Ab initio lifetime correction to scattering states for time-dependent electronic-structure calculations with incomplete basis sets

We propose a method for obtaining effective lifetimes of scattering electronic states for avoiding the artificially confinement of the wave function due to the use of incomplete basis sets in time-dependent electronic-structure calculations of atoms and molecules. In this method, using a fitting procedure, the lifetimes are extracted from the spatial asymptotic decay of the approximate scattering wave functions obtained with a given basis set. The method is based on a rigorous analysis of the complex-energy solutions of the Schr{\"o}dinger equation. It gives lifetimes adapted to any given basis set without using any empirical parameters. The method can be considered as an ab initio version of the heuristic lifetime model of Klinkusch et al. [J. Chem. Phys. 131, 114304 (2009)]. The method is validated on the H and He atoms using Gaussian-type basis sets for calculation of high-harmonic-generation spectra

Quantum entanglement enhances the capacity of bosonic channels with memory

The bosonic quantum channels have recently attracted a growing interest, motivated by the hope that they open a tractable approach to the generally hard problem of evaluating quantum channel capacities. These studies, however, have always been restricted to memoryless channels. Here, it is shown that the classical capacity of a bosonic Gaussian channel with memory can be significantly enhanced if entangled symbols are used instead of product symbols. For example, the capacity of a photonic channel with 70%-correlated thermal noise of one third the shot noise is enhanced by about 11% when using 3.8-dB entangled light with a modulation variance equal to the shot noise.Comment: 4 pages, 4 figure

Information transmission via entangled quantum states in Gaussian channels with memory

Gaussian quantum channels have recently attracted a growing interest, since they may lead to a tractable approach to the generally hard problem of evaluating quantum channel capacities. However, the analysis performed so far has always been restricted to memoryless channels. Here, we consider the case of a bosonic Gaussian channel with memory, and show that the classical capacity can be significantly enhanced by employing entangled input symbols instead of product symbols.Comment: 13 pages, 5 figures, Workshop on Quantum entanglement in physical and information sciences, Pisa, December 14-18, 200

Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density

We construct improved quantum Monte Carlo estimators for the spherically- and system-averaged electron pair density (i.e. the probability density of finding two electrons separated by a relative distance u), also known as the spherically-averaged electron position intracule density I(u), using the general zero-variance zero-bias principle for observables, introduced by Assaraf and Caffarel. The calculation of I(u) is made vastly more efficient by replacing the average of the local delta-function operator by the average of a smooth non-local operator that has several orders of magnitude smaller variance. These new estimators also reduce the systematic error (or bias) of the intracule density due to the approximate trial wave function. Used in combination with the optimization of an increasing number of parameters in trial Jastrow-Slater wave functions, they allow one to obtain well converged correlated intracule densities for atoms and molecules. These ideas can be applied to calculating any pair-correlation function in classical or quantum Monte Carlo calculations.Comment: 13 pages, 9 figures, published versio

Curing basis-set convergence of wave-function theory using density-functional theory: a systematically improvable approach

The present work proposes to use density-functional theory (DFT) to correct for the basis-set error of wave-function theory (WFT). One of the key ideas developed here is to define a range-separation parameter which automatically adapts to a given basis set. The derivation of the exact equations are based on the Levy-Lieb formulation of DFT, which helps us to define a complementary functional which corrects uniquely for the basis-set error of WFT. The coupling of DFT and WFT is done through the definition of a real-space representation of the electron-electron Coulomb operator projected in a one-particle basis set. Such an effective interaction has the particularity to coincide with the exact electron-electron interaction in the limit of a complete basis set, and to be finite at the electron-electron coalescence point when the basis set is incomplete. The non-diverging character of the effective interaction allows one to define a mapping with the long-range interaction used in the context of range-separated DFT and to design practical approximations for the unknown complementary functional. Here, a local-density approximation is proposed for both full-configuration-interaction (FCI) and selected configuration-interaction approaches. Our theory is numerically tested to compute total energies and ionization potentials for a series of atomic systems. The results clearly show that the DFT correction drastically improves the basis-set convergence of both the total energies and the energy differences. For instance, a sub kcal/mol accuracy is obtained from the aug-cc-pVTZ basis set with the method proposed here when an aug-cc-pV5Z basis set barely reaches such a level of accuracy at the near FCI level

Simulating quantum correlations as a distributed sampling problem

It is known that quantum correlations exhibited by a maximally entangled qubit pair can be simulated with the help of shared randomness, supplemented with additional resources, such as communication, post-selection or non-local boxes. For instance, in the case of projective measurements, it is possible to solve this problem with protocols using one bit of communication or making one use of a non-local box. We show that this problem reduces to a distributed sampling problem. We give a new method to obtain samples from a biased distribution, starting with shared random variables following a uniform distribution, and use it to build distributed sampling protocols. This approach allows us to derive, in a simpler and unified way, many existing protocols for projective measurements, and extend them to positive operator value measurements. Moreover, this approach naturally leads to a local hidden variable model for Werner states.Comment: 13 pages, 2 figure

Simulation of bipartite qudit correlations

We present a protocol to simulate the quantum correlations of an arbitrary bipartite state, when the parties perform a measurement according to two traceless binary observables. We show that $\log(d)$ bits of classical communication is enough on average, where $d$ is the dimension of both systems. To obtain this result, we use the sampling approach for simulating the quantum correlations. We discuss how to use this method in the case of qudits.Comment: 7 page

Modular decomposition of protein-protein interaction networks

We introduce an algorithmic method, termed modular decomposition, that defines the organization of protein-interaction networks as a hierarchy of nested modules. Modular decomposition derives the logical rules of how to combine proteins into the actual functional complexes by identifying groups of proteins acting as a single unit (sub-complexes) and those that can be alternatively exchanged in a set of similar complexes. The method is applied to experimental data on the pro-inflammatory tumor necrosis factor-α (TNF-α)/NFκB transcription factor pathway