The dynamics in a confined turbulent convection flow is dominated by multiple long-lived macroscopic circulation states that are visited subsequently by the system in a Markov-type hopping process. In the present work, we analyze the short transition paths between these subsequent macroscopic system states by a data-driven learning algorithm that extracts the low-dimensional transition manifold and the related new coordinates, which we term collective variables, in the state space of the complex turbulent flow. We therefore transfer and extend concepts for conformation transitions in stochastic microscopic systems, such as in the dynamics of macromolecules, to a deterministic macroscopic flow. Our analysis is based on long-term direct numerical simulation trajectories of turbulent convection in a closed cubic cell at a Prandtl number $\text{Pr}=0.7$ and Rayleigh numbers $\text{Ra}={10}^6$ and ${10}^7$ for a time lag of ${10}^5$ convective free-fall time units. The simulations resolve vortices and plumes of all physically relevant scales, resulting in a state space spanned by more than 3.5 million degrees of freedom. The transition dynamics between the large-scale circulation states can be captured by the transition manifold analysis with only two collective variables, which implies a reduction of the data dimension by a factor of more than a million. Our method demonstrates that cessations and subsequent reversals of the large-scale flow are unlikely in the present setup, and thus it paves the way for the development of efficient reduced-order models of the macroscopic complex nonlinear dynamical system.

Hamiltonian learning is an important procedure in quantum system identification, calibration, and successful operation of quantum computers. Through queries to the quantum system, this procedure seeks to obtain the parameters of a given Hamiltonian model and description of noise sources. Standard techniques for Hamiltonian learning require careful design of queries and $O\left({\epsilon }^{-2}\right)$ queries in achieving learning error $\epsilon$ due to the standard quantum limit. With the goal of efficiently and accurately estimating the Hamiltonian parameters within learning error $\epsilon$ through minimal queries, we introduce an active learner that is given an initial set of training examples and the ability to interactively query the quantum system to generate new training data. To ensure applicability on near-term quantum hardware, the active learner operates in batch mode as opposed to sequentially, proposing batches of queries to be made during learning. We formally specify and experimentally assess the performance of this Hamiltonian active learning (HAL) algorithm for learning the six parameters of a two-qubit cross-resonance Hamiltonian on four different superconducting IBM quantum devices. Compared with standard techniques for the same problem and a specified learning error, HAL achieves more than a $95\%$ reduction in queries required, and upwards of $33\%$ reduction over a sequential active learner. Moreover, with access to prior information on a subset of Hamiltonian parameters and given the ability to select queries with linearly (or exponentially) longer system interaction times during learning, HAL can exceed the standard quantum limit and achieve Heisenberg (or super-Heisenberg) limited convergence rates during learning.

The Markov chain Monte Carlo (MCMC) method, especially the Metropolis-Hastings (MH) algorithm, is a widely used technique for sampling from a target probability distribution $P$ on a state space $\mathrm{\Omega }$ and applied to various problems such as estimation of parameters in statistical models in the Bayesian approach. Quantum algorithms for MCMC have been proposed, yielding the quadratic speedup with respect to the spectral gap $\mathrm{\Delta }$ compared to classical counterparts. In this paper, we consider the quantum version of the MH algorithm in the case that calculating $P$ is costly because the log-likelihood $L$ for a state $x\in \mathrm{\Omega }$ is obtained via computing the sum of many terms, $\frac{1}{M}{\sum }_{i=0}^{M-1}\ell (i,x)$. We propose calculating $L$ by quantum Monte Carlo integration and combine it with the existing method called quantum simulated annealing (QSA) to generate the quantum state that encodes $P$ in amplitudes. We consider not only state generation but also finding a credible interval for a parameter, a common task in Bayesian inference. In the proposed method for credible interval calculation, the number of queries to the quantum circuit to compute $\ell$ scales on $\mathrm{\Delta }$, the required accuracy $\epsilon$, and the standard deviation $\sigma$ of $\ell$ as $\tilde{O}(\sigma /{\epsilon }^2{\mathrm{\Delta }}^{3/2})$, in contrast to $\tilde{O}(M/\epsilon {\mathrm{\Delta }}^{1/2})$ for QSA with $L$ calculated exactly. Therefore, the proposed method is advantageous if $\sigma$ scales on $M$ sublinearly. As one such example, we consider parameter estimation in a gravitational wave experiment, where $\sigma =O\left(M^{1/2}\right)$.

We explore anomalous skin effects at non-Hermitian impurities by studying their interplay with potential disorder and by exactly solving a minimal lattice model. A striking feature of the solvable single-impurity model is that the presence of anisotropic hopping terms can induce a scale-free accumulation of all eigenstates opposite to the bulk hopping direction, although the nonmonotonic behavior is fine tuned and further increasing such hopping weakens and eventually reverses the effect. The interplay with bulk potential disorder, however, qualitatively enriches this phenomenology leading to a robust nonmonotonic localization behavior as directional hopping strengths are tuned. Nonmonotonicity persists even in the limit of an entirely Hermitian bulk with a single non-Hermitian impurity.

Despite exhibiting novel radiation features, the operation of the proposed quantum free-electron laser would have the drawback that the number of emitted photons is limited by one per electron, significantly reducing the output power of such a device. We show that relying on different resonances of the initial momentum of the electrons increases the number of emitted photons, but also increases the required length of the undulator impeding an experimental realization. Moreover, we investigate how multiphoton processes influence the dynamics in the deep quantum regime.

Over the last decades, quantum optics has evolved from high-quality-factor cavities in the early experiments toward new cavity designs involving leaky modes. Despite very reliable models, in the concepts of cavity quantum electrodynamics, photon leakage is most of the time treated phenomenologically. Here, we take a different approach, and starting from first principles, we define an inside-outside representation which is derived from the original true-mode representation, in which one can determine the effective Hamiltonian and Poynting vector. Unlike the phenomenological model, they allow a full description of a leaking single photon produced in the cavity and propagating in free space. This is applied for a laser-driven atom-cavity system. In addition, we propose an atom-cavity nonresonant scheme for single-photon generation, and we rigorously analyze the outgoing single photon in time and frequency domains for different coupling regimes. Finally, we introduce a particular coupling regime ensuring adiabatic elimination for which the pulse shape of the outgoing single photon is tailored using a specifically designed driving field envelope.

Time-varying quantum channels (TVQCs) have been proposed as a model to include fluctuations of the relaxation ($T_1$) and dephasing times ($T_2$). In previous works, realizations of multiqubit TVQCs have been assumed to be equal for all the qubits of an error correction block, implying that the random variables that describe the fluctuations of $T_1$ and $T_2$ are block-to-block uncorrelated but qubit-wise perfectly correlated for the same block. In this article, we perform a correlation analysis of the fluctuations of the relaxation times of five multiqubit quantum processors. Our results show that it is reasonable to assume that the fluctuations of the relaxation and dephasing times of superconducting qubits are local to each of the qubits of the system. Based on these results, we discuss the multiqubit TVQCs when the fluctuations of the decoherence parameters for an error correction block are qubit-wise uncorrelated (as well as from block-to-block), a scenario we have named the fast time-varying quantum channel (FTVQC). Furthermore, we lower-bound the quantum capacity of general FTVQCs based on a quantity we refer to as the ergodic quantum capacity. Finally, we use numerical simulations to study the performance of quantum error correction codes when they operate over FTVQCs.

The effect of curvature on an ensemble of repulsive active Brownian particles (ABPs) moving on a spherical surface is studied. Surface curvature strongly affects the dynamics of ABPs, as it introduces a new time scale $\tau =R/v_0$, with curvature radius $R$ and propulsion velocity $v_0$, in addition to the rotational diffusion time ${\tau }_r$. The time scale $\tau$ is related to a stop-and-go motion caused by the recurrent alignment of the propulsion direction with the surface normal. This implies that motility-induced phase separation (MIPS) disappears for small $R$. Furthermore, it causes a narrowing of the MIPS regime in the phase diagram of Péclet number Pe and particle area fraction $\varphi$. Also, the phase-separation boundary at low $\varphi$ attains a turning point at small $R$, allowing for the possibility of a reentrant behavior. For a system of two pores with unequal radii connected by a small passage, the density in each pore is found to be inversely proportional to local particle mobility. Notably, this relation breaks down when MIPS occurs in either sphere or when the noise is high. ABPs move against the density gradient owing to their spatially varying velocity. The magnitude of the directional flux from one pore to the other is proportional to the particles effective diffusion constant in the pore. Moreover, fluctuations in the number of ABPs within the pores near the MIPS transition are found to induce transient MIPS states.

In this paper, we formally prove how, by cyclically varying the parameters of a generalized two-level discrete and non-Hermitian Hamiltonian, the respective state vector converts to the instantaneous eigenstate of the system in the adiabatic limit, irrespective of how the state was initially prepared or of the form of the cyclic trajectory followed within the parameter space $\left(\mathcal{R}\right)$ or of whether a singularity/exceptional point is encircled or not. Our proof also applies to continuous configurations in the limit of infinitesimally small discrete time steps. The observed mode switching behavior, which is a clear signature of the irreversible nature of non-Hermitian arrangements, can be either of symmetric (clockwise [CW] and counterclockwise [CCW] encirclements in $\mathcal{R}$ space lead to state conversion to the same instantaneous eigenstate) or asymmetric (CW and CCW encirclements in $\mathcal{R}$ space lead to state conversion to different instantaneous eigenstates). As a specific example, we investigate the case of rhombic parametric trajectories for a discrete parity-time $\left(\mathcal{P}\mathcal{T}\right)$-symmetric-like setting. Exact analytical solutions are retrieved in terms of Weber/parabolic cylinder (large rhombic loops) and Airy functions (small rhombic loops), with their asymptotic behavior dictated by the Stokes phenomenon. Both analytical derivations and numerical computations indicate that the observed mode conversion is primarily an artifact of the adiabatic character of the state vector evolution, while the encirclement or not of a singularity/exceptional point affects only the magnitude of the required adiabaticity rate for mode switching to take place. Overall, our results provide a deeper theoretical insight on slowly varying discrete non-Hermitian Hamiltonian systems, and pave the way towards exploring the dynamics underpinning the traversal of higher-dimensional cyclic parametric trajectories in the vicinity (or not) of higher-order spectral singularities for both continuous and discrete settings under linear or nonlinear conditions.

We investigate the robustness of two-qubit gates to deviations of experimental controls on a neutral atom platform utilizing Rydberg states. We construct robust controlled-Z gates—employing techniques from quantum optimal control—that retain high Bell-state fidelity $F>0.999$ in the presence of significant deviations of the coupling strength to the Rydberg state. Such deviations can arise from laser intensity noise and atomic motion in an inhomogeneous coupling field. We also discuss methods to mitigate errors due to deviations of the laser detuning. The designed pulses operate on timescales that are short compared to the fundamental decay timescale set by spontaneous emission and blackbody radiation. We account for the finite lifetime of the Rydberg state in both the optimization and fidelity calculations—this makes the gates conducive to noisy intermediate-scale quantum experiments, meaning that our protocols can reduce infidelity on near-term quantum computing devices. We calculate physical properties associated with infidelity for strontium-88 atoms—including lifetimes, polarizabilities, and blockade strengths—and use these calculations to identify optimal Rydberg states for our protocols, which allows for further minimization of infidelity.

Laser plasma instabilities, such as stimulated Raman scattering (SRS) and two-plasmon decay (TPD), are basic phenomena in intense laser science and applications. In direct-drive inertial confinement fusion (ICF) where a fuel capsule is imploded by high-power lasers, SRS and TPD are generally problematic because hot electrons (HEs) generated by SRS and TPD cause fuel preheating, whereas HEs with acceptable energy are expected to contribute to ablation pressure enhancement. In all cases, it is necessary to clarify the occurrence of SRS, TPD, and subsequent HE generation. The ablator of a fuel capsule in direct-drive ICF typically consists of carbon with a variable amount of hydrogen (H). We investigated the H effects in the ablator on SRS, TPD, and HEs under direct-drive ICF conditions at the GEKKO laser facility in planer geometry. The experimental results showed an increase in SRS, TPD, and HEs when H was present in the ablator. The analysis indicated that the variations in plasma inhomogeneity and plasma temperature obtained by H addition were insufficient to explain the observed results. Thus, the enhancement is mainly attributed to the high ion acoustic wave damping driven by the H ions into the plasmas, suggesting that Langmuir decay instability caused SRS saturation, whereas other mechanisms, such as cavitation, could overwhelm the TPD saturation. These results suggest that a suitable choice of H concentration in the ablator is critical for mitigating and controlling the extent of SRS, TPD, and HEs to achieve robust and efficient implosion in direct-drive ICF.

The $A\mathrm{Yb}C{h}_2$ ($A=\text{alkali}\text{metal}, Ch=\text{chalcogen}$) delafossites are a family of crystals which have a triangular lattice of effective $S=1/2$ moments on their Yb atoms. They hold great promise for the realization of the triangular quantum spin liquid state because of their defect-minimized growth and the ability to interchange chemical constituencies among the family. Here we use ab initio computations to evaluate the exchange couplings of four realized (and one theoretical) rhombohedral delafossite structures and examine the influence of chemical substitution on promoting the development of a quantum spin liquid state. We find good agreement with experiment regarding the antiferromagnetic nearest-neighbor exchange $J_1$, but our calculations underestimate $J_2$.

Current hardware for quantum computing suffers from high levels of noise, and so to achieve practical fault-tolerant quantum computing will require powerful and efficient methods to correct for errors in quantum circuits. Here, we explore the role and effectiveness of using noise tailoring techniques to improve the performance of error correcting codes. Noise tailoring methods such as randomized compiling (RC) convert complex coherent noise processes to effective stochastic noise. While it is known that this can be leveraged to design efficient diagnostic tools, we explore its impact on the performance of error correcting codes. Of particular interest is the important class of coherent errors, arising from control errors, where RC has the maximum effect—converting these into purely stochastic errors. For these errors, we show here that RC delivers an improvement in performance of the concatenated Steane code by several orders of magnitude. We also show that below a threshold rotation angle, the gains in logical fidelity can be arbitrarily magnified by increasing the size of the codes. These results suggest that using randomized compiling can lead to a significant reduction in the resource overhead required to achieve fault tolerance.

We present our results for simultaneous measurement of the refractive indices of gallium arsenide (GaAs) and aluminum gallium arsenide $\left({\mathrm{Al}}_x{\mathrm{Ga}}_{1\text{−}x}\mathrm{As}\right)$ in the spectral region from $2.0\mu \mathrm{m}\mathrm{to}7.1\mu \mathrm{m}$ $\left(5000{\mathrm{cm}}^{-1}\mathrm{to}1400{\mathrm{cm}}^{-1}\right)$. We obtain these values from a monocrystalline superlattice Bragg mirror of excellent purity (background doping $\le 1\times {10}^{-14}/{\mathrm{cm}}^3$), grown via molecular beam epitaxy. To recover the refractive indices over such a broad wavelength range, we fit a dispersion model for each material. In a novel combination of well-established methods, we measure both a photometrically accurate transmittance spectrum of the Bragg mirror via Fourier-transform infrared spectrometry and the individual physical layer thicknesses of the structure via scanning electron microscopy. To infer the uncertainty of the refractive index values, we estimate relevant measurement uncertainties and propagate them via a Monte Carlo method. This highly-adaptable approach conclusively yields propagated relative uncertainties on the order of ${10}^{-4}$ over the measured spectral range for both GaAs and ${\mathrm{Al}}_{0.929}{\mathrm{Ga}}_{0.071}\mathrm{As}$. The fitted model can also approximate the refractive index for MBE-grown ${\mathrm{Al}}_x{\mathrm{Ga}}_{1\text{−}x}\mathrm{As}$ for $0\le x\le 1$. Both these updated values and the measurement approach will be essential in the design, fabrication, and characterization of next-generation active and passive optical devices in a spectral region that is of high interest in many fields, e.g., laser design and cavity-enhanced spectroscopy in the mid-infrared.

We describe a numerical method that simulates the interaction of the helium atom with sequences of femtosecond and attosecond light pulses. The method, which is based on the close-coupling expansion of the electronic configuration space in a $B$-spline bipolar spherical harmonic basis, can accurately reproduce the excitation and single ionization of the atom, within the electrostatic approximation. The time-dependent Schrödinger equation is integrated with a sequence of second-order split-exponential unitary propagators. The asymptotic channel-, energy-, and angularly resolved photoelectron distributions are computed by projecting the wave packet at the end of the simulation on the multichannel scattering states of the atom, which are separately computed within the same close-coupling basis. This method is applied to simulate the pump-probe ionization of helium in the vicinity of the $2s/2p$ excitation threshold of the ${\mathrm{He}}^{+}$ ion. This work confirms the qualitative conclusions of one of our earliest publications [Argenti and Lindroth, Phys. Rev. Lett. 105, 053002 (2010)], in which we demonstrated the control of the $2s/2p$ ionization branching ratio. Here we take those calculations to convergence and show how correlation brings the periodic modulation of the branching ratios in almost phase opposition. The residual total ionization probability to the $2s+2p$ channels is dominated by the beating between the $s{p}_{2,3}^{+}$ and the $s{p}_{2,4}^{+}$ doubly excited states, which is consistent with the modulation of the complementary signal in the $1s$ channel, measured in 2010 by Chang and coworkers [Gilbertson et al., Phys. Rev. Lett. 105, 263003 (2010)].

Employing large-scale quantum Monte Carlo simulations, we systematically compute the energy spectra of the two-dimensional (2D) spin-1/2 Heisenberg model with long-range interactions. With the $1/r^{\alpha }$ ferromagnetic and staggered antiferromagnetic interactions, we find the explicit range in $\alpha$ for the short-range Goldstone-type (gapless), anomalous Goldstone-type (gapless), and Higgs-type (gapped) spectra. Accompanied by the spin-wave analysis, our numerical results vividly reveal how the long-range interactions alter the usual linear and quadratic magnon dispersions in 2D quantum magnets and give rise to anomalous dynamical exponents. Moreover, we find the explicit case where the gapped excitation emerges at a noninteger decay exponent $\alpha$ for the antiferromagnetic Hamiltonian. This work provides the first set of unbiased dynamical data of long-range quantum many-body systems and suggests that many universally accepted low-energy customs for short-range systems need to be substantially modified for long-range ones, which are of immediate relevance to the ongoing experimental efforts from quantum simulators to 2D quantum moiré materials.

Starting with the quantum brachistochrone problem of the infinitesimal form, we solve the minimal time and corresponding time-dependent Hamiltonian to drive a pure quantum state with limited resources along arbitrary preassigned trajectories. It is also shown that out of all possible trajectories with limited resources, which are physically accessible and which are not. The solution is then generalized to the mixed quantum state cases and applied to trajectories parametrized by single or multiple parameters with a discrete or continuous spectrum. We then compare the solution to that of the counterdiabatic driving and show how the Berry phase is directly involved in both driving processes.

Using a nonperturbative classical model for ionic motion through one-dimensional (1D) solids, we explore how thermal lattice vibrations affect ionic transport properties. Based on analytic and numerical calculations, we find that the mean dissipation experienced by the mobile ion is similar to that of the nonthermal case, with thermal motion only contributing stochastic noise. A nonmonotonic dependence of drag on speed, predicted in earlier work, persists in the presence of thermal motion. The inverse relation between drag and speed at high speeds results in non-Fickian diffusion dominated by Lévy flights. This suppression of drag at high speeds, combined with enhanced activation frequency, improves the particle mobility at high temperatures, where typical particles move faster.

We develop a topological classification of non-Hermitian effective Hamiltonians that depend on momentum and frequency. Such effective Hamiltonians are in one-to-one correspondence to single-particle Green's functions of systems that satisfy translational invariance in space and time but may be interacting or open. We employ $K$ theory, which for the special case of noninteracting systems leads to the well-known 10-fold-way topological classification of insulators and fully gapped superconductors. Relevant theorems for $K$ groups are reformulated and proven in the more transparent language of Hamiltonians instead of vector bundles. We obtain 54 symmetry classes for frequency-dependent non-Hermitian Hamiltonians satisfying antiunitary symmetries. Employing dimensional reduction, the group structure for all these classes is calculated. This classification leads to a group structure with one component from the momentum dependence, which corresponds to the non-Hermitian generalization of topological insulators and superconductors, and two additional parts resulting from the frequency dependence. These parts describe winding of the effective Hamiltonian in the frequency direction and in combined momentum-frequency space.