Understanding of unconventional superconductivity is crucial for engineering materials with specific order parameters or elevated superconducting transition temperatures. However, for many materials, the pairing mechanism and symmetry of the order parameter remain unclear: reliable and efficient methods of predicting the order parameter and its response to tuning parameters are lacking. Here, we investigate the response of superconductivity in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ to structural distortions via the random phase approximation (RPA) and functional renormalization group (FRG), starting from realistic models of the electronic structure. Our results suggest that RPA misses the interplay of competing fluctuation channels. FRG reproduces key experimental findings. We predict a magic octahedral rotation angle, maximizing the superconducting $T_c$ and a dominant $d_{x^2-y^2}$ pairing symmetry. To enable experimental verification, we provide calculations of the phase-referenced Bogoliubov Quasiparticle Interference imaging. Our work demonstrates a designer approach to tuning unconventional superconductivity with relevance and applicability for a wide range of quantum materials.

On a global level, ecological communities are being perturbed at an unprecedented rate by human activities and environmental instabilities. Yet, we understand little about what factors facilitate or impede long-term persistence of these communities. While observational studies indicate that increased biodiversity must, somehow, be driving stability, theoretical studies have argued the exact opposite viewpoint instead. This encouraged many researchers to participate in the ongoing diversity-stability debate. Within this context, however, there has been a severe lack of studies that consider spatial features explicitly, even though nearly all habitats are spatially embedded. To this end, we study here the linear stability of meta-ecosystems on networks that describe how discrete patches are connected by dispersal between them. By combining results from random-matrix theory and network theory, we are able to show that there are three distinct features that underlie stability: edge density, tendency to triadic closure, and isolation or fragmentation. Our results appear to further indicate that network sparsity does not necessarily reduce stability, and that connections between patches are just as important, if not more so, to consider when studying the stability of large ecological systems.

We study topological states of matter in quasicrystals, which do not rely on crystalline order. In the absence of a band-structure description and spin-orbit coupling, we show that a three-dimensional quasicrystal can nevertheless form a topological insulator. It relies on a combination of noncrystallographic rotational symmetry of quasicrystals and electronic orbital space symmetry, which is the quasicrystalline counterpart of the topological crystalline insulator. The resulting topological state obeys a nontrivial twisted bulk-boundary correspondence and lacks a good metallic surface. The topological surface states, localized on the top and bottom planes respecting the quasicrystalline symmetry, exhibit a different kind of multifractality with probability density concentrated mostly on high-symmetry patches. They form a near-degenerate manifold of immobile states whose number scales proportionally to the macroscopic sample size. This can present an opportunity for a platform for topological surface physics distinct from the crystalline counterpart.

We consider a discrete-time random walk on a line starting at $x_0\ge 0$ where a cost is incurred at each jump. We obtain an exact analytical formula for the distribution of the total cost of a trajectory until the process crosses the origin for the first time. The formula is valid for arbitrary jump distribution and cost function (heavy and light tailed alike), provided they are symmetric and continuous. We analyze the formula in different scaling regimes and find a high degree of universality with respect to the details of the jump distribution and the cost function. Applications are given to the motion of an active run-and-tumble particle in one dimension and extensions to multiple cost variables are considered. The analytical results are in perfect agreement with numerical simulations.

We are presenting an all-optical platform for on-demand and nonintrusive studies of coalescence of micron-sized liquid droplets in air. The platform has the purpose to mimic the airborne conditions occurring in typical environments where droplet interactions are involved. By means of the Förster resonance energy transfer mechanism, we have been able to track the dynamics of two coalescing glycerol droplets, with a radius of $\sim 10\mu \mathrm{m}$ and a temporal resolution of $86\mu \mathrm{s}$. At the onset of coalescence, a fast mixing is observed. Such an effect depletes the fluorescence of the donor fluorophore to half its initial intensity on a timescale below the temporal resolution of our platform, whereas a complete mixing is observed to occur on a timescale of seconds. The experimental platform design and findings facilitate an increased understanding of the microphysics of collisions, coalescence, and the subsequent mixing/diffusion of droplets on the micrometer lengthscale and the microsecond timescale.

Two nonidentical quantum emitters, when placed within a cavity and coherently excited at the two-photon resonance, can reach stationary states of nearly maximal entanglement. In Vivas-Viaña, Martín-Cano, and Sánchez Muñoz [Phys. Rev. Lett. 133, 173601 (2024)], we introduce a frequency-resolved Purcell effect stabilizing entangled $W$ states among strongly interacting quantum emitters embedded in a cavity. Here we delve deeper into a specific configuration with a particularly rich phenomenology: two interacting quantum emitters under coherent excitation at the two-photon resonance. This scenario yields two resonant cavity frequencies where the combination of two-photon driving and Purcell-enhanced decay stabilizes the system into the subradiant and superradiant states, respectively. By considering the case of nondegenerate emitters and exploring the parameter space of the system, we show that this mechanism is merely one among a complex family of phenomena that can generate both stationary and metastable entanglement when driving the emitters at the two-photon resonance. We provide a global perspective of this landscape of mechanisms and contribute analytical characterizations and insights into these phenomena, establishing connections with previous reports in the literature and discussing how some of these effects can be optically detected.

Despite the attempts to apply a quantum annealer to Boltzmann sampling, it is still impossible to perform accurate sampling at arbitrary temperatures. Conventional distribution correction methods such as importance sampling and resampling cannot be applied, because the analytical expression of sampling distribution is unknown for a quantum annealer. Stein correction [Q. Liu and J. Lee, in Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, Proceedings of Machine Learning Research (PMLR, 2017), Vol. 54, pp. 952–961] can correct the samples by weighting without the knowledge of the sampling distribution, but the naive implementation requires the solution of a large-scale quadratic program, hampering usage in practical problems. In this article, a fast and approximate method based on a random feature map and exponentiated gradient updates is developed to compute the sample weights and is used to correct the samples generated by $\mathrm{D}$-Wave quantum annealers. In benchmarking problems, it is observed that the residual error of thermal average calculations is reduced significantly. If combined with our method, quantum annealers may emerge as a viable alternative to long-established Markov chain Monte Carlo methods.

We study multifractal properties in time evolution of a single particle subject to repeated measurements. For quantum systems, we consider circuit models consisting of local unitary gates and local projective measurements. For classical systems, we consider models for estimating the trajectory of a particle evolved under local transition processes by partially measuring particle occupations. In both cases, multifractal behaviors appear in the ensemble of wave functions or probability distributions conditioned on measurement outcomes after a sufficiently long time. While the nature of particle transport (diffusive or ballistic) qualitatively affects the multifractal properties, they are even quantitatively robust to the measurement rate or specific protocols. On the other hand, multifractality is generically lost by generalized measurements allowing erroneous outcomes or by postselection of the outcomes with no particle detection. We demonstrate these properties by numerical simulations and also propose several simplified models, which allow us to analytically obtain multifractal properties in the monitored single-particle systems.

In recent years, Quantum Machine Learning (QML) has increasingly captured the interest of researchers. Among the components in this domain, activation functions hold a fundamental and indispensable role. Our research focuses on the development of activation functions quantum circuits for integration into fault-tolerant quantum computing architectures, with an emphasis on minimizing $T$-depth. Specifically, we present novel implementations of ReLU and leaky ReLU activation functions, achieving constant $T$-depths of 4 and 8, respectively. Leveraging quantum lookup tables, we extend our exploration to other activation functions such as the sigmoid. This approach enables us to customize precision and $T$-depth by adjusting the number of qubits, making our results more adaptable to various application scenarios. This study represents a significant advancement towards enhancing the practicality and application of quantum machine learning.

We present a theoretical study of the scattering of spin waves by a domain wall (DW) in a ferrimagnetic (FiM) spin chain in which two sublattices carry spins of unequal magnitudes. We find that a narrow but atomically smooth FiM DW exhibits a different behavior in comparison with similarly smooth ferromagnetic and antiferromagnetic DWs due to the inequivalence of the two sublattices. Specifically, for sufficiently weak anisotropy, the smaller spin at the center of the DW is found to become precisely normal to the easy axis, selecting an arbitrary direction in the $xy$ plane and thereby breaking the U(1) spin-rotational symmetry spontaneously. This particular form of a FiM DW does not occur in antiferromagnetic systems and is shown to lead to a strong dependence of spin-wave scattering pattern on the state of polarization of the spin wave, which can be either right-handed or left-handed, suggesting the utilization of such a narrow DW as a spin-wave filter. Moreover, we find that in the case of an atomically sharp DW, where all the spins point either up or down due to strong easy-axis anisotropy and therefore the polarization of the spin wave is conserved upon transmission, the wave vector of the spin-wave changes after passing through the DW leading to a change in the group velocity of the spin wave. This change of the wave vector indicates the acceleration or deceleration of the spin waves and thus a sharp FiM DW could serve as a spin-wave accelerator or decelerator in spintronics devices, offering a functionality absent in a ferromagnetic and an antiferromagnetic counterpart. Our results indicate that FiM spin textures can interact with spin waves distinctly from ferromagnetic and antiferromagnetic counterparts, suggesting that they may offer spin-wave functionalities that are absent in more conventional magnets.

We theoretically investigate the properties of magnetically levitated superconducting elements confined in anti-Helmholtz traps, for application in magnetomechanical experiments. We study both the translational modes and the librational mode. The librational mode gives an additional degree of freedom that levitated spheres do not have access to. We compare levitated particles of different shapes: ellipsoids (with analytical and numerical treatment), cylinders, and rectangular cuboids (numerical treatment). We find that the stable orientations of the particles depend on their aspect ratios.

We study whether a generic isolated quantum system initially set out of equilibrium can be considered as localized close to its initial state. Our approach considers the time evolution in the Krylov basis, which maps the system's dynamics onto that of a particle moving in a one-dimensional lattice where both the energy in the lattice sites and the tunneling from one lattice site to the next are inhomogeneous. By tying the dynamical propagation in the Krylov basis to that in the basis of microstates, we infer qualitative criteria that allow distinguishing systems that remain localized close to their initial state from systems that undergo quantum thermalization. These criteria are system-dependent and involve the expectation values and standard deviations of both the coupling strengths between Krylov states and their energy. We verify their validity by inspecting two cases: Anderson localization as a function of dimension and the out-of-equilibrium dynamics of a many-body dipolar spin system. We finally investigate the Wigner surmise and the eigenstate thermalization hypothesis that have both been proposed to characterize quantum chaotic systems. We show that when the average value of the nondiagonal terms in the Lanczos matrix is large compared to their fluctuations and to the fluctuations of the energy expectation values, which typically corresponds to delocalized quantum systems according to our criteria, there can be level repulsion of eigenenergies (also known as spectral rigidity), similar to that of the Wigner-Dyson statistics of energy levels; and we also demonstrate that in the same regime, the expectation values of typical local observables only weakly vary as a function of eigenstates, an important condition for the eigenstate thermalization hypothesis. Our demonstration assumes that, in the chaotic regime, the observable is sufficiently diagonal in the basis of Krylov states.

Generalized quantum impurity models—which feature a few localized and strongly correlated degrees of freedom coupled to itinerant conduction electrons—describe diverse physical systems, from magnetic moments in metals to nanoelectronics quantum devices such as quantum dots or single-molecule transistors. Correlated materials can also be understood as self-consistent impurity models through dynamical mean-field theory. Accurate simulation of such models is challenging, especially at low temperatures, due to many-body effects from electronic interactions, resulting in strong renormalization. In particular, the interplay between local impurity complexity and Kondo physics is highly nontrivial. A common approach, which we further develop in this work, is to consider instead a simpler effective impurity model that still captures the low-energy physics of interest. The mapping from a bare to an effective model is typically done perturbatively, but even this can be difficult for complex systems, and the resulting effective model parameters can nevertheless be quite inaccurate. Here we develop a nonperturbative, unsupervised machine learning approach to systematically obtain low-energy effective impurity-type models, based on the renormalization-group framework. The method is shown to be general and flexible, as well as accurate and systematically improvable. We benchmark the method against exact results for the Anderson impurity model, and we provide an outlook for more complex models beyond the reach of existing methods.

Weak values of quantum observables are a powerful tool for investigating quantum phenomena. Some methods for measuring weak values in the laboratory require weak interactions and postselection, while others are deterministic, but require statistics over a number of experiments that grows linearly with the dimension of the measured system in the worst case over all possible observables. Here we propose a deterministic dimension-independent scheme for estimating weak values of arbitrary observables. The scheme is based on controlled SWAP operations and associates states and observables in the mathematical expression of the weak value to preparations devices and measurement devices in the experimental setup, respectively. Thanks to this feature, it provides insights into the relation between states of two identical quantum systems at a single moment of time and states of a single quantum system at two moments of time, also known as two-time states. Specifically, our scheme provides an alternative expression for two-time states and establishes a link between two-time states accessible through the controlled-SWAP scheme and bipartite quantum states with positive partial transpose.