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The single-ion anisotropy and magnetic interactions in spin-ice systems give rise to unusual non-collinear spin textures, such as Pauling states and magnetic monopoles. The effective spin correlation strength ($J_{eff}$) determines the relative energies of the different spin-ice states. With this work, we display the capability of capacitive torque magnetometry in characterizing the magneto-chemical potential associated with monopole formation. We build a magnetic phase diagram of Ho$_2$Ti$_2$O$_7$, and show that the magneto-chemical potential depends on the spin-sublattice ($\alpha$ or $\beta$), i.e., the Pauling state, involved in the transition. Monte-Carlo simulations using the dipolar-spin-ice Hamiltonian support our findings of a sublattice-dependent magneto-chemical potential, but the model underestimates the $J_{eff}$ for the $\beta$-sublattice. Additional simulations, including next-nearest neighbor interactions ($J_2$), show that long-range exchange terms in the Hamiltonian are needed to describe the measurements. This demonstrates that torque magnetometry provides a sensitive test for $J_{eff}$ and the spin-spin interactions that contribute to it., Comment: Main text: 12 pages, 5 figures, 1 table; Supplemental Materials: 12 pages, 7 figures, 6 tables

Low temperature optical spectroscopy in applied magnetic fields provides clear evidence of magnetoelastic coupling in the spin ice material Ho$_2$Ti$_2$O$_7$. In far-IR reflectometry measurements, we observe field dependent features around 30, 61, 72 and 78~meV, energies corresponding to crystal electronic field (CEF) doublets. The calculations of the crystal-field Hamiltonian model confirm that the observed features in IR spectra are consistent with magnetic-dipole-allowed excitations from the ground state to higher $^5$I$_8$ CEF levels. We present the CEF parameters that best describe our field-dependent IR reflectivity measurements. Additionally, we identify a weak field-dependent shoulder near one of the CEF doublets. This indicates that this level is split even in zero-field, which we associate with a vibronic bound state. Modeling of the observed splitting shows that the phonon resides at slightly lower energy compared to the CEF level that it couples to, which is in contrast with previously published inelastic neutron measurements. The magnetic field dependence of the vibronic state shows a gradual decoupling of the phonon with the CEF level as it shifts. This approach should work in pyrochlores and other systems that have magnetic dipole transitions in the IR spectroscopic range, which can elucidate the presence and the ability to tune the nature of vibronic states in a wide variety of materials.

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

Seemingly different interpretations or descriptions of Einstein's model for the heat capacity of a solid can be found in textbooks and the literature. The purpose of this note is to clarify the equivalence of the different descriptions, which all lead to the same Einstein expression for the heat capacity of a solid of N atoms., Comment: 7 pages, Submitted to the American Journal of Physics

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.

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

The Australian bushfires around the turn of the year 2020 generated an unprecedented perturbation of stratospheric composition, dynamical circulation and radiative balance. Here we show from satellite observations that the resulting planetary-scale blocking of solar radiation by the smoke is larger than any previously documented wildfires and of the same order as the radiative forcing produced by moderate volcanic eruptions. A striking effect of the solar heating of an intense smoke patch was the generation of a self-maintained anticyclonic vortex measuring 1000 km in diameter and featuring its own ozone hole. The highly stable vortex persisted in the stratosphere for over 13 weeks, travelled 66,000 km and lifted a confined bubble of smoke and moisture to 35 km altitude. Its evolution was tracked by several satellite-based sensors and was successfully resolved by the European Centre for Medium-Range Weather Forecasts operational system, primarily based on satellite data. Because wildfires are expected to increase in frequency and strength in a changing climate, we suggest that extraordinary events of this type may contribute significantly to the global stratospheric composition in the coming decades., Comment: to appear in Communications Earth & Environment

Through the quantification of physical activity energy expenditure (PAEE), health care monitoring has the potential to stimulate vital and healthy ageing, inducing behavioural changes in older people and linking these to personal health gains. To be able to measure PAEE in a monitoring environment, methods from wearable accelerometers have been developed, however, mainly targeted towards younger people. Since elderly subjects differ in energy requirements and range of physical activities, the current models may not be suitable for estimating PAEE among the elderly. Because past activities influence present PAEE, we propose a modeling approach known for its ability to model sequential data, the Recurrent Neural Network (RNN). To train the RNN for an elderly population, we used the GOTOV dataset with 34 healthy participants of 60 years and older (mean 65 years old), performing 16 different activities. We used accelerometers placed on wrist and ankle, and measurements of energy counts by means of indirect calorimetry. After optimization, we propose an architecture consisting of an RNN with 3 GRU layers and a feedforward network combining both accelerometer and participant-level data. In this paper, we describe our efforts to go beyond the standard facilities of a GRU-based RNN, with the aim of achieving accuracy surpassing the state of the art. These efforts include switching aggregation function from mean to dispersion measures (SD, IQR, ...), combining temporal and static data (person-specific details such as age, weight, BMI) and adding symbolic activity data as predicted by a previously trained ML model. The resulting architecture manages to increase its performance by approximatelly 10% while decreasing training input by a factor of 10. It can thus be employed to investigate associations of PAEE with vitality parameters related to metabolic and cognitive health and mental well-being., Comment: For a revised, updated and published version (Jan 2022, open access) refer to the Journal of Data Mining and Knowledge Discovery, DOI https://doi.org/10.1007/s10618-021-00817-w. To make our experiments, scripts and results accessible to other researchers (open-source) we shared our scripts with the published version (Jan 2022)

Antiferromagnets and ferromagnets are archetypes of the two distinct (type-A and type-B) ways of spontaneously breaking a continuous symmetry. Although type-B Nambu--Goldstone modes arise in various systems, the ferromagnet was considered pathological due to the stability and symmetry-breaking nature of its exact ground state. However, here we show that symmetry-breaking in ferrimagnets closely resembles the ferromagnet. In particular, there is an extensive ground state degeneracy, there is no Anderson tower of states, and the maximally polarized ground state is thermodynamically stable. Our results are derived analytically for the Lieb--Mattis ferrimagnet and numerically for the Heisenberg ferrimagnet. We argue that these properties are generic for type-B symmetry-broken systems, where the order parameter operator is a symmetry generator., Comment: 10 pages, 4 figures

Perhaps the most important aspect of symmetry in physics is the idea that a state does not need to have the same symmetries as the theory that describes it. This phenomenon is known as spontaneous symmetry breaking. In these lecture notes, starting from a careful definition of symmetry in physics, we introduce symmetry breaking and its consequences. Emphasis is placed on the physics of singular limits, showing the reality of symmetry breaking even in small-sized systems. Topics covered include Nambu-Goldstone modes, quantum corrections, phase transitions, topological defects and gauge fields. We provide many examples from both high energy and condensed matter physics. These notes are suitable for graduate students., Comment: 149 pages; matches published version

The DC Josephson effect is the flow of supercurrent across a weak link between two superconductors with a different value of their order parameter, the phase. We generalize this notion to any kind of spontaneous continuous symmetry breaking. The quantity that flows between the two systems is identified as the Noether current associated with the broken symmetry. The AC Josephson effect is identified as the oscillations due to the energy difference between the two systems caused by an imposed asymmetric chemical potential. As an example of novel physics, a Josephson effect is predicted between two crystalline solids, potentially measurable as a force periodic in the separation distance., Comment: RevTeX, 5 pages, 2 figures

Protecting quantum information from errors is essential for large-scale quantum computation. Quantum error correction (QEC) encodes information in entangled states of many qubits, and performs parity measurements to identify errors without destroying the encoded information. However, traditional QEC cannot handle leakage from the qubit computational space. Leakage affects leading experimental platforms, based on trapped ions and superconducting circuits, which use effective qubits within many-level physical systems. We investigate how two-transmon entangled states evolve under repeated parity measurements, and demonstrate the use of hidden Markov models to detect leakage using only the record of parity measurement outcomes required for QEC. We show the stabilization of Bell states over up to 26 parity measurements by mitigating leakage using postselection, and correcting qubit errors using Pauli-frame transformations. Our leakage identification method is computationally efficient and thus compatible with real-time leakage tracking and correction in larger quantum processors., Comment: 22 pages, 15 figures

In the Abelian-Higgs model, or Ginzburg-Landau model of superconductivity, the existence of an infrared stable charged fixed point ensures that there is a parameter range where the superconducting phase transition is second order, as opposed to fluctuation-induced first order as one would infer from the Coleman-Weinberg mechanism. We study the charged and neutral fixed points of a two-field generalization of the Abelian-Higgs model, where two N-component fields are coupled to two gauge fields and to each other, using the functional renormalization group. Focusing mostly on three dimensions, in the neutral case, this is a model for two-component Bose-Einstein condensation, and we confirm the fixed-point structure established in earlier works using different methods. The charged model is a dual theory of two-dimensional dislocation-mediated quantum melting. We find the existence of three charged fixed points for all N>2, while there are additional fixed points for N=2., Comment: RevTeX. 14 pages, 4 figures. Matches published version

Variational quantum eigensolvers offer a small-scale testbed to demonstrate the performance of error mitigation techniques with low experimental overhead. We present successful error mitigation by applying the recently proposed symmetry verification technique to the experimental estimation of the ground-state energy and ground state of the hydrogen molecule. A finely adjustable exchange interaction between two qubits in a circuit QED processor efficiently prepares variational ansatz states in the single-excitation subspace respecting the parity symmetry of the qubit-mapped Hamiltonian. Symmetry verification improves the energy and state estimates by mitigating the effects of qubit relaxation and residual qubit excitation, which violate the symmetry. A full-density-matrix simulation matching the experiment dissects the contribution of these mechanisms from other calibrated error sources. Enforcing positivity of the measured density matrix via scalable convex optimization correlates the energy and state estimate improvements when using symmetry verification, with interesting implications for determining system properties beyond the ground-state energy., Comment: 7 pages, 4 figures + 6 pages, 4 figures in supplemental material