Applying Grover's algorithm to AES: quantum resource estimates

We present quantum circuits to implement an exhaustive key search for the Advanced Encryption Standard (AES) and analyze the quantum resources required to carry out such an attack. We consider the overall circuit size, the number of qubits, and the circuit depth as measures for the cost of the presented quantum algorithms. Throughout, we focus on Clifford$+T$ gates as the underlying fault-tolerant logical quantum gate set. In particular, for all three variants of AES (key size 128, 192, and 256 bit) that are standardized in FIPS-PUB 197, we establish precise bounds for the number of qubits and the number of elementary logical quantum gates that are needed to implement Grover's quantum algorithm to extract the key from a small number of AES plaintext-ciphertext pairs.Comment: 13 pages, 3 figures, 5 tables; to appear in: Proceedings of the 7th International Conference on Post-Quantum Cryptography (PQCrypto 2016

Supersymmetric Higgs Yukawa Couplings to Bottom Quarks at next-to-next-to-leading Order

The effective bottom Yukawa couplings are analyzed for the minimal supersymmetric extension of the Standard Model at two-loop accuracy within SUSY-QCD. They include the resummation of the dominant corrections for large values of tg(beta). In particular the two-loop SUSY-QCD corrections to the leading SUSY-QCD and top-induced SUSY-electroweak contributions are addressed. The residual theoretical uncertainties range at the per-cent level.Comment: 25 pages, 9 figures, added comments and references, typos corrected, results unchanged, published versio

NLL+NNLO predictions for jet-veto efficiencies in Higgs-boson and Drell-Yan production

Using the technology of the CAESAR approach to resummation, we examine the jet-veto efficiency in Higgs-boson and Drell-Yan production at hadron colliders and show that at next-to-leading logarithmic (NLL) accuracy the resummation reduces to just a Sudakov form factor. Matching with NNLO calculations results in stable predictions for the case of Drell-Yan production, but reveals substantial uncertainties in gluon-fusion Higgs production, connected in part with the poor behaviour of the perturbative series for the total cross section. We compare our results to those from POWHEG with and without reweighting by HqT, as used experimentally, and observe acceptable agreement. In an appendix we derive the part of the NNLL resummation corrections associated with the radius dependence of the jet algorithm.Comment: 30 pages, 8 figures; v2 as published in JHE

Inadequacy of zero-width approximation for a light Higgs boson signal

In the Higgs search at the LHC, a light Higgs boson (115 GeV <~ M_H <~ 130 GeV) is not excluded by experimental data. In this mass range, the width of the Standard Model Higgs boson is more than four orders of magnitude smaller than its mass. The zero-width approximation is hence expected to be an excellent approximation. We show that this is not always the case. The inclusion of off-shell contributions is essential to obtain an accurate Higgs signal normalisation at the 1% precision level. For gg (-> H) -> VV, V= W,Z, O(10%) corrections occur due to an enhanced Higgs signal in the region M_VV > 2 M_V, where also sizable Higgs-continuum interference occurs. We discuss how experimental selection cuts can be used to exclude this region in search channels where the Higgs invariant mass cannot be reconstructed. We note that the H -> VV decay modes in weak boson fusion are similarly affected.Comment: 26 pages, 18 figures, 6 tables; added references, expanded introduction, version to appear in JHE

Heavy Higgs signal-background interference in gg → VV in the Standard Model plus real singlet

For the Standard Model extended with a real scalar singlet field, the modification of the heavy Higgs signal due to interference with the continuum background and the off-shell light Higgs contribution is studied for gg --> ZZ, WW --> 4 lepton processes at the Large Hadron Collider. Interference effects can range from O(10%) to O(1) effects for integrated cross sections. Despite a strong cancellation between the heavy Higgs-continuum and the heavy Higgs-light Higgs interference, the full interference is clearly non-negligible and modifies the heavy Higgs line shape. A |M_VV - M_h2| < Gamma_h2 cut mitigates interference effects to O(10%) or less. A public program that allows to simulate the full interference is presented.Comment: 22 pages, 15 figures, 9 tables; added results and references, improved discussion, corrected v2 results (heavy top approximation was inadvertently active, results deviate by less than 5%), conclusions unchanged, updated gg2VV code, version to appear in EPJ

Analytic Results for Higgs Production in Bottom Fusion

We evaluate analytically the cross section for Higgs production plus one jet through bottom quark fusion. By considering the small pT limit we derive expressions for the resummation coefficients governing the structure of large logarithms, and compare these expressions with those available in the literature.Comment: 14 pages, 7 figure

Predictions for Higgs production at the Tevatron and the associated uncertainties

We update the theoretical predictions for the production cross sections of the Standard Model Higgs boson at the Fermilab Tevatron collider, focusing on the two main search channels, the gluon-gluon fusion mechanism $gg \to H$ and the Higgs-strahlung processes $q \bar q \to VH$ with $V=W/Z$, including all relevant higher order QCD and electroweak corrections in perturbation theory. We then estimate the various uncertainties affecting these predictions: the scale uncertainties which are viewed as a measure of the unknown higher order effects, the uncertainties from the parton distribution functions and the related errors on the strong coupling constant, as well as the uncertainties due to the use of an effective theory approach in the determination of the radiative corrections in the $gg \to H$ process at next-to-next-to-leading order. We find that while the cross sections are well under control in the Higgs--strahlung processes, the theoretical uncertainties are rather large in the case of the gluon-gluon fusion channel, possibly shifting the central values of the next-to-next-to-leading order cross sections by more than $\approx 40$. These uncertainties are thus significantly larger than the $\approx 10$ error assumed by the CDF and D0 experiments in their recent analysis that has excluded the Higgs mass range $M_H=$162-166 GeV at the 95% confidence level. These exclusion limits should be, therefore, reconsidered in the light of these large theoretical uncertainties.Comment: 40 pages, 12 figures. A few typos are corrected and some updated numbers are provide

Foliar water uptake: a common water acquisition strategy for plants of the redwood forest

Evaluations of plant water use in ecosystems around the world reveal a shared capacity by many different species to absorb rain, dew, or fog water directly into their leaves or plant crowns. This mode of water uptake provides an important water subsidy that relieves foliar water stress. Our study provides the first comparative evaluation of foliar uptake capacity among the dominant plant taxa from the coast redwood ecosystem of California where crown-wetting events by summertime fog frequently occur during an otherwise drought-prone season. Previous research demonstrated that the dominant overstory tree species, Sequoia sempervirens, takes up fog water by both its roots (via drip from the crown to the soil) and directly through its leaf surfaces. The present study adds to these early findings and shows that 80% of the dominant species from the redwood forest exhibit this foliar uptake water acquisition strategy. The plants studied include canopy trees, understory ferns, and shrubs. Our results also show that foliar uptake provides direct hydration to leaves, increasing leaf water content by 2–11%. In addition, 60% of redwood forest species investigated demonstrate nocturnal stomatal conductance to water vapor. Such findings indicate that even species unable to absorb water directly into their foliage may still receive indirect benefits from nocturnal leaf wetting through suppressed transpiration. For these species, leaf-wetting events enhance the efficacy of nighttime re-equilibration with available soil water and therefore also increase pre-dawn leaf water potentials

Bayesian estimates of linkage disequilibrium

[Background] The maximum likelihood estimator of D' – a standard measure of linkage disequilibrium – is biased toward disequilibrium, and the bias is particularly evident in small samples and rare haplotypes. [Results] This paper proposes a Bayesian estimation of D' to address this problem. The reduction of the bias is achieved by using a prior distribution on the pair-wise associations between single nucleotide polymorphisms (SNP)s that increases the likelihood of equilibrium with increasing physical distances between pairs of SNPs. We show how to compute the Bayesian estimate using a stochastic estimation based on MCMC methods, and also propose a numerical approximation to the Bayesian estimates that can be used to estimate patterns of LD in large datasets of SNPs. [Conclusion] Our Bayesian estimator of D' corrects the bias toward disequilibrium that affects the maximum likelihood estimator. A consequence of this feature is a more objective view about the extent of linkage disequilibrium in the human genome, and a more realistic number of tagging SNPs to fully exploit the power of genome wide association studies.Research supported by NIH/NHLBI grant R21 HL080463-01, NIH/NIDDK 1R01DK069646-01A1 and the Spanish research program [projects TIN2004-06204-C03-02 and TIN2005-02516]

Composite Higgs Boson Pair Production at the LHC

The measurement of the trilinear and quartic Higgs self-couplings is necessary for the reconstruction of the Higgs potential. This way the Higgs mechanism as the origin of electroweak symmetry breaking can be tested. The couplings are accessible in multi-Higgs production processes at the LHC. In this paper we investigate the prospects of measuring the trilinear Higgs coupling in composite Higgs models. In these models, the Higgs boson emerges as a pseudo-Goldstone boson of a strongly interacting sector, and the Higgs potential is generated by loops of the Standard Model (SM) gauge bosons and fermions. The Higgs self-couplings are modified compared to the SM and controlled by the compositeness parameter $\xi$ in addition to the Higgs boson mass. We construct areas of sensitivity to the trilinear Higgs coupling in the relevant parameter space for various final states