAOA and TFIM (transverse field Ising model) circuits across supported simulators, showing how performance varies significantly with problem type. All simulations are deployed on the Frontier supercomputer using QFw's MPI-based orchestration for distributed, multinode execution. These results underscore the need for simulatoragnostic infrastructure to enable systematic evaluation and highperformance scaling of quantum workloads. QFw provides a practical and extensible path toward reproducible quantum algorithm development across diverse application domains.

Chundury, Srikar [ORNL] (ORCID:0009000183359259)↗

DOE OSTI2024

Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance

A recent quantum simulation of observables of the kicked Ising model on 127 qubits implemented circuits that exceed the capabilities of exact classical simulation. We show that several approximate classical methods, based on sparse Pauli dynamics and tensor network algorithms, can simulate these observables orders of magnitude faster than the quantum experiment and can also be systematically converged beyond the experimental accuracy. Our most accurate technique combines a mixed Schrödinger and Heisenberg tensor network representation with the Bethe free entropy relation of belief propagation to compute expectation values with an effective wave function–operator sandwich bond dimension >16,000,000, achieving an absolute accuracy, without extrapolation, in the observables of <0.01, which is converged for many practical purposes. We thereby identify inaccuracies in the experimental extrapolations and suggest how future experiments can be implemented to increase the classical hardness.

Science & Technology - Other Topics↗

DOE OSTI2026

Magnetic hysteresis experiments performed on quantum annealers

While quantum annealers have emerged as versatile and controllable platforms for experimenting on correlated spin systems, the important phenomenology of magnetic memory and hysteresis remain unexplored on hardware designed to escape metastable states via quantum tunneling. Here, we present the first general protocol to experiment on magnetic hysteresis on programmable quantum annealers and implement it on three D-Wave superconducting qubit quantum annealers, using up to thousands of spins, for both ferromagnetic and disordered Ising models, and across different graph topologies. We observe hysteresis loops whose area depends nonmonotonically on quantum fluctuations, exhibiting both expected and unexpected features, such as disorder-induced steps and nonmonotonicities. Our work establishes quantum annealers as a platform for probing nonequilibrium emergent magnetic phenomena, thereby broadening the role of analog quantum computers into foundational questions in condensed matter physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Strangeness-neutral equation of state for QCD with a critical point

We present a strangeness-neutral equation of state for QCD that exhibits critical behavior and matches lattice QCD results for the Taylor-expanded thermodynamic variables up to fourth-order in µ B /T. It is compatible with the SMASH hadronic transport approach and has a range of temperatures and baryonic chemical potentials relevant for phase II of the Beam Energy Scan at RHIC. We provide an updated version of the software BES-EoS, which produces an equation of state for QCD that includes a critical point in the 3D Ising model universality class. This new version also includes isentropic trejectories and the critical contribution to the correlation length. Since heavy-ion collisions have zero global net-strangeness density and a fixed ratio of electric charge to baryon number, the BES-EoS is more suitable to describe this system. Comparison with the previous version of the EoS is thoroughly discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Replica symmetry breaking in spin glasses in the replica-free Keldysh formalism

We show that the algebra of Parisi ultrametric matrices is recovered by the real-time, replica-free, Dyson-Keldysh equations of infinite-range quantum spin glasses in the late time glassy limit. This connects to earlier results on classical and quantum systems showing how ultrametricity emerges from the persistent slow aging dynamics of the glass phase. The stationary spin glass state thereby spontaneously breaks thermal symmetry, or the Kubo-Martin-Schwinger relation of a state in global thermal equilibrium. We describe the Keldysh path integral of the infinite-range Ising model in transverse and longitudinal fields, and in the context of the Landau expansion of the action functional, show how the long-time limit connects to the full replica symmetry breaking obtained in the equilibrium formalism. We also illustrate our formalism by applying it to the spherical quantum p p -spin model, which only exhibits one-step replica symmetry breaking.

Lang, Johannes (ORCID:0000000283533392)↗

DOE OSTI2020

Bootstrapping mixed correlators in three-dimensional cubic theories II

Conformal field theories (CFTs) with cubic global symmetry in 3D are relevant in a variety of condensed matter systems and have been studied extensively with the use of perturbative methods like the \varepsilon ε expansion. In an earlier work, we used the nonperturbative numerical conformal bootstrap to provide evidence for the existence of a previously unknown 3D CFT with cubic symmetry, dubbed “Platonic CFT”. In this work, we make further use of the numerical conformal bootstrap to perform a three-dimensional scan in the space of scaling dimensions of three low-lying operators. We find a three-dimensional isolated allowed region in parameter space, which includes both the 3D (decoupled) Ising model and the Platonic CFT. The essential assumptions on the spectrum of operators used to provide the isolated allowed region include the existence of a stress-energy tensor and the irrelevance of certain operators (in the renormalization group sense).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Long-lived Bell states in an array of optical clock qubits

The generation of long-lived entanglement on an optical clock transition is a key requirement to unlocking the promise of quantum metrology. Arrays of neutral atoms constitute a capable quantum platform for accessing such physics, where Rydberg-based interactions may generate entanglement between individually controlled and resolved atoms. To this end, we leverage the programmable state preparation afforded by optical tweezers along with the efficient strong confinement of a 3d optical lattice to prepare an ensemble of strontium atom pairs in their motional ground state. We engineer global single-qubit gates on the optical clock transition and two-qubit entangling gates via adiabatic Rydberg dressing, enabling the generation of Bell states, $|\psi{\rangle}$ $= \frac{1}{\sqrt{2}}(|gg\rangle$ $+ i|ee\rangle{)}$, with a fidelity of $\mathcal{F}$ = 92.8(2:0)%. For use in quantum metrology, it is furthermore critical that the resulting entanglement be long lived; we find that the coherence of the Bell state has a lifetime of $τ_{bc}$ = 4:2(6) s via parity correlations and simultaneous comparisons between entangled and unentangled ensembles. Such Bell states can be useful for enhancing metrological stability and bandwidth. Further rearrangement of hundreds of atoms into arbitrary configurations using optical tweezers will enable implementation of many-qubit gates and cluster state generation, as well as explorations of the transverse field Ising model and Hubbard models with entangled or finite-range-interacting tunnellers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Energy storage and coherence in closed and open quantum batteries

We study the role of coherence in closed and open quantum batteries. We obtain upper bounds to the work performed or energy exchanged by both closed and open quantum batteries in terms of coherence. Specifically, we show that the energy storage can be bounded by the Hilbert-Schmidt coherence of the density matrix in the spectral basis of the unitary operator that encodes the evolution of the battery. We also show that an analogous bound can be obtained in terms of the battery's Hamiltonian coherence in the basis of the unitary operator by evaluating their commutator. We apply these bounds to a 4-state quantum system and the anisotropic XY Ising model in the closed system case, and the Spin-Boson model in the open case.

97 MATHEMATICS AND COMPUTING↗

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 OSTI2022

Quantum algorithms from fluctuation theorems: Thermal-state preparation

Fluctuation theorems provide a correspondence between properties of quantum systems in thermal equilibrium and a work distribution arising in a non-equilibrium process that connects two quantum systems with Hamiltonians H 0 and H 1 = H 0 + V. Building upon these theorems, we present a quantum algorithm to prepare a purification of the thermal state of H 1 at inverse temperature β ≥ 0 starting from a purification of the thermal state of H 0 . The complexity of the quantum algorithm, given by the number of uses of certain unitaries, is $\mathcal{O}$ (e β(ΔA - w l )/2 ), where ΔA is the free-energy difference between H 1 and H 0 , and w l is a work cutoff that depends on the properties of the work distribution and the approximation error ϵ > 0. If the non-equilibrium process is trivial, this complexity is exponential i β∥V∥, where ∥V∥ is the spectral norm of V. This represents a significant improvement of prior quantum algorithms that have complexity exponential in β∥H 1 ∥ in the regime where ∥V∥$\ll$ ∥H 1 ∥. The dependence of the complexity in ϵ varies according to the structure of the quantum systems. It can be exponential in 1/ϵ in general, but we show it to be sublinear in 1/ϵ if H 0 and H 1 commute, or polynomial in 1/ϵ if H 0 and H 1 are local spin systems. The possibility of applying a unitary that drives the system out of equilibrium allows one to increase the value of w l and improve the complexity even further. To this end, we analyze the complexity for preparing the thermal state of the transverse field Ising model using different non-equilibrium unitary processes and see significant complexity improvements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Dimension Reduction and Redundancy Removal through Successive Schmidt Decompositions

Quantum computers are believed to have the ability to process huge data sizes, which can be seen in machine learning applications. In these applications, the data, in general, are classical. Therefore, to process them on a quantum computer, there is a need for efficient methods that can be used to map classical data on quantum states in a concise manner. On the other hand, to verify the results of quantum computers and study quantum algorithms, we need to be able to approximate quantum operations into forms that are easier to simulate on classical computers with some errors. Motivated by these needs, in this paper, we study the approximation of matrices and vectors by using their tensor products obtained through successive Schmidt decompositions. We show that data with distributions such as uniform, Poisson, exponential, or similar to these distributions can be approximated by using only a few terms, which can be easily mapped onto quantum circuits. The examples include random data with different distributions, the Gram matrices of iris flower, handwritten digits, 20newsgroup, and labeled faces in the wild. Similarly, some quantum operations, such as quantum Fourier transform and variational quantum circuits with a small depth, may also be approximated with a few terms that are easier to simulate on classical computers. Furthermore, we show how the method can be used to simplify quantum Hamiltonians: In particular, we show the application to randomly generated transverse field Ising model Hamiltonians. The reduced Hamiltonians can be mapped into quantum circuits easily and, therefore, can be simulated more efficiently.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Understanding the Formation of Complex Phases: The Case of FeSi 2

One of the fundamental goals of materials science is to understand and predict the formation of complex phases. In this study, FeSi 2 is considered as an illustration of complex phase formation. Although Fe and Si both crystallize with a simple structure, namely, body-centered cubic (bcc A2) and diamond (A4) structures, respectively, it is rather intriguing to note the existence of two complex structures in the Si-rich part of the phase diagram around FeSi 2 : α-FeSi 2 at high temperatures (HT) with a slight iron-deficient structure and β-FeSi2 (also referred to as Fe 3 Si 7 ) at low temperatures (LT). We re-analyze the geometry of these two phases and rely on approximant phases that make the relationship between these two phases simple. To complete the analysis, we also introduce a surrogate of the C16 phase that is observed in FeGe 2 . We clearly identify the relationship that exists between these three approximant phases, corroborated by a ground-state analysis of the Ising model for describing ordering that takes place between the transition metal element and the “vacancies”. This work is further supported by ab initio electronic structure calculations based on density functional theory in order to investigate properties and transformation paths. Finally, extension to other alloys, including an entire class of alloys, is discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Embedding a Critical Point in a Hadron to Quark–Gluon Crossover Equation of State

It is shown how to embed a critical point in a smooth background equation of state so as to yield the critical exponents and critical amplitude ratios expected of a transition in the same universality class as the liquid–gas phase transition and the 3D Ising model. There are only two independent critical exponents; the relations α + 2β + $\gamma$ = 2 and β(δ - 1) = $\gamma$ arise automatically, as does a new relation between the two critical amplitudes. The resulting equation of state has parameters which may be inferred by hydrodynamic modeling of heavy-ion collisions in the Beam Energy Scan II at the Relativistic Heavy Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Real time evolution for ultracompact Hamiltonian eigenstates on quantum hardware

In this work we present a detailed analysis of variational quantum phase estimation (VQPE), a method based on real-time evolution for ground and excited state estimation on near-term hardware. We derive the theoretical ground on which the approach stands, and demonstrate that it provides one of the most compact variational expansions to date for solving strongly correlated Hamiltonians. At the center of VQPE lies a set of equations, with a simple geometrical interpretation, which provides conditions for the time evolution grid in order to decouple eigenstates out of the set of time evolved expansion states, and connects the method to the classical filter diagonalization algorithm. Further, we introduce what we call the unitary formulation of VQPE, in which the number of matrix elements that need to be measured scales linearly with the number of expansion states, and we provide an analysis of the effects of noise which substantially improves previous considerations. The unitary formulation allows for a direct comparison to iterative phase estimation. Our results mark VQPE as both a natural and highly efficient quantum algorithm for ground and excited state calculations of general many-body systems. We demonstrate a hardware implementation of VQPE for the transverse field Ising model. Further, we illustrate its power on a paradigmatic example of strong correlation (Cr2 in the SVP basis set), and show that it is possible to reach chemical accuracy with as few as ~50 timesteps.

Klymko, Katherine↗

DOE OSTI2021

Computing Free Energies with Fluctuation Relations on Quantum Computers

One of the most promising applications for quantum computers is the dynamic simulation of quantum materials. Current hardware, however, sets stringent limitations on how long such simulations can run before decoherence begins to corrupt results. The Jarzynski equality, a fluctuation theorem that allows for the computation of equilibrium free energy differences from an ensemble of short, non-equilibrium dynamics simulations, can make use of such short-time simulations on quantum computers. Here, we present a quantum algorithm based on the Jarzynski equality for computing free energies of quantum materials. We demonstrate our algorithm using the transverse field Ising model on both a quantum simulator and real quantum hardware. As the free energy is a central thermodynamic property that allows one to compute virtually any equilibrium property of a physical system, the ability to perform this algorithm for larger quantum systems in the future has implications for a wide range of applications including the construction of phase diagrams, prediction of transport properties and reaction constants, and computer-aided drug design.

Bassman, Lindsay↗

DOE OSTI2021

Leveraging Randomized Compiling for the QITE Algorithm

The success of the current generation of Noisy Intermediate-Scale Quantum (NISQ) hardware shows that quantum hardware may be able to tackle complex problems even without error correction. One outstanding issue is that of coherent errors arising from the increased complexity of these devices. These errors can accumulate through a circuit, making their impact on algorithms hard to predict and mitigate. Iterative algorithms like Quantum Imaginary Time Evolution are susceptible to these errors. This article presents the combination of both noise tailoring using Randomized Compiling and error mitigation with a purification. We also show that Cycle Benchmarking gives an estimate of the reliability of the purification. We apply this method to the Quantum Imaginary Time Evolution of a Transverse Field Ising Model and report an energy estimation and a ground state infidelity both below 1\%. Our methodology is general and can be used for other algorithms and platforms. We show how combining noise tailoring and error mitigation will push forward the performance of NISQ devices.

Ville, Jean-Loup↗

DOE OSTI2025

Time correlations from steady-state expectation values

Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis requires solving the system evolution. Here, we use recent results of quantum metrology with continuous measurements to derive general lower bounds on the relaxation and second-order correlation times that are both easy to calculate and measure. These bounds are based solely on steady-state expectation values and their derivatives with respect to a control parameter, and can be readily extended to the autocorrelation of arbitrary observables. We validate our method on two examples of critical quantum systems: a critical driven-dissipative resonator, where the bound matches analytical results for the dynamics, and the infinite-range Ising model, where only the steady state is solvable and thus the bound provides information beyond the reach of existing analytical approaches. Our results can be applied to experimentally characterize ultrafast systems, and to theoretically analyze many-body models with dynamics that are analytically or numerically hard.

Górecki, Wojciech [INFN, Pavia]↗

DOE OSTI2025

Time correlations from steady-state expectation values

Górecki, Wojciech [INFN, Pavia]↗