Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the evolution of classical computation, an alternative paradigm merging the flexibility of digital quantum computation with the robustness of analog quantum simulation has emerged. This universal paradigm is known as digital-analog quantum computing. Here, we introduce an efficient digital-analog quantum algorithm to compute the quantum Fourier transform, a subroutine widely employed in several relevant quantum algorithms. We show that, under reasonable assumptions about noise models, the fidelity of the quantum Fourier transformation improves considerably using this approach when the number of qubits involved grows. This suggests that, in the noisy intermediate-scale quantum era, hybrid protocols combining digital and analog quantum computing could be a sensible approach to reach useful quantum supremacy.

Contextuality is a signature of operational nonclassicality in the outcome statistics of an experiment. This notion of nonclassicality applies to a breadth of physical phenomena. Here, we establish its relation to two fundamental nonclassical entities in quantum theory; measurement incompatibility and steering. We show that each is necessary and sufficient the failure of operational contextuality. We exploit the established connection to contextuality to provide a novel approach to problems in measurement incompatibility and steering.

A disordered material that cannot relax to equilibrium, such as an amorphous or glassy solid, responds to deformation in a way that depends on its past. In experiments we train a two-dimensional athermal amorphous solid with oscillatory shear, and show that a suitable readout protocol reveals the shearing amplitude. When shearing alternates between two amplitudes, signatures of both values are retained only if the smaller one is applied last. We show that these behaviors arise because individual clusters of rearrangements are hysteretic and dissipative, and because different clusters respond differently to shear. These roles for hysteresis and disorder are reminiscent of the return-point memory seen in ferromagnets and many other systems. Accordingly, we show how a simple model of a ferromagnet can reproduce key results of our experiments and of previous simulations. Unlike ferromagnets, amorphous solids' disorder is unquenched; they require “training” to develop this behavior.

We show that homogeneous lattice gauge theories can realize nonequilibrium quantum phases with long-range spatiotemporal order protected by gauge invariance instead of disorder. We study a kicked ${\mathbb{Z}}_2$-Higgs gauge theory and find that it breaks the discrete temporal symmetry by a period doubling. In a limit solvable by Jordan-Wigner analysis we extensively study the time-crystal properties for large systems and further find that the spatiotemporal order is robust under the addition of a solvability-breaking perturbation preserving the ${\mathbb{Z}}_2$ gauge symmetry. The protecting mechanism for the nonequilibrium order relies on the Hilbert space structure of lattice gauge theories, so that our results can be directly extended to other models with discrete gauge symmetries.

An accurate calculation of the properties of quantum many-body systems is one of the most important yet intricate challenges of modern physics and computer science. In recent years, the tensor network ansatz has established itself as one of the most promising approaches enabling striking efficiency of simulating static properties of one-dimensional systems and abounding numerical applications in condensed matter theory. In higher dimensions, however, a connection to the field of computational complexity theory has shown that the accurate normalization of the two-dimensional tensor networks called projected entangled pair states (PEPS) is $\#\mathsf{P}$-complete. Therefore an efficient algorithm for PEPS contraction would allow solving exceedingly difficult combinatorial counting problems, which is considered highly unlikely. Due to the importance of understanding two- and three-dimensional systems the question currently remains: Are the known constructions typical of states relevant for quantum many-body systems? In this work, we show that an accurate evaluation of normalization or expectation values of PEPS is as hard to compute for typical instances as for special configurations of highest computational hardness. We discuss the structural property of average-case hardness in relation to the current research on efficient algorithms attempting tensor network contraction, hinting at a wealth of possible further insights into the average-case hardness of important problems in quantum many-body theory.

The motion of a neutrally buoyant, rigid circular cylinder in simple shear flow of a Newtonian fluid between parallel walls is calculated for various particle Reynolds numbers, ${\mathrm{Re}}_p=G{a}^2/\nu$, via the lattice Boltzmann method. Here, $G$ is the velocity gradient of the ambient shear, $a$ is the radius of the particle cross section, and $\nu$ is the kinematic viscosity of the fluid. An inertial lift force perpendicular to the ambient shear has a single zero crossing at the center of the channel below a critical ${\mathrm{Re}}_p$, corresponding to a single transverse equilibrium position. Above this critical ${\mathrm{Re}}_p$, the equilibrium position undergoes a pitchfork bifurcation, with an unstable zero-force equilibrium at the center and two equidistant stable equilibria off center. The trajectories of a force- and torque-free particle reach the stable equilibria independently of the initial particle position, with the exception of the aforementioned unstable equilibria. The critical ${\mathrm{Re}}_p$ increases with increasing confinement ratio $\kappa$ (i.e., the ratio of the radius of the particle cross section to channel width) and occurs below the transition to unsteady flow. Finally, we suggest how this inertial bifurcation could be used to develop novel particle separation techniques.

Despite successful modeling of graphene as a 0.34-nm-thick optical film synthesized by exfoliation or chemical vapor deposition (CVD), graphene-induced shift of surface-plasmon resonance (SPR) of gold films has remained controversial. Here we report the resolution of this controversy by developing a clean CVD graphene transfer method and extending Maxwell-Garnett effective-medium theory (EMT) to two-dimensional (2D) materials. A SPR shift of 0.24° is obtained and it agrees well with 2D EMT in which wrinkled graphene is treated as a 3-nm graphene/air layered composite, in agreement with the average roughness measured by atomic force microscopy. Because the anisotropic built-in boundary condition of 2D EMT is compatible with graphene's optical anisotropy, graphene can be modeled as a film thicker than 0.34 nm without changing its optical property; however, its actual roughness, i.e., effective thickness, will significantly alter its response to strong out-of-plane fields, leading to a larger SPR shift.

We construct the effective field theory for time-reversal symmetry-breaking multi-Weyl semimetals (MWSMs), composed of a single pair of Weyl nodes of (anti)monopole charge $n$, with $n=1,2,3$ in crystalline environment. From both the continuum and lattice models, we show that a MWSM with $n>1$ can be constructed by placing $n$ flavors of linearly dispersing simple Weyl fermions (with $n=1$) in a bath of an $\text{SU}\left(2\right)$ non-Abelian static background gauge field. Such an $\text{SU}\left(2\right)$ field preserves certain crystalline symmetry (fourfold rotational or $C_4$ in our construction), but breaks the Lorentz symmetry, resulting in nonlinear band spectra, namely, $E\sim {(p_x^2+p_y^2)}^{n/2}$, but $E\sim |p_z|$, for example, where momenta $\mathbf{p}$ is measured from the Weyl nodes. Consequently, the effective field theory displays $\text{U}\left(1\right)\times \text{SU}\left(2\right)$ non-Abelian anomalies, yielding the anomalous Hall effect, its non-Abelian generalization, and various chiral conductivities. The anomalous violation of conservation laws is determined by the monopole charge $n$ and a specific algebraic property of the $\text{SU}\left(2\right)$ Lie group, which we further substantiate by numerically computing the regular and isospin densities from the lattice models of MWSMs. These predictions are also supported from a strongly coupled (holographic) description of MWSMs. Altogether our findings unify the field-theoretic descriptions of MWSMs of arbitrary monopole charge $n$ (featuring $n$ copies of the Fermi arc surface states), predict signatures of non-Abelian anomaly in table-top experiments, and pave the way to explore the structure of anomalies for multifold fermions, transforming under arbitrary half-integer or integer spin representations.

Quantum impurity models are prevalent throughout many body physics, providing some prime examples of strongly correlated systems. Aside from being of great interest in themselves, they can provide deep insight into the effects of strong correlations in general. The classic example is the Kondo model wherein a magnetic impurity is screened at low energies by a noninteracting metallic bath. Here we consider a magnetic impurity coupled to a quantum wire with pairing interaction which dynamically generates a mass gap. Using Bethe ansatz, we solve the system exactly finding that it exhibits both screened and unscreened phases for an antiferromagnetic impurity. We determine the ground-state density of states and magnetization in both phases as well as the excitations. In contrast to the well studied case of magnetic impurities in superconductors, we find that there are no intragap bound states in the spectrum. The phase transition is not associated to a level crossing but with quantum fluctuations.

We introduce valence bond fluctuations, or bipartite fluctuations associated to bond-bond correlation functions, to characterize quantum spin liquids and the entanglement properties of them. Using analytical and numerical approaches, we find an identical scaling law between valence bond fluctuations and entanglement entropy in the two-dimensional Kitaev spin model and in one-dimensional chain analogs. We also show how these valence bond fluctuations can locate, via the linear scaling prefactor, the quantum phase transitions between the three gapped and the gapless Majorana semimetal phases in the honeycomb model. We then study the effect of a uniform magnetic field along the [111] direction opening a gap in the intermediate phase which becomes topological. We still obtain a robust signal to characterize the transitions toward the three gapped phases. The area-law behavior of such bipartite fluctuations in two dimensions is also distinguishable from the one in the Néel magnetic state that follows a volume square growth.

Two-loop self-energy corrections to the bound-electron $g$ factor are investigated theoretically to all orders in the nuclear binding strength parameter $Z\alpha$. The separation of divergences is performed by dimensional regularization, and the contributing diagrams are regrouped into specific categories to yield finite results. We evaluate numerically the loop-after-loop terms, and the remaining diagrams by treating the Coulomb interaction in the electron propagators up to first order. The results show that such two-loop terms are mandatory to take into account for projected near-future stringent tests of quantum electrodynamics and for the determination of fundamental constants through the $g$ factor.

Scalable quantum information processing will require quantum networks of qubits with the ability to coherently transfer quantum states between the desired sender and receiver nodes. Here we propose a scheme to implement a quantum router that can direct quantum states from an input qubit to a preselected output qubit. The path taken by the transferred quantum state is controlled by the state of one or more ancilla qubits. This enables directed transport between a sender and a number of receiver nodes, as well as generation of distributed entanglement in the network. We demonstrate the general idea using a two-output setup and discuss how the quantum routing may be expanded to several outputs. We also present a possible realization of our ideas with superconducting circuits.

The dynamics of active particles is of interest at many levels and is the focus of theoretical and experimental research. There have been many attempts to describe the dynamics of particles affected by random active forces in terms of an effective temperature. This kind of description is tempting due to the similarities (or lack thereof) to systems in or near thermal equilibrium. However, the generality and validity of the effective temperature is not yet fully understood. Here we study the dynamics of trapped particles subjected to both thermal and active forces. The particles are not overdamped. Expressions for the effective temperature due to the potential and kinetic energies are derived, and they differ from each other. A third possible effective temperature can be derived from the escape time of the particle from the trap, using a Kramers-like expression for the mean escape time. We find that over a large fraction of the parameter space, the potential energy effective temperature is in agreement with the escape temperature, while the kinetic effective temperature only agrees with the former two in the overdamped limit. Moreover, we show that the specific implementation of the random active force, and not only its first two moments and the two point autocorrelation function, affects the escape-time distribution.

We propose two-dimensional (2D) Ising-type ferromagnetic semiconductors ${\mathrm{TcSiTe}}_3, {\mathrm{TcGeSe}}_3$, and ${\mathrm{TcGeTe}}_3$ with high Curie temperatures around 200–500 K. Owing to large spin-orbit couplings, the large magnetocrystalline anisotropy energy (MAE), large anomalous Hall conductivity, and large magneto-optical Kerr effect were discovered in these intriguing 2D materials. By comparing all possible 2D $M{\text{GeTe}}_3$ materials ($M=3d,4d,5d$ transition metals), we found a large orbital moment around $0.5{\mu }_B$ per atom and a large MAE for ${\mathrm{TcGeTe}}_3$. The large orbital moments are revealed to be from the comparable crystal fields and electron correlations in these Tc-based 2D materials. The microscopic mechanism of the high Curie temperature is also addressed. Our findings reveal the unique magnetic behaviors of 2D Tc-based materials and present a family of 2D ferromagnetic semiconductors with large MAE and Kerr rotation angles that would have wide applications in designing spintronic devices.

Bloch-Boltzmann transport theory fails to describe the carrier diffusion in current crystalline organic semiconductors, where the presence of large-amplitude thermal molecular motions causes substantial dynamical disorder. The charge transport mechanism in this original situation is now understood in terms of a transient localization of the carriers' wave functions, whose applicability is, however, limited to the strong disorder regime. To deal with the ever-improving performances of new materials, we develop here a unified theoretical framework that includes transient localization theory as a limiting case and smoothly connects with the standard band description when molecular disorder is weak. The theory, which specifically addresses the emergence of dynamical localization corrections to semiclassical transport, is used to determine a “transport phase diagram” of high-mobility organic semiconductors.

We use spatially resolved magneto-optical Kerr microscopy to track the complete microstates of arrays of perpendicular anisotropy nanomagnets during magnetization hysteresis cycles. These measurements, along with our statistical methodology, allow us to disentangle the intertwined effects of nearest-neighbor interactions, disorder, and stochasticity on magnetization switching. We find that the nearest-neighbor correlations depend on both interaction strength and disorder. We also find that although the global characteristics of the hysteretic switching are repeatable, the exact microstate sampled is stochastic with the behavior of individual islands varying between nominally identical runs. These protocols provide another way of understanding the relationship between macrohistory and microhistory in artificial magnetic arrays.

Degenerate plasmas, in which quantum effects dictate the behavior of free electrons, are ubiquitous on earth and throughout space. Transitions between bound and free electron states determine basic plasma properties, yet the effects of degeneracy on these transitions have only been theorized. Here, we use an x-ray free electron laser to create and characterize a degenerate plasma. We observe a core electron fluorescence spectrum that cannot be reproduced by models that ignore free electron degeneracy. We show that degeneracy acts to restrict the available electron energy states, thereby slowing the rate of transitions to and from the continuum. We couple degeneracy and bound electron dynamics in an existing collisional-radiative code, which agrees well with observations. The impact of the shape of the cross section, and hence the magnitude of the correction due to degeneracy, is also discussed. This study shows that degeneracy in plasmas can significantly influence experimental observables such as the emission spectra, and that these effects can be included parametrically in well-established atomic physics codes. This work narrows the gap in understanding between the condensed-matter and plasma phases, which coexist in myriad scenarios.

Heliconical cholesteric liquid crystals are expected to be more sensitive to torque induced by light field since their structure allows both bend and twist in molecular orientations, differently from the conventional cholesterics in which only twist deformation is involved, requiring much higher fields. We report here a demonstration of tuning the helical pitch in heliconical cholesterics induced by an optical torque. Experimental observations are in agreement with expectations of the classical theory extended to include the effect of the optical field. A dual control of the helical pitch is achieved including both the low-frequency electric field applied along the helix axis and the optical field orthogonal to it.

We study the pump-probe response of three insulating cuprates and develop a model for its recombination kinetics. The dependence on time, fluence, and both pump and probe photon energies implies many-body recombination on femtosecond timescales, characterized by anomalously large trapping and Auger coefficients. The fluence dependence follows a universal form that includes a characteristic volume scale, which we associate with the holon-doublon excitation efficiency. This volume varies strongly with pump photon energy and peaks at nearly twice the charge-transfer energy, suggesting that the variation is caused by carrier multiplication through impact ionization.

We introduce a new class of solutions to the Laplace equation, dubbed logopoles, and use them to derive a new relation between solutions in prolate spheroidal and spherical coordinates. The main novelty is that it involves spherical harmonics of the second kind, which have rarely been considered in physical problems because they are singular on the entire $z$ axis. Logopoles, in contrast, have a finite line singularity like solid spheroidal harmonics, but are also closely related to solid spherical harmonics and can be viewed as an extension of the standard multipole ladder toward the negative multipolar orders. As part of our derivations, we also found a new integral representation for the spherical harmonics of the second kind in terms of their source distributions. As an example application, we use logopoles to construct a fast converging series solution for the problem of a point charge interaction with a dielectric sphere, which extends the basic image approximations introduced by Kelvin, Kirkwood, and Friedman. We believe these new solutions will prove a fruitful alternative to either spherical or spheroidal harmonics in a wide range of other physical problems.