With an increasing number of experiments observing phonon thermal Hall effect in magnets, it is theoretically desired to have a minimal model for the phonon thermal Hall effect. In this work, we study a simple model of acoustic phonons and uncorrelated paramagnetic doublets. When the doublets are non-Kramers, a linear pseudospin-phonon coupling is allowed by time-reversal symmetry and yields resonant phonon-pseudospin scattering. We compute the thermal longitudinal and Hall conductivities of the model and find qualitative agreement with recent experiments in ${\mathrm{Pr}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ [Uehara et al., Nat. Commun. 13, 4604 (2022)].

We present a systematic study of statistical mechanics for non-Hermitian quantum systems. Our work reveals that the stability of a non-Hermitian system necessitates the existence of a single path-dependent conserved quantity, which, in conjunction with the system's Hamiltonian, dictates the equilibrium state. By elucidating the relationship between the Hamiltonian and the supported conserved quantity, we propose criteria for discerning equilibrium states with finite relaxation times. Although our findings indicate that only non-Hermitian systems with real energy spectrum precisely possess such conserved quantities, we also demonstrate that an effective conserved quantity can manifest in certain systems with complex energy spectra. The effective conserved quantity, alongside the effective transitions within their associated subspace, collectively determines the system's equilibrium state. Our results provide valuable insights into non-Hermitian systems across more realistic contexts and hold potential for applications in a diverse range of physical systems.

We present the theoretical framework required to describe the statistics of microwave networks that serve to model quantum graphs. The networks are described by impedance and admittance matrices relating the voltages and currents at the network's ports. As we show, these matrices can be calculated in a number of ways. Normal modes of the network are characterized by a discrete set of wave numbers corresponding to the propagation constants on the network's bonds for which the determinant of the admittance matrix vanishes. The distribution of the spacings between adjacent eigenmode wave numbers is found to depend on the nature of the way bonds are connected at nodes. The critical quantity is the reflection coefficient presented at a node to a wave on a bond. As the reflection coefficient increases, the spacing distribution changes from one characteristic of the spacing of eigenvalues of a Gaussian orthogonal ensemble matrix to a Poisson distribution. The effect of loss is studied, and the scaling of the variance of the impedance values on network size, degree distribution, and other parameters is characterized. We attempted to find universal scaling relations for the distribution of impedance values for networks of different sizes. Finally, we compare the distribution of impedance values predicted by the model with those measured in a network of cables.

We performed ab initio molecular dynamics simulations for pressures and temperatures from 300–5000 GPa and 3000–30 000 K in order to determine the equation of state of solid and liquid iron. By employing a thermodynamic integration technique, we derive the ab initio entropy and Gibbs free energy of both phases, which allows us to construct solid and liquid adiabats and discuss implications for shock experiments. We derive the melting line by equating solid and liquid Gibbs free energies and represent it by a Simon fit $6469\mathrm{K}(1+(P/\mathrm{GPa}-300)/434.82{)}^{0.54369}$. Near 300 GPa, our melting line is higher than extrapolations of previous melting laws that were obtained with simulations at lower pressures but is in very good agreement with the most recent experiments by Kraus et al. Science 375, 202 (2022), that reached TPa pressures. The slope of our melting line is consistently steeper than that of our adiabats, which implies that the crystallization of iron in the cores of terrestrial planets always starts from their centers, like on Earth. We also construct models for Super-Earth interiors and compare with temperature profiles from published evolution models. These temperatures in many earlier publications are rather low, so that our melting line would imply completely frozen cores. Only later models by Stamenković et al. [Astrophys. J. 748, 41 (2012)] and Boujibar et al. [J. Geophys. Res. Planets 125, e2019JE006124 (2020)] consider a much wider range of interior temperatures, which imply that the core of Super-Earths may remain in a state with a partially molten core for a long time and the resulting buoyancy force will contribute to convection and the magnetic field generation.

Generating samples from the output distribution of a quantum circuit is a ubiquitous task used as a building block of many quantum algorithms. Here we show how to accomplish this task on a noisy quantum processor lacking full-blown error correction for a special class of quantum circuits dominated by Clifford gates. Our approach is based on coherent Pauli checks (CPCs) that detect errors in a Clifford circuit by verifying commutation rules between random Pauli-type check operators and the considered circuit. Our main contributions are as follows. First, we derive a simple formula for the probability that a Clifford circuit protected by CPCs contains a logical error. In the limit of a large number of checks, the logical error probability is shown to approach the value $\approx 7\epsilon n/5$, where $n$ is the number of qubits and $\epsilon$ is the depolarizing error rate. Our formula agrees nearly perfectly with the numerical simulation results. Second, we show that CPCs are well suited for quantum processors with a limited qubit connectivity. For example, the difference between all-to-all and linear qubit connectivity is only a $3\times$ increase in the number of cnot gates required to implement CPCs. Third, we describe simplified one-sided CPCs, which are well suited for mitigating measurement errors in the single-shot settings. Finally, we report an experimental demonstration of CPCs with up to 10 logical qubits and more than 100 logical cnot gates. Our experimental results show that CPCs provide a marked improvement in the logical error probability for the considered task of sampling the output distribution of quantum circuits.

We investigate theoretically a type of microwave memory that is composed of a single transmon qubit and a coupling resonator. The synergy of the parametric modulation of the qubit resonance frequency and a microwave directly driving the qubit transition can constitute effective three-level $\mathrm{\Lambda }$-type electromagnetically induced transparency. We demonstrate that the dynamical control of such a parametric modulation allows for the possibility of microwave storage and retrieval using a single qubit. Our results pave the way towards the practical implementation of quantum information in superconducting circuits.

Poincaré inertio-gravity modes described by the shallow water equations in a rotating frame have nontrivial topology, providing a perspective on the origin of equatorially trapped Kelvin and Yanai waves. We investigate the topology of rotating shallow water equations and continuously stratified primitive equations with and without background shear flow. Continuously stratified fluids support waves that are analogous to the edge modes of weak three-dimensional topological insulators. Background shear flow not only breaks the Hermiticity and homogeneity of the system but also leads to instabilities. By introducing a gauge-invariant winding number, we show that singularities in the phase of the Poincaré waves of the unforced shallow-water equations and primitive equations persist in the presence of both horizontal and vertical shear flows. Thus, the bulk Poincaré bands have nontrivial topology and we expect and confirm the persistence of the equatorial waves in the presence of shear along the equator where the Coriolis parameter $f$ changes signs.

Hyperuniform many-particle systems are characterized by a structure factor $S\left(\mathbf{k}\right)$ that is precisely zero as $\left|\mathbf{k}\right|\to 0$; and stealthy hyperuniform systems have $S\left(\mathbf{k}\right)=0$ for the finite range $0<\left|\mathbf{k}\right|\le K$, called the “exclusion region.” Through a process of collective-coordinate optimization, energy-minimizing disordered stealthy hyperuniform systems of moderate size have been made to high accuracy, and their novel physical properties have shown great promise. However, minimizing $S\left(\mathbf{k}\right)$ in the exclusion region is computationally intensive as the system size becomes large. In this paper, we present an improved methodology to generate such states using double-double precision calculations on graphical processing units (GPUs) that reduces the deviations from zero within the exclusion region by a factor of approximately ${10}^{30}$ for system sizes more than an order of magnitude larger. We further show that this ultrahigh accuracy is required to draw conclusions about their corresponding characteristics, such as the nature of the associated energy landscape and the presence or absence of Anderson localization, which might be masked, even when deviations are relatively small.

We propose a method to calculate wave functions and energies not only of the ground state but also of low-lying excited states using a deep neural network and the unsupervised machine learning technique. For systems composed of identical particles, a simple method to perform symmetrization for bosonic systems and antisymmetrization for fermionic systems is also proposed.

Complex spin textures in itinerant electron magnets hold promises for next-generation memory and information technology. The long-ranged and often frustrated electron-mediated spin interactions in these materials give rise to intriguing localized spin structures such as skyrmions. Yet, simulations of magnetization dynamics for such itinerant magnets are computationally difficult due to the need for repeated solutions to the electronic structure problems. We present a convolutional neural network (CNN) model to accurately and efficiently predict the electron-induced magnetic torques acting on local spins. Importantly, as the convolutional operations with a fixed kernel (receptive field) size naturally take advantage of the locality principle for many-electron systems, CNNs offer a scalable machine learning approach to spin dynamics. We apply our approach to enable large-scale dynamical simulations of skyrmion phases in itinerant spin systems. By incorporating the CNN model into Landau-Lifshitz-Gilbert dynamics, our simulations successfully reproduce the relaxation process of the skyrmion phase and stabilize a skyrmion lattice in larger systems. The CNN model also allows us to compute the effective receptive fields, thus providing a systematic and unbiased method for determining the locality of the original electron models.

Simulating time evolution of generic quantum many-body systems using classical numerical approaches has an exponentially growing cost either with evolution time or with the system size. In this work we present a polynomially scaling hybrid quantum-classical algorithm for time evolving a one-dimensional uniform system in the thermodynamic limit. This algorithm uses a layered uniform sequential quantum circuit as a variational Ansatz to represent infinite translation-invariant quantum states. We show numerically that this Ansatz requires a number of parameters polynomial in the simulation time for a given accuracy. Furthermore, this favorable scaling of the Ansatz is maintained during our variational evolution algorithm. All steps of the hybrid optimization are designed with near-term digital quantum computers in mind. After benchmarking the evolution algorithm on a classical computer, we demonstrate the measurement of observables of this uniform state using a finite number of qubits on a cloud-based quantum processing unit. With more efficient tensor contraction schemes, this algorithm may also offer improvements as a classical numerical algorithm.

Metallic states near the Mott insulator show a variety of quantum phases, including various magnetic, charge-ordered states and high-temperature superconductivity in various transition metal oxides and organic solids. The emergence of a variety of phases and their competitions are likely intimately associated with quantum transitions between the electron-correlation-driven Mott insulator and metals characterized by its criticality, and is related to many central questions of condensed matter. The quantum criticality is, however, not well understood when the transition is controlled by the bandwidth through physical parameters such as pressure. Here, we quantitatively estimate the universality class of the transition characterized by a comprehensive set of critical exponents by using a variational Monte Carlo method implemented as an open-source innovated quantum many-body solver, with the help of established scaling laws at a typical bandwidth-controlled Mott transition. The criticality indicates a weaker charge and density instability in contrast to the filling-controlled transition realized by carrier doping, implying a weaker instability to superconductivity as well. The present comprehensive clarification opens up a number of routes for quantitative experimental studies for complete understanding of elusive quantum Mott transition and nearby strange metal that cultivate future design of functionality.

In recent years, certain molecular crystals have been reported to possess surprising flexibility by undergoing significant elastic or plastic deformation in response to mechanical loads. However, despite this experimental evidence, there currently exists no atomistic mechanism to explain the physical origin of this phenomenon from numerical simulations. In this study, we investigate the mechanical behavior of three naphthalene diimide derivatives, which serve as representative examples, using direct molecular dynamics simulations. Our simulation trajectory analysis suggests that molecular rotational freedom is the key factor in determining a crystal's mechanical response, ranging from brittle fracture to elastic or plastic deformation under mechanical bending. Additionally, we propose a rotation-dependent potential energy surface as a means to classify organic materials' mechanical responses and identify new candidates for future investigation.

Quantum chromodynamics (QCD)—the theory of quarks and gluons—has been studied for decades, but it is yet to be fully understood. A recent example is the prediction and experimental discovery of tetraquarks, which opened a new research field. Crucially, numerous unsolved questions regarding the standard model can exclusively be addressed by nonperturbative calculations. Quantum computers can solve problems for which well-established QCD methods are inapplicable, such as real-time evolution. We take a key step in exploring this possibility by designing a real-time evolution of tetraquark and pentaquark physics in one-dimensional SU(3) gauge theory. We also perform an experiment on a superconducting quantum computer demonstrating an elementary cell consisting of two staggered sites containing quarks and antiquarks with all three colors. This experiment represents an exciting step in quantum computation involving quarks with the gauge group of QCD.