The effect of noise correlations on randomized benchmarking

Among the most popular and well studied quantum characterization, verification and validation techniques is randomized benchmarking (RB), an important statistical tool used to characterize the performance of physical logic operations useful in quantum information processing. In this work we provide a detailed mathematical treatment of the effect of temporal noise correlations on the outcomes of RB protocols. We provide a fully analytic framework capturing the accumulation of error in RB expressed in terms of a three-dimensional random walk in "Pauli space." Using this framework we derive the probability density function describing RB outcomes (averaged over noise) for both Markovian and correlated errors, which we show is generally described by a gamma distribution with shape and scale parameters depending on the correlation structure. Long temporal correlations impart large nonvanishing variance and skew in the distribution towards high-fidelity outcomes -- consistent with existing experimental data -- highlighting potential finite-sampling pitfalls and the divergence of the mean RB outcome from worst-case errors in the presence of noise correlations. We use the Filter-transfer function formalism to reveal the underlying reason for these differences in terms of effective coherent averaging of correlated errors in certain random sequences. We conclude by commenting on the impact of these calculations on the utility of single-metric approaches to quantum characterization, verification, and validation.Comment: Updated and expanded to include full derivation. Related papers available from http://www.physics.usyd.edu.au/~mbiercuk/Publications.htm

Patterns, causes, and consequences of marine larval dispersal

Quantifying the probability of larval exchange among marine populations is key to predicting local population dynamics and optimizing networks of marine protected areas. The pattern of connectivity among populations can be described by the measurement of a dispersal kernel. However, a statistically robust, empirical dispersal kernel has been lacking for any marine species. Here, we use genetic parentage analysis to quantify a dispersal kernel for the reef fish Elacatinus lori, demonstrating that dispersal declines exponentially with distance. The spatial scale of dispersal is an order of magnitude less than previous estimates—the median dispersal distance is just 1.7 km and no dispersal events exceed 16.4 km despite intensive sampling out to 30 km from source. Overlaid on this strong pattern is subtle spatial variation, but neither pelagic larval duration nor direction is associated with the probability of successful dispersal. Given the strong relationship between distance and dispersal, we show that distance-driven logistic models have strong power to predict dispersal probabilities. Moreover, connectivity matrices generated from these models are congruent with empirical estimates of spatial genetic structure, suggesting that the pattern of dispersal we uncovered reflects long-term patterns of gene flow. These results challenge assumptions regarding the spatial scale and presumed predictors of marine population connectivity. We conclude that if marine reserve networks aim to connect whole communities of fishes and conserve biodiversity broadly, then reserves that are close in space (<10 km) will accommodate those members of the community that are short-distance dispersers.We thank Diana Acosta, Alben David, Kevin David, Alissa Rickborn, and Derek Scolaro for assistance with field work; Eliana Bondra for assistance with molecular work; and Peter Carlson for assistance with otolith work. We are grateful to Noel Anderson, David Lindo, Claire Paris, Robert Warner, Colleen Webb, and two anonymous reviewers for comments on this manuscript. This work was supported by National Science Foundation (NSF) Grant OCE-1260424, and C.C.D. was supported by NSF Graduate Research Fellowship DGE-1247312. All work was approved by Belize Fisheries and Boston University Institutional Animal Care and Use Committee. (OCE-1260424 - National Science Foundation (NSF); DGE-1247312 - NSF Graduate Research Fellowship)Published versio

Matching concepts across HOL libraries

Many proof assistant libraries contain formalizations of the same mathematical concepts. The concepts are often introduced (defined) in different ways, but the properties that they have, and are in turn formalized, are the same. For the basic concepts, like natural numbers, matching them between libraries is often straightforward, because of mathematical naming conventions. However, for more advanced concepts, finding similar formalizations in different libraries is a non-trivial task even for an expert. In this paper we investigate automatic discovery of similar concepts across libraries of proof assistants. We propose an approach for normalizing properties of concepts in formal libraries and a number of similarity measures. We evaluate the approach on HOL based proof assistants HOL4, HOL Light and Isabelle/HOL, discovering 398 pairs of isomorphic constants and types

Energy dependence on fractional charge for strongly interacting subsystems

The energies of a pair of strongly-interacting subsystems with arbitrary noninteger charges are examined from closed and open system perspectives. An ensemble representation of the charge dependence is derived, valid at all interaction strengths. Transforming from resonance-state ionicity to ensemble charge dependence imposes physical constraints on the occupation numbers in the strong-interaction limit. For open systems, the chemical potential is evaluated using microscopic and thermodynamic models, leading to a novel correlation between ground-state charge and an electronic temperature.Comment: 4 pages, 3 figs.; as accepted (Phys. Rev. Lett.

Properties of Pt Schottky Type Contacts On High-Resistivity CdZnTe Detectors

In this paper we present studies of the I-V characteristics of CdZnTe detectors with Pt contacts fabricated from high-resistivity single crystals grown by the high-pressure Brigman process. We have analyzed the experimental I-V curves using a model that approximates the CZT detector as a system consisting of a reversed Schottky contact in series with the bulk resistance. Least square fits to the experimental data yield 0.78-0.79 eV for the Pt-CZT Schottky barrier height, and <20 V for the voltage required to deplete a 2 mm thick CZT detector. We demonstrate that at high bias the thermionic current over the Schottky barrier, the height of which is reduced due to an interfacial layer between the contact and CZT material, controls the leakage current of the detectors. In many cases the dark current is not determined by the resistivity of the bulk material, but rather the properties of the contacts; namely by the interfacial layer between the contact and CZT material.Comment: 12 pages, 11 figure

Gravitational waves from first order phase transitions during inflation

We study the production, spectrum and detectability of gravitational waves in models of the early Universe where first order phase transitions occur during inflation. We consider all relevant sources. The self-consistency of the scenario strongly affects the features of the waves. The spectrum appears to be mainly sourced by collisions of bubble of the new phases, while plasma dynamics (turbulence) and the primordial gauge fields connected to the physics of the transitions are generally subdominant. The amplitude and frequency dependence of the spectrum for modes that exit the horizon during inflation are different from those of the waves produced by quantum vacuum oscillations of the metric or by first order phase transitions not occurring during inflation. A moderate number of slow (but still successful) phase transitions can leave detectable marks in the CMBR, but the signal weakens rapidly for faster transitions. When the number of phase transitions is instead large, the primordial gravitational waves can be observed both in the CMBR or with LISA (marginally) and especially DECIGO. We also discuss the nucleosynthesis bound and the constraints it places on the parameters of the models.Comment: minor changes in the text and the references to match the published versio

Mechanism of Lysine 48 Selectivity during Polyubiquitin Chain Formation by the Ube2R1/2 Ubiquitin-Conjugating Enzyme

Lysine selectivity is of critical importance during polyubiquitin chain formation because the identity of the lysine controls the biological outcome. Ubiquitins are covalently linked in polyubiquitin chains through one of seven lysine residues on its surface and the C terminus of adjacent protomers. Lys 48-linked polyubiquitin chains signal for protein degradation; however, the structural basis for Lys 48 selectivity remains largely unknown. The ubiquitin-conjugating enzyme Ube2R1/2 has exquisite specificity for Lys 48, and computational docking of Ube2R1/2 and ubiquitin predicts that Lys 48 is guided to the active site through a key electrostatic interaction between Arg 54 on ubiquitin and Asp 143 on Ube2R1/2. The validity of this interaction was confirmed through biochemical experiments. Since structural examples involving Arg 54 in protein-ubiquitin complexes are exceedingly rare, these results provide additional insight into how ubiquitin-protein complexes can be stabilized. We discuss how these findings relate to how other ubiquitin-conjugating enzymes direct the lysine specificity of polyubiquitin chains

Mechanism of Lysine 48 Selectivity during Polyubiquitin Chain Formation by the Ube2R1/2 Ubiquitin-Conjugating Enzyme

Lysine selectivity is of critical importance during polyubiquitin chain formation because the identity of the lysine controls the biological outcome. Ubiquitins are covalently linked in polyubiquitin chains through one of seven lysine residues on its surface and the C terminus of adjacent protomers. Lys 48-linked polyubiquitin chains signal for protein degradation; however, the structural basis for Lys 48 selectivity remains largely unknown. The ubiquitin-conjugating enzyme Ube2R1/2 has exquisite specificity for Lys 48, and computational docking of Ube2R1/2 and ubiquitin predicts that Lys 48 is guided to the active site through a key electrostatic interaction between Arg 54 on ubiquitin and Asp 143 on Ube2R1/2. The validity of this interaction was confirmed through biochemical experiments. Since structural examples involving Arg 54 in protein-ubiquitin complexes are exceedingly rare, these results provide additional insight into how ubiquitin-protein complexes can be stabilized. We discuss how these findings relate to how other ubiquitin-conjugating enzymes direct the lysine specificity of polyubiquitin chains

Phase-resolved NuSTAR and Swift-XRT Observations of Magnetar 4U 0142+61

We present temporal and spectral analysis of simultaneous 0.5-79 keV Swift-XRT and NuSTAR observations of the magnetar 4U 0142+61. The pulse profile changes significantly with photon energy between 3 and 35 keV. The pulse fraction increases with energy, reaching a value of ~20%, similar to that observed in 1E 1841-045 and much lower than the ~80% pulse fraction observed in 1E 2259+586. We do not detect the 55-ks phase modulation reported in previous Suzaku-HXD observations. The phase-averaged spectrum of 4U 0142+61 above 20 keV is dominated by a hard power law with a photon index, $\Gamma$ ~ 0.65, and the spectrum below 20 keV can be described by two blackbodies, a blackbody plus a soft power law, or by a Comptonized blackbody model. We study the full phase-resolved spectra using the electron-positron outflow model of Beloborodov (2013). Our results are consistent with the parameters of the active j-bundle derived from INTEGRAL data by Hascoet et al. (2014). We find that a significant degeneracy appears in the inferred parameters if the footprint of the j-bundle is allowed to be a thin ring instead of a polar cap. The degeneracy is reduced when the footprint is required to be the hot spot inferred from the soft X-ray data.Comment: 14 pages, 8 figures, 4 tables. Accepted for publication in Ap