Alternative Computational Scheme Research Articles

Improving the Designs of Nearest Neighbour Quantum Circuits for 1D and 2D Architectures

In recent years, the semiconductor industry is increasingly considering alternative computation schemes and in this conjuncture quantum computing has come up as a promising alternative due its ability to perform parallel computations (by exploiting superposition) and capacity to solve some of the intractable problems exponentially faster. But one of the criteria in the realization of quantum circuits is that corresponding descriptions demand a so-called nearest neighbour (NN) constraint to be satisfied. One of the possible solutions towards satisfying such constraints is through the insertion of SWAP gates that makes the qubit interactions within a gate adjacent. But since the incorporation of SWAP gates increases the cost of the circuits, strategies should be employed which satisfy the NN constraint while placing SWAP gates so that the cost are reduced. In this work, we propose improved design strategies to realize low-cost NN-compliant quantum circuits. Two approaches are introduced, where the first approach relies on a graph traversal process and uses heuristics in critical decision-making conditions to design a 1D NN-compliant representation. The second approach considers qubit-to-qubit interactions and realizes the circuits in a 2D platform based on some weighted metric. Both the designs are evaluated over a wide spectrum of benchmarks and results have been compared with related works. In those comparisons, we have seen that our approaches perform fairly better than the reported ones.

P -wave heavy quarkonium spectrum with next-to-next-to-next-to-leading logarithmic accuracy

We compute the heavy quarkonium mass of $l\not= 0$ (angular momentum) states, with otherwise arbitrary quantum numbers, with next-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. This constitutes the first observable in heavy quarkonium for which two orders of the weak-coupling expansion sensitive to the ultrasoft scale are known and the resummation of ultrasoft logarithms is made. We also obtain, for the first time, resummed N$^3$LL expressions for the different fine and hyperfine energy splittings of these states, which are not sensitive to the ultrasoft scale but still require resummation of (hard) logarithms. We do this analysis for the equal and non-equal mass cases. We also study an alternative computational scheme that treats the static potential exactly. We then perform a comprehensive phenomenological analysis: we apply these results to the $n=2$, $l=1$ bottomonium, $B_c$ and charmonium systems and study their convergence.

Data-driven computation of molecular reaction coordinates.

The identification of meaningful reaction coordinates plays a key role in the study of complex molecular systems whose essential dynamics are characterized by rare or slow transition events. In a recent publication, precise defining characteristics of such reaction coordinates were identified and linked to the existence of a so-called transition manifold. This theory gives rise to a novel numerical method for the pointwise computation of reaction coordinates that relies on short parallel MD simulations only, but yields accurate approximation of the long time behavior of the system under consideration. This article presents an extension of the method towards practical applicability in computational chemistry. It links the newly defined reaction coordinates to concepts from transition path theory and Markov state model building. The main result is an alternative computational scheme that allows for a global computation of reaction coordinates based on commonly available types of simulation data, such as single long molecular trajectories or the push-forward of arbitrary canonically distributed point clouds. It is based on a Galerkin approximation of the transition manifold reaction coordinates that can be tuned to individual requirements by the choice of the Galerkin ansatz functions. Moreover, we propose a ready-to-implement variant of the new scheme, which computes data-fitted, mesh-free ansatz functions directly from the available simulation data. The efficacy of the new method is demonstrated on a small protein system.

The charm/bottom quark mass from heavy quarkonium at N3LO

We determine the charm and bottom quark masses using the N3LO perturbative expression of the ground state (pseudoscalar) energy of the bottomonium, charmonium and Bc systems: the ηb, ηc and Bc masses. We work in the renormalon subtracted scheme, which allows us to control the divergence of the perturbation series due to the pole mass renormalon. Our result for the overline{mathrm{MS}} masses reads {overline{m}}_cleft({overline{m}}_cright)=1223(33) MeV and {overline{m}}_bleft({overline{m}}_bright)=4186(37) MeV. We also extract a value of αs from a renormalon-free combination of the ηb, ηc and Bc masses: αs(Mz) = 0.1195(53). We explore the applicability of the weak coupling approximation to bottomonium n = 2 states. Finally, we consider an alternative computational scheme that treats the static potential exactly and study its convergence properties.

Ultra high energy particles propagation and the transition from galactic to extra-galactic cosmic rays

We discuss the basic features of the propagation of Ultra High Energy Cosmic Rays in astrophysical backgrounds, comparing two alternative computation schemes to compute the expected fluxes. We also discuss the issue of the transition among galactic and extra-galactic cosmic rays using theoretical results on fluxes to compare different models.

Computing the probabilities of HLA-like matching

We present several alternative computation schemes, accompanied with appropriate software, to compute the probabilities of the (2n+1) possible match levels between the alleles in n genetic sites of a given individual, and the alleles in the same n sites of an individual who is drawn randomly from a given population. The modeling generalizes the asymmetric HLA-criterion which defines the donor-recipient immunological compatibility in kidney or bone-marrow transplantation. We discuss our algorithms by order of their run-time complexity with respect to n. We show the advantage of using computational schemes over explicit expressions even for the HLA present-day count of n=3.

On the Effects of Filterbank Design and Energy Computation on Robust Speech Recognition

In this paper, we examine how energy computation and filterbank design contribute to the overall front-end robustness, especially when the investigated features are applied to noisy speech signals, in mismatched training-testing conditions. In prior work (“Auditory Teager energy cepstrum coefficients for robust speech recognition,” D. Dimitriadis, P. Maragos, and A. Potamianos, in Proc. Eurospeech'05, Sep. 2005), a novel feature set called “Teager energy cepstrum coefficients” (TECCs) has been proposed, employing a dense, smooth filterbank and alternative energy computation schemes. TECCs were shown to be more robust to noise and exhibit improved performance compared to the widely used Mel frequency cepstral coefficients (MFCCs). In this paper, we attempt to interpret these results using a combined theoretical and experimental analysis framework. Specifically, we investigate in detail the connection between the filterbank design, i.e., the filter shape and bandwidth, the energy estimation scheme and the automatic speech recognition (ASR) performance under a variety of additive and/or convolutional noise conditions. For this purpose: 1) the performance of filterbanks using triangular, Gabor, and Gammatone filters with various bandwidths and filter positions are examined under different noisy speech recognition tasks, and 2) the squared amplitude and Teager-Kaiser energy operators are compared as two alternative approaches of computing the signal energy. Our end-goal is to understand how to select the most efficient filterbank and energy computation scheme that are maximally robust under both clean and noisy recording conditions. Theoretical and experimental results show that: 1) the filter bandwidth is one of the most important factors affecting speech recognition performance in noise, while the shape of the filter is of secondary importance, and 2) the Teager-Kaiser operator outperforms (on the average and for most noise types) the squared amplitude energy computation scheme for speech recognition in noisy conditions, especially, for large filter bandwidths. Experimental results show that selecting the appropriate filterbank and energy computation scheme can lead to significant error rate reduction over both MFCC and perceptual linear predicion (PLP) features for a variety of speech recognition tasks. A relative error rate reduction of up to ~ 30% for MFCCs and ~ 39% for PLPs is shown for the Aurora-3 Spanish Task.

Performance of plane‐wave‐based LDA+U and GGA+U approaches to describe magnetic coupling in molecular systems

This work explores the performance of periodic plane wave density functional theory calculations with an on-site Coulomb correction to the standard LDA and GGA exchange-correlation potential--commonly used to describe strongly correlated solids--in describing the magnetic coupling constant of a series of molecular compounds representative of dinuclear Cu complexes and of organic diradicals. The resulting LDA+U or GGA+U formalisms, lead to results comparable to experiment and to those obtained by means of standard hybrid functionals provided that the value of the U parameter is adequately chosen. Hence, these methods offer an alternative efficient computational scheme to correct LDA and GGA approaches to adequately describe the electronic structure and magnetic coupling in large molecular magnetic systems, although at the expenses of introducing an empirical (U) parameter. For all investigated copper dinuclear systems, the LDA+U and GGA+U approaches lead to an improvement in the description of magnetic properties over the original LDA and GGA schemes with an accuracy similar to that arising from the hybrid B3LYP functional, by increasing the on-site Coulomb repulsion with a moderate U value. Nevertheless, the introduction of an arbitrary U value in the 0-10 eV range most often provides the correct ground-state spin distribution and the correct sign of the magnetic coupling constant.

TD‐DFT modeling of the circular dichroism for a tryptophan zipper peptide with coupled aromatic residues

In this work, time dependent density functional theory (TD-DFT) is used to provide a reliable basis for interpretation of the electronic spectra of coupled tryptophan (Trp) residues, particularly those in a model Trpzip beta-hairpin peptide. Pairs of isolated indoles form chiral coupled chromophores whose computed electronic ultraviolet circular dichroism (CD) is in excellent agreement with observed transition wavelengths and intensities. The calculations were compared to experimental data for pairwise coupling in mutant Trpzip peptides that are recently available. A study of variation of the basis set, geometry optimization, and the solvent environment on the spectra showed limited impact on bandshapes. An alternative simplified computational scheme, dependent on the transition dipole coupling (TDC) mechanism, is shown to give a representation of qualitative aspects of the intense CD for the (1)B bands at 228 and 213 nm. The results confirm the origin of the Trpzip diagnostic CD as primarily a dipolar interaction between Trp sidechains, and show that quantum computations of electronic CD can provide a reliable basis for interpretation of these chirally coupled aromatic spectral phenomena.

Enhancement of Computational Efficiency of Reliability Optimization Method by Approximate Evaluation of Sub-Optimization Problem

Alternative computational scheme is presented fur reliability based optimal design using a modified advanced first order second moment (AFOSH) method. Both design variables and design parameters are considered as random variables about their nominal values. Each probability constraint is transformed into a sub -optimization problem and then is resolved with the modified Hasofer- Lind-Rackwitz-Fiessler (HL-RF) method for computational efficiency and convergence. A method of design sensitivity analysis for probability constraint is presented and tested through simple examples. The suggested method is examined by solving several examples and the results are compared with those of other methods.

Vertex models for the hard-square and hard-hexagon gases, and critical parameters from the scaling transformation

In a general formulation of hard-core lattice gas models the hard-square and hard-hexagon models are expressed in terms of vertex models. It is shown that the hard-square gas is a 16-vertex model on the square lattice, and in one of its representations is equivalent to a lattice ramrod model first considered by Nagle (1968). A lattice transformation of the hard-hexagon model generates a special case of the 64-vertex model on the triangular lattice. In these two reductions clear differences between these two hard-core models emerge, and it is probably not surprising that they exhibit quite different critical behaviour. It is also shown that the block-site scaling transformation can be used to provide an alternative computational scheme for obtaining accurate numerical estimates of critical point parameters for these models. The method is illustrated by calculations performed on the hard-square gas.

An expansion for evaluating sensitivity to a random parameter

An uncertain parameter in a linear system is represented as a random variable. Sensitivity of the system is measured in terms of the difference between its output when the parameter has its nominal value, and its output when the parameter has a randomly chosen value. More specifically, the measure is the mean value of the integral squared difference. Given a system described by a linear time-invariant differential equation and an assumed parameter distribution, this measure can be evaluated directly, in closed form. This direct approach is not possible when the system includes a time delay. The latter case could be solved by a Monte Carlo evaluation of the expectation. An alternative computational scheme using orthonormal functions is proposed. This method requires approximate solution of an infinite set of differential equations by solving an associated finite set. Walsh functions are convenient when the parameter distribution is of the truncated variety, which is natural for an uncertain parameter, and they lead to loosely coupled equations which are amenable to the necessary truncation. The significant features of the method are displayed by a simplified example, without time delay, in order to compare this method with the exact evaluation and with a Monte Carlo evaluation.

Letter to the Editor—An Ill-Conceived Proposal for Apportionment of the U.S. House of Representatives

Burt and Harris advocate the use of minimum range for the apportionment of the U.S. House of Representatives. In this note we suggest that (1) their statements on fairness are ill-considered, (2) their statements on uniqueness are misleading, and (3) the computation they suggest is unnecessarily long. Our discussion of (2) and (3) involves the presentation of an alternative computational scheme. In an appendix, we present a formal proof that the alternative computational scheme always works.

Simultaneous Equations

IN the May issue of AIRCRAFT ENGINEERING Captain J. Morris describes a method for the solution of linear algebraic equations by iteration. The main objects of the present note are to show how the statement of the method and the proof of its convergence may be greatly condensed by the use of matrices, and to indicate an alternative computational scheme which involves far less recording of numbers, and therefore less risk of error, than that proposed by Morris.