Stability and production of positron-diatomic molecule complexes

The energies at geometries close to the equilibrium for the e$^+$BeO and e$^+$LiF ground states were computed by means of diffusion Monte Carlo simulations. These results allow us to predict the equilibrium geometries and the vibrational frequencies for these exotic systems,and to discuss their stability with respect to the various dissociation channels. Since the adiabatic positron affinities were found to be smaller than the dissociation energies for both complexes, we propose these two molecules as possible candidates in the challenge to produce and detect stable positron-molecule systems.Comment: submitted to Phys. Rev. Let

Delayed Rejection Variational Monte Carlo

A new acceleration algorithm to address the problem of multiple time scales in variational Monte Carlo simulations is presented. Core electrons usually require smaller time steps than valence electrons. After a first attempted move has been rejected, the delayed rejection algorithm attempts a second move with a smaller time step, so moves of both valence and core electrons can be accepted. Results on Be and Ne atoms as test cases are presented. Correlation time and both average accepted displacement and acceptance ratio as a function of the distance from the nucleus evidence the efficiency of the proposed algorithm in dealing with the multiple time scales problem.

Quantum Monte Carlo investigation of small He-4 clusters with a He-3 impurity

Small helium (He-4) clusters containing the lighter isotope He-3 are studied by means of quantum Monte Carlo methods. Accurate ground state energies and structural properties are obtained using accurate trial wave functions and the Tang-Tonnies-Yiu (TTY) helium-helium pair potential. The dimer He-4-He-3 is not bound; as well as the trimer (HeHe2)-He-4-He-3. The smallest cluster containing He-3 is He-4(2) He-3 with a nonrigid structure having a marked linear contribution. Interestingly, this weakly bound system, with an energy one order of magnitude less than the He-4(3) trimer, is able to bind another He-3 atom, forming the tetramer He-4(2) He-3(2), which shows the odd feature of having five out of six unbound pairs. In general, the substitution of a single He-4 atom in a pure cluster with a He-3 atom leads to an energetic destabilization, as the pair He-4-He-3 is not bound. The isotopic impurity is found to perturb only weakly the distributions of the remaining He-4 atoms, which retain the high floppiness already found in the pure clusters. As the number of atoms increases the isotopic impurity has the marked tendency to stay on the surface of the cluster. This behavior is consistent with the formation of the so-called "Andreev states" of a single He-3 in liquid He-4 helium and droplets, where the impurity tends to form single-particle states on the surface of the pure He-4

Decoherence and classicalization of continuous-time quantum walks on graphs

We address decoherence and classicalization of continuous-time quantum walks (CTQWs) on graphs. In particular, we investigate three different models of decoherence, and employ the quantum-classical (QC) dynamical distance as a figure of merit to assess whether, and to which extent, decoherence classicalizes the CTQW, i.e. turns it into the analogue classical process. We show that the dynamics arising from intrinsic decoherence, i.e. dephasing in the energy basis, do not fully classicalize the walker and partially preserves quantum features. On the other hand, dephasing in the position basis, as described by the Haken-Strobl master equation or by the quantum stochastic walk (QSW) model, asymptotically destroys the quantumness of the walker, making it equivalent to a classical random walk. We also investigate the speed of the classicalization process, and observe a faster convergence of the QC-distance to its asymptotic value for intrinsic decoherence and the QSW models, whereas in the Haken-Strobl scenario, larger values of the decoherence rate induce localization of the walker.Comment: 15 pages, 4 figure

Delayed Rejection Variational Monte Carlo

A new acceleration algorithm to address the problem of multiple time scales in variational Monte Carlo simulations is presented. After a first attempted move has been rejected, the delayed rejection algorithm attempts a second move with a smaller time step, so that even moves of the core electrons can be accepted. Results on Be and Ne atoms as test cases are presented. Correlation time and both average accepted displacement and acceptance ratio as a function of the distance from the nucleus evidence the efficiency of the proposed algorithm in dealing with the multiple time scales problem.Comment: To be published on the Journal of Chemical Physic

Robust wave function optimization procedures in quantum Monte Carlo methods

The energy variance optimization algorithm over a fixed ensemble of configurations in variational Monte Carlo is formally identical to a problem of fitting data: we reexamine it from a statistical maximum-likelihood point of view. We detect the origin of the problem of convergence that is often encountered in practice and propose an alternative procedure for optimization of trial wave functions in quantum Monte Carlo. We successfully test this proposal by optimizing a trial wave function for the Helium trimer.Comment: Submitted for publicatio

Gaussian boson sampling validation via detector binning

Gaussian boson sampling (GBS), a computational problem conjectured to be hard to simulate on a classical machine, has been at the forefront of recent years' experimental and theoretical efforts to demonstrate quantum advantage. The classical intractability of the sampling task makes validating these experiments a challenging and essential undertaking. In this paper, we propose binned-detector probability distributions as a suitable quantity to statistically validate GBS experiments employing photon-number-resolving detectors. We show how to compute such distributions by leveraging their connection with their respective characteristic function. The latter may be efficiently and analytically computed for squeezed input states as well as for relevant classical hypothesis like squashed states. Our scheme encompasses other validation methods based on marginal distributions and correlation functions. Additionally, it can accommodate various sources of noise, such as losses and partial distinguishability, a feature that have received limited attention within the GBS framework so far. We also illustrate how binned-detector probability distributions behave when Haar-averaged over all possible interferometric networks, extending known results for Fock boson sampling

Linear Expansions of Correlated Functions: Variational Monte Carlo Case Study

ABSTRACT: The relative performance of trial wave functions expressed as linear combination of correlated exponentials has been tested on a variety of systems. The results are compared against other correlated functions commonly used in the literature to assess the capabilities of the proposed ansatz. A possible departure from the simple exponential functional form used in previous works is discussed, along with its advantages and drawbacks. We also discuss how to implement an efficient optimization procedure for this correlated basis set

Explicitly correlated trial wave functions in Quantum Monte Carlo calculations of excited states of Be and Be-

We present a new form of explicitly correlated wave function whose parameters are mainly linear, to circumvent the problem of the optimization of a large number of non-linear parameters usually encountered with basis sets of explicitly correlated wave functions. With this trial wave function we succeeded in minimizing the energy instead of the variance of the local energy, as is more common in quantum Monte Carlo methods. We applied this wave function to the calculation of the energies of Be 3P (1s22p2) and Be- 4So (1s22p3) by variational and diffusion Monte Carlo methods. The results compare favorably with those obtained by different types of explicitly correlated trial wave functions already described in the literature. The energies obtained are improved with respect to the best variational ones found in literature, and within one standard deviation from the estimated non-relativistic limitsComment: 19 pages, no figures, submitted to J. Phys.

Compact boundary-condition-determined wave function for positronium hydride "PsH…

A simple, compact, and accurate wave function for positronium hydride is written as a product of Pade' approximants for electron-nucleus interactions and of Jastrow functions for electron-electron interactions. Most of the parameters are fixed taking into account both the correct cusp conditions when two particles collide and the correct asymptotic behavior when one or two particles go to infinity. The remaining parameters were optimized by variational Monte Carlo calculations. The energy of this single term wave function is Ϫ0.786073(6) hartree and favorably compares with very long configuration interaction expansions and even with explicitly correlated function expansions. The exam of the wave function and of various two-dimensional distribution functions shows that the PsH structure is similar to the hydrogen anion structure, with the positron slightly perturbing it and its motion strongly correlated to the electrons that are squeezed towards each other and towards the nucleus