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Artificial neural networks are becoming an integral part of digital solutions to complex problems. However, employing neural networks on quantum processors faces challenges related to the implementation of non-linear functions using quantum circuits. In this paper, we use repeat-until-success circuits enabled by real-time control-flow feedback to realize quantum neurons with non-linear activation functions. These neurons constitute elementary building blocks that can be arranged in a variety of layouts to carry out deep learning tasks quantum coherently. As an example, we construct a minimal feedforward quantum neural network capable of learning all 2-to-1-bit Boolean functions by optimization of network activation parameters within the supervised-learning paradigm. This model is shown to perform non-linear classification and effectively learns from multiple copies of a single training state consisting of the maximal superposition of all inputs., Comment: 24 pages, 22 figures, 3 tables

Drying is the most critical process of the first heating cycle of monolithic dense refractories, as the reduced permeability of the resulting microstructure may lead to explosive spalling and mechanical damage associated with dewatering. The first part of this review series pointed out the various drying stages, the role of the binder components and the techniques that can be used to follow the water release in as-cast refractory materials, when they are exposed to heat. Although defining a suitable heating schedule is a great challenge, some tools can be applied to minimize the spalling risks associated with steam pressurization. In this context, this second review article points out (i) the main drying agents and how they affect the resulting castables' microstructure (organic fibers, metallic powders, permeability enhancing active compounds, silica-based additives and chelating agents), and (ii) the effects related to the procedures commonly applied during the designing of heating routine (i.e., the role of the heating rate, ramp versus holding time), as well as the influence of the castable's dimension on the overall drying behavior. Considering the recent advances regarding the design of refractory formulations and their processing, one may expect that incorporating suitable drying additives into the prepared composition should lead to a suitable and safer water release in such dense consolidated structures. Besides that, novel engineering opportunities, such as the use of in-situ based experimental techniques (i.e., neutron and X-ray tomography) to obtain more accurate data and the development of numerical models, might help in simulating and predicting the steam pressure developed in refractory systems during their first heating.

Despite the continuous evolution on the performance of refractory ceramic products, monolithic materials still require special attention during their processing steps as various phase transformations may take place during the curing, drying and firing stages. Drying is usually the longest and the most critical process observed during the first heating cycle of refractory linings, as the enhanced particle packing and reduced permeability of the resulting microstructure may lead to recurrent explosive spalling and mechanical damage associated with dewatering and the development of high steam pressure at the inner regions of such dense materials. In this context, this review article mainly addresses (i) the theoretical aspects related to the drying process of dense refractories, (ii) the influence of the phase transformations derived from the binder additives, and (iii) the usual and advanced experimental techniques to assess the water removal from consolidated castable pieces. Many studies have pointed out that due to the complex nature of this phenomenon (i.e., considering combined thermal stresses and pore pressure, heterogeneous microstructure, evolving pore structure with temperature, etc.), the mechanisms behind the water withdrawal and castables explosive spalling are lacking further understanding and, consequently, it has been difficult to save time and energy during the first heating of industrial equipment lined with ceramic materials. On the other hand, different methods are used for refractory spalling assessment and many efforts have been carried out in applying in situ imaging techniques (such as NMR and neutron tomography) to follow the moisture evolution during such thermal treatments.

We propose a procedure to identify and classify genuine tripartite entanglement in pure 3-qubit states via the Activated Bipartite Entanglement (ABE), which is defined here as the difference between the Entanglement of Assistance and the Entanglement of Formation. We show that for pure states belonging to one of the two inequivalent classes of genuine tripartite entanglement, i.e., GHZ or W states, the ABE is always greater than zero. For separable and biseparable states it is always null. In addition, our approach is capable to distinguish between genuine tripartite entangled states, those belonging to the GHZ class from those belonging to the W class. We also present an experimental proposal, by using linear optical circuits and internal degrees of freedom of a single photon, to measure the ABE and to verify the characterization via activated entanglement. The circuit simulation shows an excellent agreement with theoretical prediction for a wide class of GHZ and W states., Comment: Improved version, 6 pages, 4 figures

A precise characterization of the incoming proton bunch parameters is required to accurately simulate the self-modulation process in the Advanced Wakefield Experiment (AWAKE). This paper presents an analysis of the parameters of the incoming proton bunches used in the later stages of the AWAKE Run 1 data-taking period. The transverse structure of the bunch is observed at multiple positions along the beamline using scintillating or optical transition radiation screens. The parameters of a model that describes the bunch transverse dimensions and divergence are fitted to represent the observed data using Bayesian inference. The analysis is tested on simulated data and then applied to the experimental data.

We present numerical simulations and experimental results of the self-modulation of a long proton bunch in a plasma with linear density gradients along the beam path. Simulation results agree with the experimental results reported in arXiv:2007.14894v2: with negative gradients, the charge of the modulated bunch is lower than with positive gradients. In addition, the bunch modulation frequency varies with gradient. Simulation results show that dephasing of the wakefields with respect to the relativistic protons along the plasma is the main cause for the loss of charge. The study of the modulation frequency reveals details about the evolution of the self-modulation process along the plasma. In particular for negative gradients, the modulation frequency across time-resolved images of the bunch indicates the position along the plasma where protons leave the wakefields. Simulations and experimental results are in excellent agreement., Comment: 13 pages, 11 figures

Structural materials are broadly used in applications such as nuclear vessels, high-temperature processes, and civil construction. Usually, during their placing and lifespan, they may present free or chemically bonded liquid phases in their structure, demanding careful attention when exposed to high heating rates. Their behavior in such conditions is a challenging problem as it comprises numerous highly nonlinear properties (not easily measured via experimental tests), strongly coupled equations and unreliable experimental benchmarks. Nonetheless, such simulations are of great interest. This work aims to provide a numerical study, checking whether its solution indeed converges and yields reliable results. Additionally, as the model needs several input parameters, this work conducts a sensitivity analysis and also assesses its applicability to more complex scenarios, as such issues remain open in the literature. In order to do that, a simple model that can be easily adapted for mixed formulations and complex geometries was proposed. It was found out that when considering unidimensional models the choices regarding the interpolation of the sorption isotherms are not essential to the numerical stability of the system. Besides that, the permeability and thermal conductivity of the material are the most important parameters that affect the simulation results of pressure, temperature and evaporable water content profiles. Finally, the 2D mesoscale simulation of concrete with polymeric fibers (based on the mixed formulation of the problem) yielded results that agreed with experimental observations. Thus, the model proposed herein can provide a solid base for future works and also important insights towards simpler methodologies.

A growing interest in designing high-alumina MgO-bonded refractory castables has been identified in recent years due to the magnesia ability to react: (i) with water at the initial processing stages of these materials (inducing the precipitation of brucite phase) or (ii) with alumina, giving rise to in situ MgAl2O4 generation at high temperatures. Nevertheless, despite the great potential of caustic magnesia to be used as a binder in such systems due to its high reactivity, it is still a challenge to control the hydration reaction rate of this oxide and the negative effects derived from the expansive feature of Mg(OH)2 formation. Thus, this work evaluated the incorporation of different contents of aluminum hydroxyl lactate (AHL) into caustic magnesia-bonded castables, aiming to control the brucite precipitation during the curing and drying steps of the prepared samples, resulting in crack-free refractories. The designed compositions were characterized via flowability, setting behavior, X-ray diffraction, cold flexural strength, porosity, permeability and thermogravimetric measurements. According to the results, instead of Mg(OH)2, hydrotalcite-like phases [Mg6Al2(OH)16(OH)2.4.5H2O and Mg6Al2(OH)16(CO3).4H2O] were the main hydrated phases identified in the AHL-containing compositions. The addition of 1.0 wt.% of aluminum hydroxyl lactate to the designed castable proved to be, so far, the best option for this magnesia source, resulting in the development of a crack-free refractory with enhanced properties and greater spalling resistance under heating.

We realize a suite of logical operations on a distance-two logical qubit stabilized using repeated error detection cycles. Logical operations include initialization into arbitrary states, measurement in the cardinal bases of the Bloch sphere, and a universal set of single-qubit gates. For each type of operation, we observe higher performance for fault-tolerant variants over non-fault-tolerant variants, and quantify the difference through detailed characterization. In particular, we demonstrate process tomography of logical gates, using the notion of a logical Pauli transfer matrix. This integration of high-fidelity logical operations with a scalable scheme for repeated stabilization is a milestone on the road to quantum error correction with higher-distance superconducting surface codes., Comment: 16 pages, 9 figures, 2 tables

Developing MgO-bonded castables is still an important subject for refractory producers and end-users based on the expansive character of the in-situ Mg(OH)2 formation. Considering that magnesia undergoes hydration when exposed to water and the generated hydrated phase needs to be properly accommodated in the resulting microstructure to inhibit the generation of cracks, it is very important to find out alternatives to control the MgO hydration reaction rate. This research investigated the use of aluminum lactate (AL) as a likely additive to change the hydration and drying behavior of vibratable castables bonded with different MgO sources (dead burnt, caustic or fumed one). Firstly, XRD, TG and DSC measurements of magnesia-based aqueous suspensions were evaluated to identify the AL effect on changing the hydration reaction products during the curing and drying steps. After that, Al2O3-MgO refractories were prepared and their flowability, curing behavior, cold flexural strength, apparent porosity, permeability and explosion resistance were evaluated. The results indicated that, instead of Mg(OH)2, Mg6Al2(OH)16(OH)2.4.5H2O/ Mg6Al2(OH)16(CO3).4H2O was the main hydrated phase identified in the AL-containing compositions. Due to this change in the hydration behavior of the refractories, the mixtures prepared with dead-burnt or magnesia fumes plus organic salt presented a longer setting time. Besides that, crack-free samples with improved permeability and green mechanical strength could be obtained when adding 0.5 wt.% or 1.0 wt.% of aluminum lactate to the tested castable compositions. Consequently, 1.0 wt.% of the selected additive favored the design of refractories with enhanced properties and greater spalling resistance, as no explosion could be observed even when subjecting the prepared samples to severe heating conditions (20C/min).

Refractory producers face many challenges in terms of producing MgO-containing castables due to the high likelihood of magnesia to hydrate in contact with water, resulting in Mg(OH)2 generation. The expansive feature of this transformation affects the performance of such refractories, as (i) if this hydrated phase is not accommodated in the formed microstructure, ceramic linings with cracks and low green mechanical strength will be obtained; and (ii) if crack-free pieces are prepared, they should present low porosity and reduced permeability, which require special attention when heating these materials. This work investigated the ability of various additives in the optimization of the drying behavior of Al2O3-MgO castables. Vibratable compositions were tested after incorporating polymeric fibers (PF), an organic salt (OAS), SiO2-based additive (SM) or permeability enhancing active compound (MP) into the dry-mixtures. Various experimental measurements were performed to infer the role of the drying agents to prevent the samples explosion and whether they would also influence other properties of the castables. As observed, OAS and MP helped to inhibit the MgO-bonded samples explosion even under severe heating conditions (2-20C/min) and increased their green mechanical strength and slag infiltration resistance when compared to the additive-free composition. On the other hand, the addition of polymeric fibers (PF) or silica-based compound (SM) to the formulations was not able to prevent the castables explosion when using a high heating rate and other side effects could also be observed when testing these materials. Thus, the selection of suitable drying agents is a key issue, as they may allow the development of MgO-bonded castables with enhanced properties and lower spalling risk during their first thermal treatment.

We use a relativistic ionization front to provide various initial transverse wakefield amplitudes for the self-modulation of a long proton bunch in plasma. We show experimentally that, with sufficient initial amplitude ($\ge(4.1\pm0.4)$ MV/m), the phase of the modulation along the bunch is reproducible from event to event, with 3 to 7% (of 2$\pi$) rms variations all along the bunch. The phase is not reproducible for lower initial amplitudes. We observe the transition between these two regimes. Phase reproducibility is essential for deterministic external injection of particles to be accelerated., Comment: Letter and Supplemental Material, 6 figures, 8 pages

The preparation of thermal equilibrium states is important for the simulation of condensed-matter and cosmology systems using a quantum computer. We present a method to prepare such mixed states with unitary operators, and demonstrate this technique experimentally using a gate-based quantum processor. Our method targets the generation of thermofield double states using a hybrid quantum-classical variational approach motivated by quantum-approximate optimization algorithms, without prior calculation of optimal variational parameters by numerical simulation. The fidelity of generated states to the thermal-equilibrium state smoothly varies from 99 to 75% between infinite and near-zero simulated temperature, in quantitative agreement with numerical simulations of the noisy quantum processor with error parameters drawn from experiment.

Plasma wakefield dynamics over timescales up to 800 ps, approximately 100 plasma periods, are studied experimentally at the Advanced Wakefield Experiment (AWAKE). The development of the longitudinal wakefield amplitude driven by a self-modulated proton bunch is measured using the external injection of witness electrons that sample the fields. In simulation, resonant excitation of the wakefield causes plasma electron trajectory crossing, resulting in the development of a potential outside the plasma boundary as electrons are transversely ejected. Trends consistent with the presence of this potential are experimentally measured and their dependence on wakefield amplitude are studied via seed laser timing scans and electron injection delay scans., Comment: 11 pages, 8 figures

Using new explicit formulas for the stationary GW/PT descendent correspondence for nonsingular projective toric 3-folds, we show that the correspondence intertwines the Virasoro constraints in Gromov-Witten theory for stable maps with the Virasoro constraints for stable pairs. Since the Virasoro constraints in Gromov-Witten theory are known to hold in the toric case, we establish the stationary Virasoro constraints for the theory of stable pairs on toric 3-folds. As a consequence, new Virasoro constraints for tautological integrals over Hilbert schemes of points on surfaces are also obtained., Comment: 65 pages

In 2017, AWAKE demonstrated the seeded self-modulation (SSM) of a 400 GeV proton beam from the Super Proton Synchrotron (SPS) at CERN. The angular distribution of the protons deflected due to SSM is a quantitative measure of the process, which agrees with simulations by the two-dimensional (axisymmetric) particle-in-cell code LCODE. Agreement is achieved for beam populations between $10^{11}$ and $3 \times 10^{11}$ particles, various plasma density gradients ($-20 \div 20\%$) and two plasma densities ($2\times 10^{14} \text{cm}^{-3}$ and $7 \times 10^{14} \text{cm}^{-3}$). The agreement is reached only in the case of a wide enough simulation box (at least five plasma wavelengths)., Comment: 8 pages, 9 figures, 1 table

We introduce the sudden variant (SNZ) of the Net Zero scheme realizing controlled-$Z$ (CZ) gates by baseband flux control of transmon frequency. SNZ CZ gates operate at the speed limit of transverse coupling between computational and non-computational states by maximizing intermediate leakage. The key advantage of SNZ is tuneup simplicity, owing to the regular structure of conditional phase and leakage as a function of two control parameters. We realize SNZ CZ gates in a multi-transmon processor, achieving $99.93\pm0.24\%$ fidelity and $0.10\pm0.02\%$ leakage. SNZ is compatible with scalable schemes for quantum error correction and adaptable to generalized conditional-phase gates useful in intermediate-scale applications., Comment: 13 pages, 11 figures and 3 tables

We briefly compare in numerical simulations the relativistic ionization front and electron bunch seeding of the self-modulation of a relativistic proton bunch in plasma. When parameters are such that initial wakefields are equal with the two seeding methods, the evolution of the maximum longitudinal wakefields along the plasma are similar. We also propose a possible seeding/injection scheme using a single plasma that we will study in upcoming simulations works., Comment: 8 pages, 3 figures, submitted to Proceedings of the European Advanced Accelerator Conference 2019 (EAAC 2019), to appear in IOP Conference Proceedings Series

We give direct experimental evidence for the observation of the full transverse self-modulation of a relativistic proton bunch propagating through a dense plasma. The bunch exits the plasma with a density modulation resulting from radial wakefield effects with a period reciprocal to the plasma frequency. We show that the modulation is seeded by using an intense laser pulse co-propagating with the proton bunch which creates a relativistic ionization front within the bunch. We show by varying the plasma density over one order of magnitude that the modulation period scales with the expected dependence on the plasma density., Comment: 4 figures, AWAKE collaboration paper, Submitted to PRL

High energy particle accelerators have been crucial in providing a deeper understanding of fundamental particles and the forces that govern their interactions. In order to increase the energy or reduce the size of the accelerator, new acceleration schemes need to be developed. Plasma wakefield acceleration, in which the electrons in a plasma are excited, leading to strong electric fields, is one such promising novel acceleration technique. Pioneering experiments have shown that an intense laser pulse or electron bunch traversing a plasma, drives electric fields of 10s GV/m and above. These values are well beyond those achieved in conventional RF accelerators which are limited to ~0.1 GV/m. A limitation of laser pulses and electron bunches is their low stored energy, which motivates the use of multiple stages to reach very high energies. The use of proton bunches is compelling, as they have the potential to drive wakefields and accelerate electrons to high energy in a single accelerating stage. The long proton bunches currently available can be used, as they undergo self-modulation, a particle-plasma interaction which longitudinally splits the bunch into a series of high density microbunches, which then act resonantly to create large wakefields. The AWAKE experiment at CERN uses intense bunches of protons, each of energy 400 GeV, with a total bunch energy of 19 kJ, to drive a wakefield in a 10 m long plasma. Bunches of electrons are injected into the wakefield formed by the proton microbunches. This paper presents measurements of electrons accelerated up to 2 GeV at AWAKE. This constitutes the first demonstration of proton-driven plasma wakefield acceleration. The potential for this scheme to produce very high energy electron bunches in a single accelerating stage means that the results shown here are a significant step towards the development of future high energy particle accelerators., Comment: 7 pages, 4 figures. Updated acknowledgements and one reference

We investigate numerically the detection of the self-modulation instability in a virtual detector located downstream from the plasma in the context of AWAKE. We show that the density structures, appearing in the temporally resolving virtual detector, map the transverse beam phase space distribution at the plasma exit. As a result, the proton bunch radius that appears to grow along the bunch in the detector results from the divergence increase along the bunch, related with the spatial growth of the self-modulated wakefields. In addition, asymmetric bunch structures in the detector are a result of asymmetries of the bunch divergence, and do not necessarily reflect asymmetric beam density distributions in the plasma., Comment: Accepted for publication in NIM-A for the proceedings of the 3rd European Advanced Accelerator Workshop. 5 pages, 2 figures

AWAKE is a proton-driven plasma wakefield acceleration experiment. % We show that the experimental setup briefly described here is ready for systematic study of the seeded self-modulation of the 400\,GeV proton bunch in the 10\,m-long rubidium plasma with density adjustable from 1 to 10$\times10^{14}$\,cm$^{-3}$. % We show that the short laser pulse used for ionization of the rubidium vapor propagates all the way along the column, suggesting full ionization of the vapor. % We show that ionization occurs along the proton bunch, at the laser time and that the plasma that follows affects the proton bunch. %, Comment: Presented as an invited talk at the EPS=Plasma Physics Conference 2017