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In order to solve problems of practical importance, quantum computers will likely need to incorporate quantum error correction, where a logical qubit is redundantly encoded in many noisy physical qubits. The large physical-qubit overhead typically associated with error correction motivates the search for more hardware-efficient approaches. Here, using a microfabricated superconducting quantum circuit, we realize a logical qubit memory formed from the concatenation of encoded bosonic cat qubits with an outer repetition code of distance $d=5$. The bosonic cat qubits are passively protected against bit flips using a stabilizing circuit. Cat-qubit phase-flip errors are corrected by the repetition code which uses ancilla transmons for syndrome measurement. We realize a noise-biased CX gate which ensures bit-flip error suppression is maintained during error correction. We study the performance and scaling of the logical qubit memory, finding that the phase-flip correcting repetition code operates below threshold, with logical phase-flip error decreasing with code distance from $d=3$ to $d=5$. Concurrently, the logical bit-flip error is suppressed with increasing cat-qubit mean photon number. The minimum measured logical error per cycle is on average $1.75(2)\%$ for the distance-3 code sections, and $1.65(3)\%$ for the longer distance-5 code, demonstrating the effectiveness of bit-flip error suppression throughout the error correction cycle. These results, where the intrinsic error suppression of the bosonic encodings allows us to use a hardware-efficient outer error correcting code, indicate that concatenated bosonic codes are a compelling paradigm for reaching fault-tolerant quantum computation., Comment: Comments on the manuscript welcome!

The study of 3D magnetic nanostructures has uncovered a range of rich phenomena including the stabilization and control of topological spin textures using nanoscale curvature, dynamic effects allowing controlled spin-wave emission, and novel ground states enabled by collective 3D frustrated interactions. From a technological perspective, 3D nanostructures offer routes to ultrahigh density data storage, massive interconnectivity within neuromorphic devices, as well as applications within health technologies, such as mechanical induction of stem cell differentiation. However, the fabrication of 3D nanomagnetic systems with feature sizes down to 10 nm poses a significant challenge. In this work we present a means of fabricating sub-100 nm 3D ferromagnetic nanowires, with both cross-sectional and longitudinal curvature, using two-photon lithography at a wavelength of 405 nm, combined with conventional deposition. Physical characterization illustrates that nanostructures with lateral features as low as 70 nm can be rapidly and reproducibly fabricated. A range of novel domain walls, with anti-vortex textures, coupled transverse textures, and hybrid vortex/anti-vortex textures are found to be enabled by the cross-sectional curvature of the system, as demonstrated by finite-element micromagnetic simulations. Magnetic force microscopy experiments in an externally applied magnetic field are used to image the injection and pinning of domain walls in the 3D magnetic nanowire. At specific field values, domain walls are observed to hop from trap to trap, providing a direct means to probe the local energy landscape. A simple model is presented demonstrating that thickness gradients and local roughness dictate the variation of pinning probability across the wire.

Quantum error correction with erasure qubits promises significant advantages over standard error correction due to favorable thresholds for erasure errors. To realize this advantage in practice requires a qubit for which nearly all errors are such erasure errors, and the ability to check for erasure errors without dephasing the qubit. We demonstrate that a "dual-rail qubit" consisting of a pair of resonantly coupled transmons can form a highly coherent erasure qubit, where transmon $T_1$ errors are converted into erasure errors and residual dephasing is strongly suppressed, leading to millisecond-scale coherence within the qubit subspace. We show that single-qubit gates are limited primarily by erasure errors, with erasure probability $p_\text{erasure} = 2.19(2)\times 10^{-3}$ per gate while the residual errors are $\sim 40$ times lower. We further demonstrate mid-circuit detection of erasure errors while introducing $< 0.1\%$ dephasing error per check. Finally, we show that the suppression of transmon noise allows this dual-rail qubit to preserve high coherence over a broad tunable operating range, offering an improved capacity to avoid frequency collisions. This work establishes transmon-based dual-rail qubits as an attractive building block for hardware-efficient quantum error correction., Comment: 9+13 pages, 16 figures

The DFN (Doyle-Fuller-Newman) model is well know for being accurate and computationally expensive. In situations where temperature gradients are important (eg fast charging) it is desirable to couple the temperature dynamics within a battery into the DFN model. This leads to even greater computational complexity. Inspired by the work of Marquis et al [1] we present the derivation of a reduced-order model based on the DFN model with temperature in the macroscale. The complexity of the reduced-order model is characterised by the local temperature plus one internal electro-chemical dimension and the electrolyte dynamics is accounted for by a simple correction term., Comment: 16 pages, 3 figures

Minor mergers are common in galaxy clusters. They have the potential to create sloshing cold fronts (SCFs) in the intracluster medium (ICM) of the cluster. However, the resilience of SCFs to subsequent minor mergers is unknown. Here we investigate the extent to which SCFs established by an off-axis minor merger are disrupted by a subsequent minor merger. We perform a suite of 13 hydrodynamic + N-body simulations of idealised triple cluster mergers in which we vary the approach direction and impact parameter of the tertiary cluster. Except for ~1 Gyr after the first core passage of the tertiary cluster, clear SCFs are present in all merger configurations. Subsequent head-on minor mergers reduce the number of SCFs significantly, while subsequent off-axis minor mergers only moderately reduce the number of SCFs. In particular, outer (>~500 kpc) SCFs are resilient. The results of this work indicate that SCFs are easily formed in the course of a minor merger and are long-lived even if a further minor merger takes place. SCFs thus should be ubiquitous, but deriving the merger history of a given cluster based on its observed SCFs might be more complex than previously thought., Comment: Accepted for publication in MNRAS, 24 pages, 18 figures. For animated figures, see http://www.youtube.com/playlist?list=PL3kemZFmnTGR6Zkmt1NCNeKUbPIrDoxmy

Individuals are gaining more control of their personal data through recent data privacy laws such the General Data Protection Regulation and the California Consumer Privacy Act. One aspect of these laws is the ability to request a business to delete private information, the so called "right to be forgotten" or "right to erasure". These laws have serious financial implications for companies and organizations that train large, highly accurate deep neural networks (DNNs) using these valuable consumer data sets. However, a received redaction request poses complex technical challenges on how to comply with the law while fulfilling core business operations. We introduce a DNN model lifecycle maintenance process that establishes how to handle specific data redaction requests and minimize the need to completely retrain the model. Our process is based upon the membership inference attack as a compliance tool for every point in the training set. These attack models quantify the privacy risk of all training data points and form the basis of follow-on data redaction from an accurate deployed model; excision is implemented through incorrect label assignment within incremental model updates., Comment: 8 pages, 7 figures

An efficient scheme is introduced that extends the generalized membership inference attack to every point in a model's training data set. Our approach leverages data partitioning to create variable sized training sets for the reference models. We then train an attack model for every single training example for a reference model configuration based upon output for each individual point. This allows us to quantify the membership inference attack vulnerability of each training data point. Using this approach, we discovered that smaller amounts of reference model training data led to a stronger attack. Furthermore, the reference models do not need to be of the same architecture as the target model, providing additional attack efficiencies. The attack may also be performed by an adversary even when they do not have the complete original data set., Comment: 8 pages, 6 figures, 8 tables

Magnetic charge propagation in bulk frustrated materials has yielded a paradigm-shift in science, allowing the symmetry between electricity and magnetism to be studied. Recent work is now suggesting magnetic charge dynamics upon the spin-ice surface may have important implications in determining the ordering and associated phase space. Here we detail a 3D artificial spin-ice, a 3D nanostructured array of magnetic islands which captures the exact geometry of bulk systems, allowing field-driven dynamics of magnetic charge to be directly visualized upon the surface. Using magnetic microscopy, we observe vastly different magnetic charge dynamics along two principle directions. These striking differences are found to be due to the surface-termination and associated coordination which yields different energetics and interaction strengths for magnetic charges upon the surface.

Three-dimensional nanostructured functional materials are important systems, allowing new means to intricately control electromagnetic properties. A key problem is realising a 3D printing methodology upon the nanoscale that can yield a range of functional materials. In this letter, it is shown that two-photon lithography when combined with femtosecond machining of sacrificial layers, can be used to realise such a vision and produce 3D functional nanomaterials of complex geometry. This is demonstrated by fabricating 3D magnetic nanowires that exhibit controlled domain wall injection and propagation. Secondly, we fabricate large scale 3D artificial spin-ice structures whose complex switching can be probed using optical magnetometry. We show that by careful analysis of the magneto-optical Kerr effect signal and by comparison with micro-magnetic simulations, depth dependent switching information can be obtained from the 3DASI lattice. The work paves the way to new materials, which exploit additional physics provided by non-trivial 3D geometries.

In 1895, Korteweg and de Vries (KdV), derived their celebrated equation describing the motion of waves of long wavelength in shallow water. In doing so they made a number of quite reasonable assumptions, incompressibility of the water and irrotational fluid. The resulting equation, the celebrated KdV equation, has been shown to be a very reasonable description of real water waves. However there are other phenomena which have an impact on the shape of the wave, that of vorticity and viscosity. This paper examines how a constant vorticity affects the shape of waves in electrohydrodynamics. For constant vorticity, the vertical component of the velocity obeys a Laplace equation and also has the usual lower boundary condition. In making the vertical component of the velocity take central stage, the Burns condition can be thus bypassed., Comment: 20 pages, 9 figures, 1 table, 12 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

Thermal electrochemical models for porous electrode batteries (such as lithium ion batteries) are widely used. Due to the multiple scales involved, solving the model accounting for the porous microstructure is computationally expensive, therefore effective models at the macroscale are preferable. However, these effective models are usually postulated ad hoc rather than systematically upscaled from the microscale equations. We present an effective thermal electrochemical model obtained using asymptotic homogenisation, which includes the electrochemical model at the cell level coupled with a thermal model that can be defined either at the cell or the battery level. The main aspects of the model are the consideration of thermal effects, the diffusion effects in the electrode particles, and the anisotropy of the material based on the microstructure, all of them incorporated in a systematic manner. We also compare the homogenised model with the standard electrochemical Doyle, Fuller & Newman model., Comment: Post-print

We compile two samples of cluster galaxies with complimentary hydrodynamic and N-body analysis using FLASH code to ascertain how their differing populations drive their rotational profiles and to better understand their dynamical histories. We select our main cluster sample from the X-ray Galaxy Clusters Database (BAX), which are populated with Sloan Digital Sky Survey (SDSS) galaxies. The BAX clusters are tested for the presence of sub-structures, acting as proxies for core mergers, culminating in sub-samples of 8 merging and 25 non-merging galaxy clusters. An additional sample of 12 galaxy clusters with known dumbbell components is procured using galaxy data from the NASA/IPAC Extragalactic Database (NED) to compare against more extreme environments. BAX clusters of each sample are stacked onto a common RA-DEC space to produce rotational profiles within the range of $0.0 - 2.5$ $r_{200}$. Merging stacks possess stronger core rotation at $\lesssim 0.5 r_{200}$ primarily contributed by a red galaxy sub-population from relaxing core mergers, this is alongside high rotational velocities from blue galaxy sub-populations, until, they mix and homogenise with the red sub-populations at $\sim r_{200}$, indicative of an infalling blue galaxy sub-population with interactive mixing between both sub-populations at $\gtrsim r_{200}$. FLASH code is utilised to simulate the merger phase between two originally independent clusters and test the evolution of their rotational profiles. Comparisons with the dumbbell clusters leads to the inference that the peculiar core rotations of some dumbbell clusters are the result of the linear motions of core galaxies relaxing onto the potential during post second infall., Comment: Accepted for publication in the Monthly Notices of the Royal Astronomical Society; 18 pages, 15 figures and 3 tables

Rheumatoid arthritis-associated joint pain is frequently observed independent of disease activity, suggesting unidentified pain mechanisms. We demonstrate that antibodies binding to cartilage, specific for collagen type II (CII) or cartilage oligomeric matrix protein (COMP), elicit mechanical hypersensitivity in mice, uncoupled from visual, histological and molecular indications of inflammation. Cartilage antibody-induced pain-like behavior does not depend on complement activation or joint inflammation, but instead on tissue antigen recognition and local immune complex (IC) formation. smFISH and IHC suggest that neuronal Fcgr1 and Fcgr2b mRNA are transported to peripheral ends of primary afferents. CII-ICs directly activate cultured WT but not FcR{\gamma} chain-deficient DRG neurons. In line with this observation, CII-IC does not induce mechanical hypersensitivity in FcR{\gamma} chain-deficient mice. Furthermore, injection of CII antibodies does not generate pain-like behavior in FcR{\gamma} chain-deficient mice or mice lacking activating Fc{\gamma}Rs in neurons. In summary, this study defines functional coupling between autoantibodies and pain transmission that may facilitate the development of new disease-relevant pain therapeutics.

Quantum correlations between parts of a composite system most clearly reveal themselves through entanglement. Designing, maintaining, and controlling entangled systems is very demanding, which raises the stakes for understanding the efficacy of entanglement-free, yet quantum, correlations, exemplified by quantum discord. Discord is defined via conditional mutual entropies of parts of a composite system, and its direct measurement is hardly possible even via full tomographic characterization of the system state. Here we design a simple protocol to detect and quantify quantum discord in an unentangled bipartite system. Our protocol relies on a characteristic of discord that can be extracted from repeated direct measurements of certain correlations between subsystems of the bipartite system. The proposed protocol opens a way of extending experimental studies of discord to electronic systems but can also be implemented in quantum-optical systems., Comment: 10 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1901.11514

We show that there is a new class of gas tails - slingshot tails - which form as a subhalo (i.e. a subcluster or early-type cluster galaxy) moves away from the cluster center towards the apocenter of its orbit. These tails can point perpendicular or even opposite to the subhalo direction of motion, not tracing the recent orbital path. Thus, the observed tail direction can be misleading, and we caution against naive conclusions regarding the subhalo's direction of motion based on the tail direction. A head-tail morphology of a galaxy's or subcluster's gaseous atmosphere is usually attributed to ram pressure stripping and the widely applied conclusion is that gas stripped tail traces the most recent orbit. However, during the slingshot tail stage, the subhalo is not being ram pressure stripped (RPS) and the tail is shaped by tidal forces more than just the ram pressure. Thus, applying a classic RPS scenario to a slingshot tail leads not only to an incorrect conclusion regarding the direction of motion, but also to incorrect conclusions in regard to the subhalo velocity, expected locations of shear flows, instabilities and mixing. We describe the genesis and morphology of slingshot tails using data from binary cluster merger simulations, discuss their observable features and how to distinguish them from classic RPS tails. We identify three examples from the literature that are not RPS tails but slingshot tails and discuss other potential candidates., Comment: 18 pages, 10 figures. Accepted for publication in ApJ

Patterning nanomagnets in three-dimensions presents a new paradigm in condensed matter physics and allows access to a plethora of fundamental phenomena including robust spin textures, magnetic metamaterials that are home to defects carrying magnetic charge and ultrahigh density devices that store information in three-dimensions. However, the nanostructuring of functional magnetic materials into complex three-dimensional geometries has thus far proven to be a formidable challenge. Here we show magnetic nanowires can be arranged into 3D frustrated magnetic nanowire lattices by using a combination of 3D polymer nanoprinting and metallic deposition. The fabricated nanowires are single domain and they switch via nucleation and propagation of domain walls. Deep nanoscale magnetic imaging and finite element simulations elucidate the spin texture present on the 3D nanostructured lattice. Our study demonstrates a generic platform for the production of 3D nanostructured magnetic materials allowing the realisation of racetrack memory devices and 3D nanostructured systems that mimic bulk frustrated crystals.

Ferromagnetic materials have been utilised as recording media within data storage devices for many decades. Confinement of the material to a two dimensional plane is a significant bottleneck in achieving ultra-high recording densities and this has led to the proposition of three dimensional (3D) racetrack memories that utilise domain wall propagation along nanowires. However, the fabrication of 3D magnetic nanostructures of complex geometry is highly challenging and not easily achievable with standard lithography techniques. Here, by using a combination of two-photon lithography and electrochemical deposition, we show a new approach to construct 3D magnetic nanostructures of complex geometry. The magnetic properties are found to be intimately related to the 3D geometry of the structure and magnetic imaging experiments provide evidence of domain wall pinning at a 3D nanostructured junction.

The abundance of cosmic voids can be described by an analogue of halo mass functions for galaxy clusters. In this work, we explore a number of void mass functions: from those based on excursion-set theory to new mass functions obtained by modifying halo mass functions. We show how different void mass functions vary in their predictions for the largest void expected in an observational volume, and compare those predictions to observational data. Our extreme-value formalism is shown to be a new practical tool for testing void theories against simulation and observation., Comment: See part I here: https://arxiv.org/abs/1502.07705