Noise in Grover's Quantum Search Algorithm

Grover's quantum algorithm improves any classical search algorithm. We show how random Gaussian noise at each step of the algorithm can be modelled easily because of the exact recursion formulas available for computing the quantum amplitude in Grover's algorithm. We study the algorithm's intrinsic robustness when no quantum correction codes are used, and evaluate how much noise the algorithm can bear with, in terms of the size of the phone book and a desired probability of finding the correct result. The algorithm loses efficiency when noise is added, but does not slow down. We also study the maximal noise under which the iterated quantum algorithm is just as slow as the classical algorithm. In all cases, the width of the allowed noise scales with the size of the phone book as N^-2/3.Comment: 17 pages, 2 eps figures. Revised version. To be published in PRA, December 199

Effects of Noisy Oracle on Search Algorithm Complexity

Grover's algorithm provides a quadratic speed-up over classical algorithms for unstructured database or library searches. This paper examines the robustness of Grover's search algorithm to a random phase error in the oracle and analyzes the complexity of the search process as a function of the scaling of the oracle error with database or library size. Both the discrete- and continuous-time implementations of the search algorithm are investigated. It is shown that unless the oracle phase error scales as O(N^(-1/4)), neither the discrete- nor the continuous-time implementation of Grover's algorithm is scalably robust to this error in the absence of error correction.Comment: 16 pages, 4 figures, submitted to Phys. Rev.

Implementation of quantum search algorithm using classical Fourier optics

We report on an experiment on Grover's quantum search algorithm showing that {\em classical waves} can search a $N$-item database as efficiently as quantum mechanics can. The transverse beam profile of a short laser pulse is processed iteratively as the pulse bounces back and forth between two mirrors. We directly observe the sought item being found in $\sim\sqrt{N}$ iterations, in the form of a growing intensity peak on this profile. Although the lack of quantum entanglement limits the {\em size} of our database, our results show that entanglement is neither necessary for the algorithm itself, nor for its efficiency.Comment: 4 pages, 3 figures; minor revisions plus extra referenc

Noise effects in the quantum search algorithm from the computational complexity point of view

We analyse the resilience of the quantum search algorithm in the presence of quantum noise modelled as trace preserving completely positive maps. We study the influence of noise on computational complexity of the quantum search algorithm. We show that only for small amounts of noise the quantum search algorithm is still more efficient than any classical algorithm.Comment: 7 pages, 2 figure

Explaining Cold-Pulse Dynamics in Tokamak Plasmas Using Local Turbulent Transport Models

A long-standing enigma in plasma transport has been resolved by modeling of cold-pulse experiments conducted on the Alcator C-Mod tokamak. Controlled edge cooling of fusion plasmas triggers core electron heating on time scales faster than an energy confinement time, which has long been interpreted as strong evidence of nonlocal transport. This Letter shows that the steady-state profiles, the cold-pulse rise time, and disappearance at higher density as measured in these experiments are successfully captured by a recent local quasilinear turbulent transport model, demonstrating that the existence of nonlocal transport phenomena is not necessary for explaining the behavior and time scales of cold-pulse experiments in tokamak plasmas.United States. Department of Energy (Award DE-FC02-99ER54512)United States. Department of Energy (Grant DESC0014264

Probing the earliest phases in the formation of massive galaxies with simulated HST+JWST imaging data from Illustris

We use the Illustris-1 simulation to explore the capabilities of the $\textit{Hubble}$ and $\textit{James Webb Space Telescope}$ data to analyze the stellar populations in high-redshift galaxies, taking advantage of the combined depth, spatial resolution, and wavelength coverage. For that purpose, we use simulated broad-band ACS, WFC3 and NIRCam data and 2-dimensional stellar population synthesis (2D-SPS) to derive the integrated star formation history (SFH) of massive (M$_{\ast}>10^{10}\,$M$_{\odot}$) simulated galaxies at $110^{11}\,$M$_{\odot}$ galaxy. In particular, we explore the potential of HST and JWST datasets reaching a depth similar to those of the CANDELS and ongoing CEERS observations, respectively, and concentrate on determining the capabilities of this dataset for characterizing the first episodes in the SFH of local M$_{\ast}>10^{11}\,$M$_{\odot}$ galaxies by studying their progenitors at $z>1$. The 2D-SPS method presented in this paper has been calibrated to robustly recover the cosmic times when the first star formation episodes occurred in massive galaxies, i.e., the first stages in their integrated SFHs. In particular, we discuss the times when the first 1% to 50% of their total stellar mass formed in the simulation. We demonstrate that we can recover these ages with typical median systematic offset of less than 5% and scatter around 20%-30%. According to our measurements on Illustris data, we are able to recover that local M$_{\ast}>10^{11}\,$M$_{\odot}$ galaxies would have started their formation by $z=16$, forming the first 5% of their stellar mass present at $z \sim 1$ by $z=4.5$, 10% by $z=3.7$, and 25% by $z=2.7$.Comment: 28 pages, 13 figures, 4 tables. ApJ in press. Summary of changes from original submission: the major change is that we now include in Sec. 6 the comparison of the results obtained for our sample of massive 1 < z < 4 progenitors with those obtained by considering all massive galaxies at 1 < z < 4 in the simulated images. Several figures and sections have been update

FAK acts as a suppressor of RTK-MAP kinase signalling in Drosophila melanogaster epithelia and human cancer cells

Receptor Tyrosine Kinases (RTKs) and Focal Adhesion Kinase (FAK) regulate multiple signalling pathways, including mitogen-activated protein (MAP) kinase pathway. FAK interacts with several RTKs but little is known about how FAK regulates their downstream signalling. Here we investigated how FAK regulates signalling resulting from the overexpression of the RTKs RET and EGFR. FAK suppressed RTKs signalling in Drosophila melanogaster epithelia by impairing MAPK pathway. This regulation was also observed in MDA-MB-231 human breast cancer cells, suggesting it is a conserved phenomenon in humans. Mechanistically, FAK reduced receptor recycling into the plasma membrane, which resulted in lower MAPK activation. Conversely, increasing the membrane pool of the receptor increased MAPK pathway signalling. FAK is widely considered as a therapeutic target in cancer biology; however, it also has tumour suppressor properties in some contexts. Therefore, the FAK-mediated negative regulation of RTK/MAPK signalling described here may have potential implications in the designing of therapy strategies for RTK-driven tumours

Characterizing the Average Interstellar Medium Conditions of Galaxies at z∼z\sim 5.6-9 with UV and Optical Nebular Lines

Ultraviolet (UV; rest-frame $\sim1200-2000$ A) spectra provide a wealth of diagnostics to characterize fundamental galaxy properties, such as their chemical enrichment, the nature of their stellar populations, and their amount of Lyman-continuum (LyC) radiation. In this work, we leverage publicly released JWST data to construct the rest-frame UV-to-optical composite spectrum of a sample of 63 galaxies at $5.6<z<9$, spanning the wavelength range from 1500 to 5200 A. Based on the composite spectrum, we derive an average dust attenuation $E(B-V)_\mathrm{gas}=0.16^{+0.10}_{-0.11}$ from \hb/\hg, electron density $n_e = 570^{+510}_{-290}$ cm$^{-3}$ from the [O II] doublet ratio, electron temperature $T_e = 17000^{+1500}_{-1500}$ K from the [O III] $\lambda4363$/ [O III] $\lambda5007$ ratio, and an ionization parameter $\log(U)=-2.18^{+0.03}_{-0.03}$ from the [O III]/[O II] ratio. Using a direct $T_e$ method, we calculate an oxygen abundance $12+\log\mathrm{(O/H)}=7.67\pm0.08$ and the carbon-to-oxygen (C/O) abundance ratio $\log\mathrm{(C/O)}=-0.87^{+0.13}_{-0.10}$. This C/O ratio is smaller than compared to $z=0$ and $z=2$ - 4 star-forming galaxies, albeit with moderate significance. This indicates the reionization-era galaxies might be undergoing a rapid build-up of stellar mass with high specific star-formation rates. A UV diagnostic based on the ratios of C III] $\lambda\lambda1907,1909$/He II $\lambda1640$ versus O III] $\lambda1666$/He II $\lambda1640$ suggests that the star formation is the dominant source of ionization, similar to the local extreme dwarf galaxies and $z\sim2$ - 4 He II-detected galaxies. The [O III]/[O II] and C IV/C III] ratios of the composite spectrum are marginally larger than the criteria used to select galaxies as LyC leakers, suggesting that some of the galaxies in our sample are strong contributors to the reionizing radiation.Comment: 21 pages, 7 figures, 4 tables. Submitted. Comments are welcom

NGDEEP Epoch 1: Spatially Resolved Hα\alpha Observations of Disk and Bulge Growth in Star-Forming Galaxies at z∼z \sim 0.6-2.2 from JWST NIRISS Slitless Spectroscopy

We study the H$\alpha$ equivalent width, EW(H$\alpha$), maps of 19 galaxies at $0.6 < z < 2.2$ in the Hubble Ultra Deep Field (HUDF) derived from NIRISS slitless spectroscopy as part of the Next Generation Deep Extragalactic Exploratory Public (NGDEEP) Survey. Our galaxies mostly lie on the star-formation main sequence with a stellar mass range of $\mathrm{10^9 - 10^{11} M_\odot}$, and are therefore characteristic of "typical" star-forming galaxies at these redshifts. Leveraging deep HST and JWST broad-band images, spanning 0.4-4 $\mu$m, we perform spatially-resolved fitting of the spectral energy distributions (SEDs) for these galaxies and construct specific star formation rate (sSFR) and stellar-mass-weighted age maps. We compare these to the EW(H$\alpha$) maps with a spatial resolution of $\sim$1 kpc. The pixel-to-pixel EW(H$\alpha$) increases with increasing sSFR and with decreasing age, with the average trend slightly different from the relations derived from integrated fluxes of galaxies from the literature. Quantifying the radial profiles of EW(H$\alpha$), sSFR, and age, the majority (84%) of galaxies show positive EW(H$\alpha$) gradients, positive sSFR gradients, and negative age gradients, in line with the the inside-out quenching scenario. A few galaxies (16%) show inverse (and flat) trends possibly due to merging or starbursts. Comparing the distributions of EW(H$\alpha$) and sSFR to the star formation history models as a function of galactocentric radius, the central region of galaxies (e.g., their bulges) have experienced, at least one, rapid star-formation episodes, which leads to the formation of bulge, while their outer regions (e.g., disks) grow in a more steady-state. These results demonstrate the ability to study resolved star formation in distant galaxies with JWST NIRISS.Comment: 22 pages, 11 figure