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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Fokker-Planck Equation Governing the Distribution of Walkers in Auxiliary-Field Quantum Monte Carlo

Auxiliary-field quantum Monte Carlo (AFQMC) is typically formulated as an open-ended random walk in an overcomplete space of Slater determinants, implemented through a Langevin equation. However, the explicit form of the underlying Fokker-Planck equation governing the walker population distribution has remained unknown. Here, in this Letter, we derive the Fokker-Planck equation for AFQMC and propose a novel numerical scheme to solve it. The solution of the Fokker-Planck equation reveals the wave function actually sampled by the AFQMC algorithm. Interestingly, we find that even when the exact ground state is used as a guiding wave function in constrained path AFQMC, contrary to the common assumption, the wave function sampled by AFQMC is not exact. Beyond clarifying several fundamental aspects of AFQMC, the availability of a Fokker-Planck equation formulation opens new avenues for systematically improving its accuracy, which we outline in this Letter.

Monte Carlo methods↗
DOE OSTI2023

Towards Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States

The phase diagram of strong interactions in nature at finite temperature and chemical potential remains largely theoretically unexplored due to inadequacy of Monte-Carlo–based computational techniques in overcoming a sign problem. Quantum computing offers a sign-problem-free approach, but evaluating thermal expectation values is generally resource intensive on quantum computers. To facilitate thermodynamic studies of gauge theories, we propose a generalization of the thermal-pure-quantum-state formulation of statistical mechanics applied to constrained gauge-theory dynamics, and numerically demonstrate that the phase diagram of a simple low-dimensional gauge theory is robustly determined using this approach, including mapping a chiral phase transition in the model at finite temperature and chemical potential. Quantum algorithms, resource requirements, and algorithmic and hardware error analysis are further discussed to motivate future implementations. Thermal pure quantum states, therefore, may present a suitable candidate for efficient thermal simulations of gauge theories in the era of quantum computing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Reproducibility of fixed-node diffusion Monte Carlo across diverse community codes: The case of water–methane dimer

Fixed-node diffusion quantum Monte Carlo (FN-DMC) is a widely trusted many-body method for solving the Schrödinger equation, known for its reliable predictions of material and molecular properties. Furthermore, its excellent scalability with system complexity and near-perfect utilization of computational power make FN-DMC ideally positioned to leverage new advances in computing to address increasingly complex scientific problems. Even though the method is widely used as a computational gold standard, reproducibility across the numerous FN-DMC code implementations has yet to be demonstrated. This difficulty stems from the diverse array of DMC algorithms and trial wave functions, compounded by the method’s inherent stochastic nature. Here, this study represents a community-wide effort to assess the reproducibility of the method, affirming that yes, FN-DMC is reproducible (when handled with care). Using the water–methane dimer as the canonical test case, we compare results from eleven different FN-DMC codes and show that the approximations to treat the non-locality of pseudopotentials are the primary source of the discrepancies between them. In particular, we demonstrate that, for the same choice of determinantal component in the trial wave function, reliable and reproducible predictions can be achieved by employing the T-move, the determinant locality approximation, or the determinant T-move schemes, while the older locality approximation leads to considerable variability in results. These findings demonstrate that, with appropriate choices of algorithmic details, fixed-node DMC is reproducible across diverse community codes—highlighting the maturity and robustness of the method as a tool for open and reliable computational science.

Della Pia, Flaviano [Univ. of Cambridge (United Ki↗
DOE OSTI2022

Quantum-Inspired Power System Reliability Assessment

To enable an in-depth study of power system operation and planning, the assessment of standard reliability indices is inevitable. The Monte Carlo Simulation (MCS) approach is a broadly used method in replacing the analytical methods in reliability indices assessment. The accuracy of MCS, however, highly depends on the sampling size, and hence, a complicated system with large number of components requires a large sampling size and daunting computational effort. To address this shortcoming, we, in this paper attempt to take advantage of potentials of the quantum computing (QC) for power system reliability assessment by realizing the following contributions: 1) an innovative quantum model designed for reliability assessment; 2) a quantum circuit that achieves the quadratic speed up compared to the classical MCS method; 3) an efficient quantum amplitude estimation (QAE) algorithm to accurately evaluate the reliability indices. The accuracy and efficacy of the quantum reliability method are extensively verified and demonstrated on both radial and mesh distribution systems.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Analysis of Three Body Decays in Quasi-Real Photoproduction

This thesis presents preliminary measurements of the moments of angular distribution for the K?K+ mesonic final state using a quasi-real, linearly polarised photon. Two of the main points of focus for this analysis were the development of the formalism for photoproduced vector-pseudoscalar decay and the tools by which the analysis was carried out. The formalism described how the moments of angular distribution could be extracted from the angular decay variables, and how they related to resonance decays in terms of partial waves. In extracting the moments, it was found that adapted Markov Chain Monte Carlo (MCMC) methods proved to be more effective in terms of extracting results from the data compared to the sole use of gradient descent based fitting algorithms. These measurements are complementary to other decay channels and production mechanisms, with the global aim of probing the existence of exotic mesons. Data from this analysis was taken by the CLAS collaboration at the Thomas Jefferson National Accelerator Facility (JLab) by scattering from a liquid hydrogen target using a 10.6 GeV electron. This work was done within the MesonEx program at CLAS12 that aims to map the spectrum of mesons, and in doing so, gain a greater understanding of Quantum ChromoDynamics (QCD) and the strong force.

Wishart, Robert↗
DOE OSTI2023

Measurement of the production of charm jets tagged with D0 mesons in pp collisions at $\sqrt{s}$ = 5.02 and 13 TeV

The measurement of the production of charm jets, identified by the presence of a D 0 meson in the jet constituents, is presented in proton–proton collisions at centre-of-mass energies of $\sqrt{s}$= 5.02 and 13 TeV with the ALICE detector at the CERN LHC. The D 0 mesons were reconstructed from their hadronic decay D 0 → K – π + and the respective charge conjugate. Jets were reconstructed from D 0 -meson candidates and charged particles using the anti-k T algorithm, in the jet transverse momentum range 5 < p T,chjet < 50 GeV/c, pseudorapidity |η jet | < 0.9 – R, and with the jet resolution parameters R = 0.2, 0.4, 0.6. The distribution of the jet momentum fraction carried by a D 0 meson along the jet axis $\left({z}_{\Big\Vert}^{\textrm{ch}}\right)$ was measured in the range 0.4 < ${z}_{\Big\Vert}^{\textrm{ch}}$ < 1.0 in four ranges of the jet transverse momentum. Comparisons of results for different collision energies and jet resolution parameters are also presented. The measurements are compared to predictions from Monte Carlo event generators based on leading-order and next-to-leading-order perturbative quantum chromodynamics calculations. A generally good description of the main features of the data is obtained in spite of a few discrepancies at low p T,chjet . Measurements were also done for R = 0.3 at $\sqrt{s}$= 5.02 and are shown along with their comparisons to theoretical predictions in an appendix to this paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Steady-state properties of multi-orbital systems using quantum Monte Carlo

A precise dynamical characterization of quantum impurity models with multiple interacting orbitals is challenging. In quantum Monte Carlo methods, this is embodied by sign problems. A dynamical sign problem makes it exponentially difficult to simulate long times. A multi-orbital sign problem generally results in a prohibitive computational cost for systems with multiple impurity degrees of freedom even in static equilibrium calculations. Here, we present a numerically exact inchworm method that simultaneously alleviates both sign problems, enabling simulation of multi-orbital systems directly in the equilibrium or nonequilibrium steady-state. The method combines ideas from the recently developed steady-state inchworm Monte Carlo framework [Erpenbeck et al., Phys. Rev. Lett. 130, 186301 (2023)] with other ideas from the equilibrium multi-orbital inchworm algorithm [Eidelstein et al., Phys. Rev. Lett. 124, 206405 (2020)]. We verify our method by comparison with analytical limits and numerical results from previous methods.

Chemistry↗
DOE OSTI2022

Complex paths around the sign problem

The Monte Carlo evaluation of path integrals is one of a few general purpose methods to approach strongly coupled systems. It is used in all branches of physics, from QCD and nuclear physics to the correlated electron systems. However, many systems of great importance (dense matter inside neutron stars, the repulsive Hubbard model away from half filling, and dynamical and nonequilibrium observables) are not amenable to the Monte Carlo method as it currently stands due to the so-called sign problem. Here, a new set of ideas recently developed to tackle the sign problem based on the complexification of field space and the Picard-Lefshetz theory accompanying it is reviewed. The mathematical ideas underpinning this approach, as well as the algorithms developed thus far, are described together with nontrivial examples where the method has already been proved successful. Directions of future work, including the burgeoning use of machine learning techniques, are delineated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Measurement of jet substructure in boosted $t\overline{t}$ events with the ATLAS detector using 140 fb -1 of 13 TeV $pp$ collisions

Measurements of the substructure of top-quark jets are presented, using 140 fb -1 of 13 TeV pp collision data recorded with the ATLAS detector at the LHC. Top-quark jets reconstructed with the anti-k t algorithm with a radius parameter R = 1.0 are selected in top-quark pair ($t\overline{t}$) events where one top quark decays semileptonically and the other hadronically, or where both top quarks decay hadronically. The top-quark jets are required to have transverse momentum p T > 350 GeV, yielding large samples of data events with jet p T values between 350 and 600 GeV. One- and two-dimensional differential cross sections for eight substructure variables, defined using only the charged components of the jets, are measured in a particle-level phase space by correcting for the smearing and acceptance effects induced by the detector. The differential cross sections are compared with the predictions of several Monte Carlo simulations in which top-quark pair-production quantum chromodynamic matrix-element calculations at next-to-leading-order precision in the strong coupling constant α S are passed to leading-order parton shower and hadronization generators. The Monte Carlo predictions for measures of the broadness, and also the two-body structure, of the top-quark jets are found to be in good agreement with the measurements, while variables sensitive to the three-body structure of the top-quark jets exhibit some tension with the measured distributions.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

A non-orthogonal variational quantum eigensolver

Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the ground state of a system by solving a generalized eigenvalue problem in a subspace spanned by a collection of parametrized quantum states. This allows for the systematic improvement of a logical wavefunction ansatz without a significant increase in circuit complexity. To minimize the circuit complexity of this approach, we propose a strategy for efficiently measuring the Hamiltonian and overlap matrix elements between states parametrized by circuits that commute with the total particle number operator. This strategy doubles the size of the state preparation circuits but not their depth, while adding a small number of additional two-qubit gates relative to standard variational quantum eigensolver. We also propose a classical Monte Carlo scheme to estimate the uncertainty in the ground state energy caused by a finite number of measurements of the matrix elements. We explain how this Monte Carlo procedure can be extended to adaptively schedule the required measurements, reducing the number of circuit executions necessary for a given accuracy. We apply these ideas to two model strongly correlated systems, a square configuration of H4 and the π-system of hexatriene (C6H8).

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2018

A Blueprint for Demonstrating Quantum Supremacy with Superconducting Qubits

Long coherence times and high fidelity control recently achieved in scalable superconducting circuits paved the way for the growing number of experimental studies of many-qubit quantum coherent phenomena in these devices. Albeit full implementation of quantum error correction and fault tolerant quantum computation remains a challenge the near term pre-error correction devices could allow new fundamental experiments despite inevitable accumulation of errors. One such open question foundational for quantum computing is achieving the so called quantum supremacy, an experimental demonstration of a computational task that takes polynomial time on the quantum computer whereas the best classical algorithm would require exponential time and/or resources. It is possible to formulate such a task for a quantum computer consisting of less than a 100 qubits. The computational task we consider is to provide approximate samples from a non-trivial quantum distribution. This is a generalization for the case of superconducting circuits of ideas behind boson sampling protocol for quantum optics introduced by Arkhipov and Aaronson. In this presentation we discuss a proof-of-principle demonstration of such a sampling task on a 9-qubit chain of superconducting gmon qubits developed by Google. We discuss theoretical analysis of the driven evolution of the device resulting in output approximating samples from a uniform distribution in the Hilbert space, a quantum chaotic state. We analyze quantum chaotic characteristics of the output of the circuit and the time required to generate a sufficiently complex quantum distribution. We demonstrate that the classical simulation of the sampling output requires exponential resources by connecting the task of calculating the output amplitudes to the sign problem of the Quantum Monte Carlo method. We also discuss the detailed theoretical modeling required to achieve high fidelity control and calibration of the multi-qubit unitary evolution in the device. We use a novel cross-entropy statistical metric as a figure of merit to verify the output and calibrate the device controls. Finally, we demonstrate the statistics of the wave function amplitudes generated on the 9-gmon chain and verify the quantum chaotic nature of the generated quantum distribution. This verifies the implementation of the quantum supremacy protocol.

Kechedzhi, Kostyantyn↗
DOE OSTI2021

Monte Carlo simulation to study the effect of molecular spin state on the spatio-temporal evolution of equilibrium magnetic properties of magnetic tunnel junction based molecular spintronics devices

With a variable spin state, paramagnetic molecules can affect the impact of magnetic exchange coupling strength between two ferromagnetic electrodes. Our magnetic tunnel junction based molecular spintronics devices (MTJMSD) were successful in connecting paramagnetic single molecular magnet (SMM) between two ferromagnetic electrodes. Isolated SMM exhibited a wide range of spin states. However, it was extremely challenging to identify the SMM spin state when connected to the ferromagnetic electrodes. Our prior experimental and Monte Carlo Simulations (MCS) studies showed that paramagnetic molecules produced unprecedented strong antiferromagnetic coupling between two ferromagnets at room temperature. The overall antiferromagnetic coupling occurred when a paramagnetic SMM made antiferromagnetic coupling to the first electrode and ferromagnetic coupling to the second ferromagnetic electrode. This paper studies the impact of variable molecular spin states of the SMMs, producing strong antiferromagnetic coupling between the ferromagnetic electrodes of MTJMSD. The MTJMSD used in this study was represented by an 11 x 50 x 50 Ising model, with 11 being the thickness of the MTJMSD and 5 x 10 x 50 being each electrode’s size. We employed a continuous MCS algorithm to investigate SMM’s spin state’s impact as a function of molecular exchange coupling strength and thermal energy.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Classical analog of quantum models in synthetic dimensions

We introduce a classical analog of quantum matter in ultracold molecule-synthetic or Rydberg atom-synthetic dimensions, by extending the Potts model to include interactions J 1 between atoms adjacent in both real and synthetic space and studying its finite-temperature properties. For intermediate values of J 1 , the resulting phases and phase diagrams are similar to those of the clock and Villain models, in which three phases emerge. There exists a sheet phase analogous to that found in quantum synthetic dimension models between the high-temperature disordered phase and the low-temperature ferromagnetic phase. Furthermore, we also employ machine learning to uncover nontrivial features of the phase diagram using the learning by confusion approach, which is able to discern several successive phase transitions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

A light weight regularization for wave function parameter gradients in quantum Monte Carlo

The parameter derivative of the expectation value of the energy, ∂E/∂p, is a key ingredient in variational Monte Carlo (VMC) wave function optimization methods. In some cases, a naïve estimate of this derivative suffers from an infinite variance, which inhibits the efficiency of optimization methods that rely on a stable estimate of the derivative. In this work, we derive a simple regularization of the naïve estimator, which is trivial to implement in existing VMC codes, has finite variance, and a negligible bias, which can be extrapolated to zero bias with no extra cost. We use this estimator to construct an unbiased, finite variance estimation of ∂E/∂p for a multi-Slater–Jastrow trial wave function on the LiH molecule and in the optimization of a multi-Slater–Jastrow trial wave function on the CuO molecule. This regularized estimator is a simple and efficient estimator of ∂E/∂p for VMC optimization techniques.

36 MATERIALS SCIENCE↗
DOE OSTI2022

On numerical energy conservation for an implicit particle-in-cell method coupled with a binary Monte-Carlo algorithm for Coulomb collisions

We report conventional particle-in-cell (PIC) methods suffer from enhanced numerical heating (explicit PIC) or cooling (semi-implicit PIC) when coupled with a binary Monte-Carlo algorithm for Coulomb collisions. In this work, a fully-implicit θ-PIC scheme (with adjustable time-biasing parameter 1/2 ≤ θ ≤) is considered. The discrete change in energy of a closed system after a time step for this scheme scales with (1/2 - θ)C θ , where C θ is a positive definite quantity that depends on the frequency spectrum of the energy in the fields. Collisions lead to additional energy in the field fluctuations associated with high-frequency light waves produced by a numerical Bremsstrahlung process, which can result in a large increase in the numerical cooling rate for θ > 1/2. However, for θ = 1/2, energy is exactly conserved. The energy in the field fluctuations on long time scales agrees with that calculated using the equipartition theorem for a classical system in thermodynamic equilibrium.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Optimizing temperature distributions for training neural quantum states using parallel tempering

Parametrized artificial neural networks (ANNs) can be very expressive ansatzes for variational algorithms, reaching state-of-the-art energies on many quantum many-body Hamiltonians. Nevertheless, the training of the ANN can be slow and stymied by the presence of local minima in the parameter landscape. One approach to mitigate this issue is to use parallel tempering methods, and in this work, we focus on the role played by the temperature distribution of the parallel tempering replicas. Using an adaptive method that adjusts the temperatures in order to equate the exchange probability between neighboring replicas, we show that this temperature optimization can significantly increase the success rate of the variational algorithm with negligible computational cost by eliminating bottlenecks in the replicas' random walk. Furthermore, we demonstrate this using two different neural networks, a restricted Boltzmann machine and a feedforward network, which we use to study a toy problem based on a permutation invariant Hamiltonian with a pernicious local minimum and the 𝐽 1 −𝐽 2 model on a rectangular lattice.

Neural network simulations↗
DOE OSTI2020

Finite temperature auxiliary field quantum Monte Carlo in the canonical ensemble

Finite temperature auxiliary field-based quantum Monte Carlo methods, including determinant quantum Monte Carlo and Auxiliary Field Quantum Monte Carlo (AFQMC), have historically assumed pivotal roles in the investigation of the finite temperature phase diagrams of a wide variety of multidimensional lattice models and materials. Despite their utility, however, these techniques are typically formulated in the grand canonical ensemble, which makes them difficult to apply to condensates such as superfluids and difficult to benchmark against alternative methods that are formulated in the canonical ensemble. Working in the grand canonical ensemble is furthermore accompanied by the increased overhead associated with having to determine the chemical potentials that produce desired fillings. Given this backdrop, in this work, we present a new recursive approach for performing AFQMC simulations in the canonical ensemble that does not require knowledge of chemical potentials. To derive this approach, we exploit the convenient fact that AFQMC solves the many-body problem by decoupling many-body propagators into integrals over one-body problems to which non-interacting theories can be applied. We benchmark the accuracy of our technique on illustrative Bose and Fermi–Hubbard models and demonstrate that it can converge more quickly to the ground state than grand canonical AFQMC simulations. We believe that our novel use of HS-transformed operators to implement algorithms originally derived for non-interacting systems will motivate the development of a variety of other methods and anticipate that our technique will enable direct performance comparisons against other many-body approaches formulated in the canonical ensemble.

Shen, Tong (ORCID:0000000206292468)↗
DOE OSTI2021

Feasibility of DEIM for retrieving the initial field via dimensionality reduction

When parameter estimation is solved in a high-dimensional space, the dimensionality reduction strategy becomes the primary consideration for alleviating the tremendous computational cost. Here, the discrete empirical interpolation method (DEIM) is explored to retrieve the initial condition (IC) by combining the polynomial chaos (PC) based ensemble Kalman filter (i.e. PC-EnKF), where a non-intrusive PC expansion is considered as a surrogate model in place of the forward model in the prediction step of the ensemble Kalman filter, resulting in fewer forward model integrations but with a comparable accuracy as Monte Carlo-based approaches. The DEIM acts as a hyper-reduction tool to provide the low-dimensional input for the high-dimensional initial field, which can be reconstructed using the information on the sparse interpolation grid points that is adaptively obtained through PC-EnKF data assimilation method. Thus an innovative framework to reconstruct the IC is developed. The detailed procedure at each assimilation iteration includes: the determination of the spatial interpolation points, the estimation of the initial values on the interpolation locations using the optimal observations, and the reconstruction of IC in the full space. The current study uses the reconstruction field of initial conditions of the Navier-Stokes equations as an example to illustrate the efficacy of our method. The experimental results demonstrate the proposed algorithm achieves a satisfactory reconstruction for the initial field. The proposed method helps to extend the applicable area of DEIM in solving inverse problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗