Quantum Random Walks do not need a Coin Toss

Classical randomized algorithms use a coin toss instruction to explore different evolutionary branches of a problem. Quantum algorithms, on the other hand, can explore multiple evolutionary branches by mere superposition of states. Discrete quantum random walks, studied in the literature, have nonetheless used both superposition and a quantum coin toss instruction. This is not necessary, and a discrete quantum random walk without a quantum coin toss instruction is defined and analyzed here. Our construction eliminates quantum entanglement from the algorithm, and the results match those obtained with a quantum coin toss instruction.Comment: 6 pages, 4 figures, RevTeX (v2) Expanded to include relation to quantum walk with a coin. Connection with Dirac equation pointed out. Version to be published in Phys. Rev.

A structure in the early Universe at z 1.3 that exceeds the homogeneity scale of the R-W concordance cosmology

A Large Quasar Group (LQG) of particularly large size and high membership has been identified in the DR7QSO catalogue of the Sloan Digital Sky Survey. It has characteristic size (volume^1/3) ~ 500 Mpc (proper size, present epoch), longest dimension ~ 1240 Mpc, membership of 73 quasars, and mean redshift = 1.27. In terms of both size and membership it is the most extreme LQG found in the DR7QSO catalogue for the redshift range 1.0 = 1.28, which is itself one of the more extreme examples. Their boundaries approach to within ~ 2 deg (~ 140 Mpc projected). This new, huge LQG appears to be the largest structure currently known in the early universe. Its size suggests incompatibility with the Yadav et al. scale of homogeneity for the concordance cosmology, and thus challenges the assumption of the cosmological principle

Search on a Hypercubic Lattice through a Quantum Random Walk: II. d=2

We investigate the spatial search problem on the two-dimensional square lattice, using the Dirac evolution operator discretised according to the staggered lattice fermion formalism. $d=2$ is the critical dimension for the spatial search problem, where infrared divergence of the evolution operator leads to logarithmic factors in the scaling behaviour. As a result, the construction used in our accompanying article \cite{dgt2search} provides an $O(\sqrt{N}\log N)$ algorithm, which is not optimal. The scaling behaviour can be improved to $O(\sqrt{N\log N})$ by cleverly controlling the massless Dirac evolution operator by an ancilla qubit, as proposed by Tulsi \cite{tulsi}. We reinterpret the ancilla control as introduction of an effective mass at the marked vertex, and optimise the proportionality constants of the scaling behaviour of the algorithm by numerically tuning the parameters.Comment: Revtex4, 5 pages (v2) Introduction and references expanded. Published versio

SARAS 2: A Spectral Radiometer for probing Cosmic Dawn and the Epoch of Reionization through detection of the global 21 cm signal

The global 21 cm signal from Cosmic Dawn (CD) and the Epoch of Reionization (EoR), at redshifts $z \sim 6-30$, probes the nature of first sources of radiation as well as physics of the Inter-Galactic Medium (IGM). Given that the signal is predicted to be extremely weak, of wide fractional bandwidth, and lies in a frequency range that is dominated by Galactic and Extragalactic foregrounds as well as Radio Frequency Interference, detection of the signal is a daunting task. Critical to the experiment is the manner in which the sky signal is represented through the instrument. It is of utmost importance to design a system whose spectral bandpass and additive spurious can be well calibrated and any calibration residual does not mimic the signal. SARAS is an ongoing experiment that aims to detect the global 21 cm signal. Here we present the design philosophy of the SARAS 2 system and discuss its performance and limitations based on laboratory and field measurements. Laboratory tests with the antenna replaced with a variety of terminations, including a network model for the antenna impedance, show that the gain calibration and modeling of internal additives leave no residuals with Fourier amplitudes exceeding 2~mK, or residual Gaussians of 25 MHz width with amplitudes exceeding 2~mK. Thus, even accounting for reflection and radiation efficiency losses in the antenna, the SARAS~2 system is capable of detection of complex 21-cm profiles at the level predicted by currently favoured models for thermal baryon evolution.Comment: 44 pages, 17 figures; comments and suggestions are welcom

Systematic effects from an ambient-temperature, continuously-rotating half-wave plate

We present an evaluation of systematic effects associated with a continuously-rotating, ambient-temperature half-wave plate (HWP) based on two seasons of data from the Atacama B-Mode Search (ABS) experiment located in the Atacama Desert of Chile. The ABS experiment is a microwave telescope sensitive at 145 GHz. Here we present our in-field evaluation of celestial (CMB plus galactic foreground) temperature-to-polarization leakage. We decompose the leakage into scalar, dipole, and quadrupole leakage terms. We report a scalar leakage of ~0.01%, consistent with model expectations and an order of magnitude smaller than other CMB experiments have reported. No significant dipole or quadrupole terms are detected; we constrain each to be <0.07% (95% confidence), limited by statistical uncertainty in our measurement. Dipole and quadrupole leakage at this level lead to systematic error on r<0.01 before any mitigation due to scan cross-linking or boresight rotation. The measured scalar leakage and the theoretical level of dipole and quadrupole leakage produce systematic error of r<0.001 for the ABS survey and focal-plane layout before any data correction such as so-called deprojection. This demonstrates that ABS achieves significant beam systematic error mitigation from its HWP and shows the promise of continuously-rotating HWPs for future experiments.Comment: 11 pages, 8 figures; revision to submitted version, Fig. 5 and Eqs. (14) and (15) corrected; added Fig. 9 and description, text revisions for clarification, Fig. 5 revised for better calibration, corrected labeling errors and plotting bugs in Fig. 3, 4, and Eq. (14) and (15

Characterizing Atacama B-mode Search Detectors with a Half-Wave Plate

The Atacama B-Mode Search (ABS) instrument is a cryogenic ($\sim$10 K) crossed-Dragone telescope located at an elevation of 5190 m in the Atacama Desert in Chile that observed for three seasons between February 2012 and October 2014. ABS observed the Cosmic Microwave Background (CMB) at large angular scales ($40<\ell<500$) to limit the B-mode polarization spectrum around the primordial B-mode peak from inflationary gravity waves at $\ell \sim100$. The ABS focal plane consists of 480 transition-edge sensor (TES) bolometers. They are coupled to orthogonal polarizations from a planar ortho-mode transducer (OMT) and observe at 145 GHz. ABS employs an ambient-temperature, rapidly rotating half-wave plate (HWP) to mitigate systematic effects and move the signal band away from atmospheric $1/f$ noise, allowing for the recovery of large angular scales. We discuss how the signal at the second harmonic of the HWP rotation frequency can be used for data selection and for monitoring the detector responsivities.Comment: 7 pages, 3 figures, conference proceedings submitted to the Journal of Low Temperature Detector

Constrained semi-analytical models of Galactic outflows

We present semi-analytic models of galactic outflows, constrained by available observations on high redshift star formation and reionization. Galactic outflows are modeled in a manner akin to models of stellar wind blown bubbles. Large scale outflows can generically escape from low mass halos (M<10^9 M_sun) for a wide range of model parameters but not from high mass halos (M> 10^{11} M_sun). The gas phase metallicity of the outflow and within the galaxy are computed. Ionization states of different metal species are calculated and used to examine the detectability of metal lines from the outflows. The global influence of galactic outflows is also investigated. Models with only atomic cooled halos significantly fill the IGM at z~3 with metals (with -2.5>[Z/Z_sun]>-3.7), the actual extent depending on the efficiency of winds, the IMF, the fractional mass that goes through star formation and the reionization history of the universe. In these models, a large fraction of outflows at z~3 are supersonic, hot (T> 10^5 K) and have low density, making metal lines difficult to detect. They may also result in significant perturbations in the IGM gas on scales probed by the Lyman-alpha forest. On the contrary, models including molecular cooled halos with a normal mode of star formation can potentially volume fill the universe at z> 8 without drastic dynamic effects on the IGM, thereby setting up a possible metallicity floor (-4.0<[Z/Z_sun]<-3.6). Interestingly, molecular cooled halos with a ``top-heavy'' mode of star formation are not very successful in establishing the metallicity floor because of the additional radiative feedback, that they induce. (Abridged)Comment: 27 pages, 31 figures, 2 tables, pdflatex. Accepted for publication in MNRA

On Exactness Of The Supersymmetric WKB Approximation Scheme

Exactness of the lowest order supersymmetric WKB (SWKB) quantization condition $\int^{x_2}_{x_1} \sqrt{E-\omega^2(x)} dx = n \hbar \pi$, for certain potentials, is examined, using complex integration technique. Comparison of the above scheme with a similar, but {\it exact} quantization condition, $\oint_c p(x,E) dx = 2\pi n \hbar$, originating from the quantum Hamilton-Jacobi formalism reveals that, the locations and the residues of the poles that contribute to these integrals match identically, for both of these cases. As these poles completely determine the eigenvalues in these two cases, the exactness of the SWKB for these potentials is accounted for. Three non-exact cases are also analysed; the origin of this non-exactness is shown to be due the presence of additional singularities in $\sqrt{E-\omega^2(x)}$, like branch cuts in the $x-$plane.Comment: 11 pages, latex, 1 figure available on reques