An official website of the United States government
The potential energy curves (PECs) for the homonuclear He–He, Ar–Ar, Cu–Cu, and Si–Si dimers, as well as heteronuclear Cu–He, Cu–Ar, Cu–Xe, Si–He, Si–Ar, and Si–Xe dimers, are obtained in quantum Monte Carlo (QMC) calculations. It is shown that the QMC method provides the PECs with an accuracy comparable with that of the state-of-the-art coupled cluster singles and doubles with perturbative triples corrections [CCSD(T)] calculations. The QMC data are approximated by the Morse long range (MLR) and (12-6) Lennard-Jones (LJ) potentials. The MLR and LJ potentials are used to calculate the deflection angles in binary collisions of corresponding atom pairs and transport coefficients of Cu and Si vapors and their mixtures with He, Ar, and Xe gases in the range of temperature from 100 K to 10 000 K. It is shown that the use of the LJ potentials introduces significant errors in the transport coefficients of high-temperature vapors and gas mixtures. The mixtures with heavy noble gases demonstrate anomalous behavior when the viscosity and thermal conductivity can be larger than that of the corresponding pure substances. In the mixtures with helium, the thermal diffusion factor is found to be unusually large. The calculated viscosity and diffusivity are used to determine parameters of the variable hard sphere and variable soft sphere molecular models as well as parameters of the power-law approximations for the transport coefficients. The results obtained in the present work include all information required for kinetic or continuum simulations of dilute Cu and Si vapors and their mixtures with He, Ar, and Xe gases.
more »
« less
PyQMC : An all-Python real-space quantum Monte Carlo module in PySCF
We describe a new open-source Python-based package for high accuracy correlated electron calculations using quantum Monte Carlo (QMC) in real space: PyQMC. PyQMC implements modern versions of QMC algorithms in an accessible format, enabling algorithmic development and easy implementation of complex workflows. Tight integration with the PySCF environment allows for a simple comparison between QMC calculations and other many-body wave function techniques, as well as access to high accuracy trial wave functions.
more »
« less
- Award ID(s):
- 1931258
- PAR ID:
- 10440602
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 158
- Issue:
- 11
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Interacting many-electron problems pose some of the greatest computational challenges in science, with essential applications across many fields. The solutions to these problems will offer accurate predictions of chemical reactivity and kinetics, and other properties of quantum systems 1–4 . Fermionic quantum Monte Carlo (QMC) methods 5,6 , which use a statistical sampling of the ground state, are among the most powerful approaches to these problems. Controlling the fermionic sign problem with constraints ensures the efficiency of QMC at the expense of potentially significant biases owing to the limited flexibility of classical computation. Here we propose an approach that combines constrained QMC with quantum computation to reduce such biases. We implement our scheme experimentally using up to 16 qubits to unbias constrained QMC calculations performed on chemical systems with as many as 120 orbitals. These experiments represent the largest chemistry simulations performed with the help of quantum computers, while achieving accuracy that is competitive with state-of-the-art classical methods without burdensome error mitigation. Compared with the popular variational quantum eigensolver 7,8 , our hybrid quantum-classical computational model offers an alternative path towards achieving a practical quantum advantage for the electronic structure problem without demanding exceedingly accurate preparation and measurement of the ground-state wavefunction.more » « less
-
Summary Maximum simulated likelihood estimation of mixed multinomial logit models requires evaluation of a multidimensional integral. Quasi-Monte Carlo (QMC) methods such as Halton sequences and modified Latin hypercube sampling are workhorse methods for integral approximation. Earlier studies explored the potential of sparse grid quadrature (SGQ), but SGQ suffers from negative weights. As an alternative to QMC and SGQ, we looked into the recently developed designed quadrature (DQ) method. DQ requires fewer nodes to get the same level of accuracy as QMC and SGQ, is as easy to implement, ensures positivity of weights, and can be created on any general polynomial space. We benchmarked DQ against QMC in a Monte Carlo and an empirical study. DQ outperformed QMC in all considered scenarios, is practice ready, and has potential to become the workhorse method for integral approximation.more » « less
-
Li, J.; Spanos, P. D.; Chen, J. B.; Peng, Y. B. (Ed.)Infrastructure networks offer critical services to modern society. They dynamically interact with the environment, operators, and users. Infrastructure networks are unique engineered systems, large in scale and high in complexity. One fundamental issue for their reliability assessment is the uncertainty propagation from stochastic disturbances across interconnected components. Monte Carlo simulation (MCS) remains approachable to quantify stochastic dynamics from components to systems. Its application depends on time efficiency along with the capability of delivering reliable approximations. In this paper, we introduce Quasi Monte Carlo (QMC) sampling techniques to improve modeling efficiency. Also, we suggest a principled Monte Carlo (PMC) method that equips the crude MCS with Probably Approximately Correct (PAC) approaches to deliver guaranteed approximations. We compare our proposed schemes with a competitive approach for stochastic dynamic analysis, namely the Probability Density Evolution Method (PDEM). Our computational experiments are on ideal but complex enough source-terminal (S-T) dynamic network reliability problems. We endow network links with oscillators so that they can jump across safe and failed states allowing us to treat the problem from a stochastic process perspective. We find that QMC alone can yield practical accuracy, and PMC with a PAC algorithm can deliver accuracy guarantees. Also, QMC is more versatile and efficient than the PDEM for network reliability assessment. The QMC and PMC methods provide advanced uncertainty propagation techniques to support decision makers with their reliability problems.more » « less
-
Alex Keller (Ed.)Quasi-Monte Carlo (QMC) points are a substitute for plain Monte Carlo (MC) points that greatly improve integration accuracy under mild assumptions on the problem. Because QMC can give errors that are o(1/n) as n → ∞, and randomized versions can attain root mean squared errors that are o(1/n), changing even one point can change the estimate by an amount much larger than the error would have been and worsen the convergence rate. As a result, certain practices that fit quite naturally and intuitively with MC points can be very detrimental to QMC performance. These include thinning, burn-in, and taking sample sizes such as powers of 10, when the QMC points were designed for different sample sizes. This article looks at the effects of a common practice in which one skips the first point of a Sobol’ sequence. The retained points ordinarily fail to be a digital net and when scrambling is applied, skipping over the first point can increase the numerical error by a factor proportional to √n where n is the number of function evaluations used.more » « less
