The quantum path kernel: A generalized quantum neural tangent kernel for deep quantum machine learning

Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. A key issue is how to address the inherent non-linearity of classical deep learning, a problem in the quantum domain due to the fact that the composition of an arbitrary number of quantum gates, consisting of a series of sequential unitary transformations, is intrinsically linear. This problem has been variously approached in the literature, principally via the introduction of measurements between layers of unitary transformations. In this paper, we introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning typically associated with superior generalization performance in the classical domain, specifically, hierarchical feature learning. Our approach generalizes the notion of Quantum Neural Tangent Kernel, which has been used to study the dynamics of classical and quantum machine learning models. The Quantum Path Kernel exploits the parameter trajectory, i.e. the curve delineated by model parameters as they evolve during training, enabling the representation of differential layer-wise convergence behaviors, or the formation of hierarchical parametric dependencies, in terms of their manifestation in the gradient space of the predictor function. We evaluate our approach with respect to variants of the classification of Gaussian XOR mixtures - an artificial but emblematic problem that intrinsically requires multilevel learning in order to achieve optimal class separation

The quantum path kernel: A generalized neural tangent kernel for deep quantum machine learning

Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. A key issue is how to address the inherent non-linearity of classical deep learning, a problem in the quantum domain due to the fact that the composition of an arbitrary number of quantum gates, consisting of a series of sequential unitary transformations, is intrinsically linear. This problem has been variously approached in the literature, principally via the introduction of measurements between layers of unitary transformations. In this paper, we introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning typically associated with superior generalization performance in the classical domain, specifically, hierarchical feature learning. Our approach generalizes the notion of Quantum Neural Tangent Kernel, which has been used to study the dynamics of classical and quantum machine learning models. The Quantum Path Kernel exploits the parameter trajectory, i.e. the curve delineated by model parameters as they evolve during training, enabling the representation of differential layer-wise convergence behaviors, or the formation of hierarchical parametric dependencies, in terms of their manifestation in the gradient space of the predictor function.We evaluate our approach with respect to variants of the classification of Gaussian XOR mixtures - an artificial but emblematic problem that intrinsically requires multilevel learning in order to achieve optimal class separation

GeantV: Results from the prototype of concurrent vector particle transport simulation in HEP

Full detector simulation was among the largest CPU consumer in all CERN experiment software stacks for the first two runs of the Large Hadron Collider (LHC). In the early 2010's, the projections were that simulation demands would scale linearly with luminosity increase, compensated only partially by an increase of computing resources. The extension of fast simulation approaches to more use cases, covering a larger fraction of the simulation budget, is only part of the solution due to intrinsic precision limitations. The remainder corresponds to speeding-up the simulation software by several factors, which is out of reach using simple optimizations on the current code base. In this context, the GeantV R&D project was launched, aiming to redesign the legacy particle transport codes in order to make them benefit from fine-grained parallelism features such as vectorization, but also from increased code and data locality. This paper presents extensively the results and achievements of this R&D, as well as the conclusions and lessons learnt from the beta prototype.Comment: 34 pages, 26 figures, 24 table

Search for non-relativistic Magnetic Monopoles with IceCube

The IceCube Neutrino Observatory is a large Cherenkov detector instrumenting $1\,\mathrm{km}^3$ of Antarctic ice. The detector can be used to search for signatures of particle physics beyond the Standard Model. Here, we describe the search for non-relativistic, magnetic monopoles as remnants of the GUT (Grand Unified Theory) era shortly after the Big Bang. These monopoles may catalyze the decay of nucleons via the Rubakov-Callan effect with a cross section suggested to be in the range of $10^{-27}\,\mathrm{cm^2}$ to $10^{-21}\,\mathrm{cm^2}$. In IceCube, the Cherenkov light from nucleon decays along the monopole trajectory would produce a characteristic hit pattern. This paper presents the results of an analysis of first data taken from May 2011 until May 2012 with a dedicated slow-particle trigger for DeepCore, a subdetector of IceCube. A second analysis provides better sensitivity for the brightest non-relativistic monopoles using data taken from May 2009 until May 2010. In both analyses no monopole signal was observed. For catalysis cross sections of $10^{-22}\,(10^{-24})\,\mathrm{cm^2}$ the flux of non-relativistic GUT monopoles is constrained up to a level of $\Phi_{90} \le 10^{-18}\,(10^{-17})\,\mathrm{cm^{-2}s^{-1}sr^{-1}}$ at a 90% confidence level, which is three orders of magnitude below the Parker bound. The limits assume a dominant decay of the proton into a positron and a neutral pion. These results improve the current best experimental limits by one to two orders of magnitude, for a wide range of assumed speeds and catalysis cross sections.Comment: 20 pages, 20 figure

Search for the Higgs boson in events with missing transverse energy and b quark jets produced in proton-antiproton collisions at s**(1/2)=1.96 TeV

We search for the standard model Higgs boson produced in association with an electroweak vector boson in events with no identified charged leptons, large imbalance in transverse momentum, and two jets where at least one contains a secondary vertex consistent with the decay of b hadrons. We use ~1 fb-1 integrated luminosity of proton-antiproton collisions at s**(1/2)=1.96 TeV recorded by the CDF II experiment at the Tevatron. We find 268 (16) single (double) b-tagged candidate events, where 248 +/- 43 (14.4 +/- 2.7) are expected from standard model background processes. We place 95% confidence level upper limits on the Higgs boson production cross section for several Higgs boson masses ranging from 110 GeV/c2 to 140 GeV/c2. For a mass of 115 GeV/c2 the observed (expected) limit is 20.4 (14.2) times the standard model prediction.Comment: 8 pages, 2 figures, submitted to Phys. Rev. Let

Search for a High-Mass Diphoton State and Limits on Randall-Sundrum Gravitons at CDF

We have performed a search for new particles which decay to two photons using 1.2/fb of integrated luminosity from p-pbar collisions at sqrt(s) = 1.96 TeV collected using the CDF II Detector at the Fermilab Tevatron. We find the diphoton mass spectrum to be in agreement with the standard model expectation, and set limits on the cross section times branching ratio for the Randall-Sundrum graviton, as a function of diphoton mass. We subsequently derive lower limits for the graviton mass of 230 GeV/c2 and 850 GeV/c2, at the 95% confidence level, for coupling parameters (k/M_Pl) of 0.01 and 0.1 respectively.Comment: submitted to Phys. Rev. Let

Measurement of the Helicity Fractions of W Bosons from Top Quark Decays Using Fully Reconstructed top-antitop Events with CDF II

We present a measurement of the fractions F_0 and F_+ of longitudinally polarized and right-handed W bosons in top quark decays using data collected with the CDF II detector. The data set used in the analysis corresponds to an integrated luminosity of approximately 318 pb -1. We select ttbar candidate events with one lepton, at least four jets, and missing transverse energy. Our helicity measurement uses the decay angle theta*, which is defined as the angle between the momentum of the charged lepton in the W boson rest frame and the W momentum in the top quark rest frame. The cos(theta*) distribution in the data is determined by full kinematic reconstruction of the ttbar candidates. We find F_0 = 0.85 +0.15 -0.22 (stat) +- 0.06 (syst) and F_+ = 0.05 +0.11 -0.05 (stat) +- 0.03 (syst), which is consistent with the standard model prediction. We set an upper limit on the fraction of right-handed W bosons of F_+ < 0.26 at the 95% confidence level.Comment: 11 pages, 2 figures, submitted to Phys. Rev.

Top quark mass measurement using the template method at CDF

We present a measurement of the top quark mass in the lepton+jets and dilepton channels of $t\bar{t}$ decays using the template method. The data sample corresponds to an integrated luminosity of 5.6 fb$^{-1}$ of $p\bar{p}$ collisions at Tevatron with $\sqrt{s}=1.96$ TeV, collected with the CDF II detector. The measurement is performed by constructing templates of three kinematic variables in the lepton+jets and two kinematic variables in the dilepton channel. The variables are two reconstructed top quark masses from different jets-to-quarks combinations and the invariant mass of two jets from the $W$ decay in the lepton+jets channel, and a reconstructed top quark mass and $m_{T2}$, a variable related to the transverse mass in events with two missing particles, in the dilepton channel. The simultaneous fit of the templates from signal and background events in the lepton+jets and dilepton channels to the data yields a measured top quark mass of $M_{top} = 172.1 \pm 1.1(stat) \pm 0.9(syst).$Comment: submitted to Phys. Rev.

Measurement of the Inclusive Jet Cross Section in ppbar Interactions at sqrt{s}=1.96 TeV Using a Cone-based Jet Algorithm

We present a measurement of the inclusive jet cross section in ppbar interactions at sqrt{s}=1.96 TeV using 385 pb^{-1} of data collected with the CDF II detector at the Fermilab Tevatron. The results are obtained using an improved cone-based jet algorithm (Midpoint). The data cover the jet transverse momentum range from 61 to 620 GeV/c, extending the reach by almost 150 GeV/c compared with previous measurements at the Tevatron. The results are in good agreement with next-to-leading order perturbative QCD predictions using the CTEQ6.1M parton distribution functions.Comment: 19 pages, 2 figures, 1 tabl

Measurement of the ttbar Production Cross Section in ppbar Collisions at sqrt(s) = 1.96 TeV

We present a measurement of the top quark pair production cross section in ppbar collisions at sqrt(s)=1.96 TeV using 318 pb^{-1} of data collected with the Collider Detector at Fermilab. We select ttbar decays into the final states e nu + jets and mu nu + jets, in which at least one b quark from the t-quark decays is identified using a secondary vertex-finding algorithm. Assuming a top quark mass of 178 GeV/c^2, we measure a cross section of 8.7 +-0.9 (stat) +1.1-0.9 (syst) pb. We also report the first observation of ttbar with significance greater than 5 sigma in the subsample in which both b quarks are identified, corresponding to a cross section of 10.1 +1.6-1.4(stat)+2.0-1.3 (syst) pb.Comment: Accepted for publication in Physics Review Letters, 7 page