Majorana corner modes appearing in two-dimensional second-order topological superconductors have great potential applications for fault-tolerant topological quantum computations. We demonstrate that in the presence of an in-plane magnetic field, two-dimensional ($s+p$)-wave superconductors host Majorana corner modes, whose location can be manipulated by the direction of the magnetic field. In addition, we discuss the effects of edge imperfections on the Majorana corner modes. We describe how different edge shapes and edge disorder affect the number and controllability of the Majorana corner modes, which is of relevance for the implementation of topological quantum computations. We also discuss tunneling spectroscopy in the presence of the Majorana corner modes, where a lead wire is attached to the corner of the noncentrosymmetric superconductor. The zero-bias differential conductance shows a distinct periodicity with respect to the direction of the magnetic field, which demonstrates the excellent controllability of the Majorana corner modes in this setup. Our results lay the theoretical groundwork for observing and tuning Majorana corner modes in experiments on ($s+p$)-wave superconductors.

Antiresonance is a key property of dynamical systems that leads to the suppression of oscillations at select frequencies. We present the surprising example of a switched system that alternates between unstable modes, but exhibits antiresonance for a wide range of switching frequencies. We elucidate the stabilization mechanism and characterize the range of antiresonant frequencies for periodic and stochastic switching. The demonstration of antiresonance in a minimalistic variation of the Stuart-Landau model opens the door for a new paradigm in the study and design of switched systems.

Thermodynamics entails a set of mathematical conditions on quantum Markovian dynamics. In particular, strict energy conservation between the system and environment implies that the dissipative dynamical map commutes with the map of the system's unitary evolution. Employing spectral analysis, we prove the general form of the ensuing master equation. The obtained structure extends thermodynamical considerations to dynamical processes. Comparing this form with master equations obtained from microscopic derivations allows validating their compatibility with thermodynamics. It predicts that coherence is not generated spontaneously under steady-state transport. Moreover, for a bipartite system-environment it singles out the global master equation as the thermodynamically compatible choice for nondriven systems, as well as supplying insight into the validity of the secular approximation.

Simulating quantum circuits with classical computers requires resources growing exponentially in terms of system size. Real quantum computer with noise, however, may be simulated polynomially with various methods considering different noise models. In this work, we simulate random quantum circuits in one dimension with matrix product density operators (MPDOs), for different noise models such as dephasing, depolarizing, and amplitude damping. We show that the method based on matrix product states (MPSs) fails to approximate the noisy output quantum states for any of the noise models considered, while the MPDO method approximates them well. Compared with the method of matrix product operators (MPOs), the MPDO method reflects a clear physical picture of noise (with inner indices taking care of the noise simulation) and quantum entanglement (with bond indices taking care of two-qubit gate simulation). Consequently, in case of weak system noise, the resource cost of the MPDO will be significantly less than that of the MPO due to a relatively small inner dimension needed for the simulation. In case of strong system noise, a relatively small bond dimension may be sufficient to simulate the noisy circuits, indicating a regime that the noise is large enough for an “easy” classical simulation, which is further supported by a comparison with the experimental results on an IBM cloud device. Moreover, we propose a more effective tensor updates scheme with optimal truncations for both the inner and the bond dimensions, performed after each layer of the circuit, which enjoys a canonical form of the MPDO for improving simulation accuracy. With truncated inner dimension to a maximum value $\kappa$ and bond dimension to a maximum value $\chi$, the cost of our simulation scales as $\sim ND{\kappa }^3{\chi }^3$, for an $N$-qubit circuit with depth $D$.

In this paper, we investigate the dynamics of a single superconducting artificial atom capacitively coupled to a transmission line with a characteristic impedance comparable to or larger than the quantum resistance. In this regime, microwaves are reflected from the atom also at frequencies far from the atom's transition frequency. Adding a single mirror in the transmission line then creates cavity modes between the atom and the mirror. Investigating the spontaneous emission from the atom, we then find Rabi oscillations, where the energy oscillates between the atom and one of the cavity modes.

Topological superconductors represent one of the key hosts of Majorana-based topological quantum computing. Typical scenarios for one-dimensional (1D) topological superconductivity assume a broken gauge symmetry associated to a superconducting state. However, no interacting 1D many-body system is known to spontaneously break gauge symmetries. Here, we show that zero modes emerge in a many-body system without gauge symmetry breaking and in the absence of superconducting order. In particular, we demonstrate that Majorana zero modes of the symmetry-broken superconducting state are continuously connected to these zero-mode excitations, demonstrating that zero-bias anomalies may emerge in the absence of gauge symmetry breaking. We demonstrate that these many-body zero modes share the robustness features of the Majorana zero modes of symmetry-broken topological superconductors. We further show that the interface between the interacting model and a 1D topological superconductor does not support Majorana modes. We introduce a bosonization formalism to analyze these excitations and show that a ground state analogous to a topological superconducting state can be analytically found in a certain limit. Our results demonstrate that robust Majorana-like zero modes may appear in a many-body system without gauge symmetry breaking, thus introducing a family of protected excitations with no single-particle analogs.

We investigate the Hall conductance of a two-dimensional Chern insulator coupled to an environment causing gain and loss. Introducing a biorthogonal linear response theory, we show that sufficiently strong gain and loss lead to a characteristic nonanalytical contribution to the Hall conductance. Near its onset, this contribution exhibits a universal power law with a power 3/2 as a function of Dirac mass, chemical potential, and gain strength. Our results pave the way for the study of non-Hermitian topology in fermionic transport experiments.

Quantum theory is the foundation of modern physics. Some of its basic principles, such as Born's rule, however, are based on postulates which require experimental testing. Any deviation from Born's rule would result in higher-order interference and can thus be tested in an experiment. Here, we report on such a test with a quantum light source based on a color center in hexagonal boron nitride (hBN) coupled to a microcavity. Our room-temperature photon source features a narrow-linewidth, high-efficiency, high-purity, and on-demand single-photon generation. With the single-photon source we can increase the interferometric sensitivity of our three-path interferometer compared to conventional laser-based light sources by fully suppressing the detector nonlinearity. We thereby obtain a tight bound on the third-order interference term of $3.96\left(523\right)\times {10}^{-4}$. We also measure an interference visibility of 98.58% for our single photons emitted from hBN at room temperature, which provides a promising route for using the hBN platform as light source for phase-encoding schemes in quantum key distribution.

We explore the properties of steady-state noise-induced (Fano) coherences generated in a three-level V-system continuously pumped by polarized incoherent light in the absence of coherent driving. By solving the nonsecular Bloch-Redfield quantum master equation, we obtain the ratio of the stationary coherences to excited-state populations, $\mathcal{C}=(1+\frac{{\mathrm{\Delta }}^2}{\gamma (r+\gamma )}{)}^{-1}$, which quantifies the impact of steady-state coherences on excited-state dynamical observables of the V-system. The ratio is maximized when the excited-state splitting $\mathrm{\Delta }$ is small compared to either the spontaneous decay rate $\gamma$ or the incoherent pumping rate $r$. We demonstrate that while the detrimental effects of a strongly decohering environment generally suppress the coherence-to-population ratio by the factor $\simeq {\gamma }_d/\gamma$, an intriguing regime exists where the $\mathcal{C}$ ratio displays a maximum as a function of the dephasing rate ${\gamma }_d$. We attribute the surprising dephasing-induced enhancement of stationary Fano coherences to the environmental suppression of destructive interference of individual incoherent excitations generated at different times. We clarify the physical basis for the steady-state Fano coherence, whose imaginary part is identified with the nonequilibrium flux across a pair of qubits coupled to two independent thermal baths or, equivalently, the spontaneous emission flux from the right qubit to the right bath, unraveling a direct connection between the seemingly unrelated phenomena of incoherent driving of multilevel quantum systems and nonequilibrium quantum transport in qubit networks. We further establish the equivalence between the two-qubit system and a V-system, each of whose transitions is driven simultaneously by both baths. The real part of the steady-state Fano coherence is found to be proportional to the deviation of excited-state populations from their values in thermodynamic equilibrium, making it possible to observe signatures of steady-state Fano coherences in excited-state populations. Finally, we put forward an experimental proposal for observing steady-state Fano coherences by detecting the total fluorescence signal emitted by Calcium atoms excited by polarized versus isotropic incoherent light. Our analysis paves the way toward further theoretical and experimental studies of nonequilibrium coherent steady states in thermally driven atomic and molecular systems and for the exploration of their potential role in quantum thermodynamics and in biological processes.

Experimental spectroscopic studies are presented, in a 5.5–25.5 nm extreme-ultraviolet (EUV) wavelength range, of the light emitted from plasma produced by the irradiation of tin microdroplets by 5-ns-pulsed, $2\text{−}\mu \mathrm{m}$-wavelength laser light. Emission spectra are compared to those obtained from plasma driven by $1\text{−}\mu \mathrm{m}$-wavelength laser light over a range of laser intensities spanning approximately $(0.3–5)\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2$, under otherwise identical conditions. Over this range of drive laser intensities, we find that similar spectra and underlying plasma charge state distributions are obtained when keeping the ratio of 1- to $2\text{−}\mu \mathrm{m}$ laser intensities fixed at a value of 2.1(6), which is in good agreement with ralef-2d radiation-hydrodynamic simulations. Our experimental findings, supported by the simulations, indicate an approximately inversely proportional scaling $\sim {\lambda }^{-1}$ of the relevant plasma electron density, and of the aforementioned required drive laser intensities, with drive laser wavelength $\lambda$. This scaling also extends to the optical depth that is captured in the observed changes in spectra over a range of droplet diameters spanning 16–51 $\mu \mathrm{m}$ at a constant laser intensity that maximizes the emission in a 2% bandwidth around $13.5\mathrm{nm}$ relative to the total spectral energy, the bandwidth relevant for EUV lithography. The significant improvement of the spectral performance of the $2\text{−}\mu \mathrm{m}$- versus $1\text{−}\mu \mathrm{m}$ driven plasma provides strong motivation for the development of high-power, high-energy near-infrared lasers to enable the development of more efficient and powerful sources of EUV light.

We have performed accurate calculations of the hyperfine structure of the $2{}^{3}P$ state in the ${}^9\mathrm{Be}$ atom with the help of highly optimized, explicitly correlated functions, accounting for the leading finite nuclear mass, radiative, nuclear structure, and relativistic effects. By comparison with measurements, we have determined the ${}^9\mathrm{Be}$ nuclear quadrupole moment to be $Q_{\mathrm{N}}=0.05350\left(14\right)$ barns, which is not only the most accurate result but also disagrees with previous determinations.

Quantum error correction allows to actively correct errors occurring in a quantum computation when the noise is weak enough. To make this error correction competitive information about the specific noise is required. Traditionally, this information is obtained by benchmarking the device before operation. We address the question of what can be learned from only the measurements done during decoding. Such estimation of noise models was proposed for surface codes, exploiting their special structure, and in the limit of low error rates, also for other codes. However, so far it has been unclear under what general conditions noise models can be estimated from the syndrome measurements. In this work, we derive a general condition for identifiability of the error rates. For general stabilizer codes, we prove identifiability under the assumption that the rates are small enough. Without this assumption, we prove a result for perfect codes. Finally, we propose a practical estimation method with linear runtime for concatenated codes. We demonstrate that it outperforms other recently proposed methods and that the estimation is optimal in the sense that it reaches the Cramér-Rao bound. Our method paves the way for practical calibration of error corrected quantum devices during operation.

State-dependent optical tweezers can be used to trap a pair of molecules with a separation much smaller than the wavelength of the trapping light, greatly enhancing the dipole-dipole interaction between them. Here we describe a general approach to producing these state-dependent potentials using the tensor part of the ac Stark shift and show how it can be used to carry out two-qubit gates between pairs of molecules. The method is applicable to broad classes of molecules including bialkali molecules produced by atom association and those amenable to direct laser cooling.

In the electron dynamics in quantum matter, the Berry curvature of the electronic wave function provides the artificial magnetic field in momentum space, which leads to nontrivial contributions to transport coefficients. It is known that in the presence of electron-electron and/or electron-phonon interactions, there is an extra contribution to the electron dynamics due to the artificial electric field (AEF) in momentum space. In this work we construct hydrodynamic equations for the electrons in time-reversal invariant but inversion-breaking systems and find the novel hydrodynamic coefficients related to the AEF. Furthermore, we investigate the novel linear and nonlinear transport coefficients in the presence of the AEF.

Superconducting circuits incorporating Josephson tunnel junctions are widely used for fundamental research as well as for applications in fields such as quantum information and magnetometry. The quantum coherent nature of Josephson junctions makes them especially suitable for metrology applications. Josephson junctions suffice to form two sides of the quantum metrology triangle, relating frequency to either voltage or current, but not its base, which directly links voltage to current. We propose a five Josephson tunnel junction circuit in which simultaneous pumping of flux and charge results in quantized transconductance in units $4e^2/h=2e/{\mathrm{\Phi }}_0$, the ratio between the Cooper pair charge and the flux quantum. The Josephson quantized Hall conductance device (JHD) is explained in terms of intertwined Cooper pair pumps driven by the AC Josephson effect. We describe an experimental implementation of the device and discuss the optimal configuration of external parameters and possible sources of error. The JHD has a rich topological structure and demonstrates that Josephson tunnel junctions are universal, capable of interrelating frequency, voltage, and current via fundamental constants.

We introduce Weyl Josephson circuits: small Josephson junction circuits that simulate Weyl band structures. We first formulate a general approach to design circuits that are analogous to Bloch Hamiltonians of a desired dimensionality and symmetry class. We then construct and analyze a six-junction device that produces a three-dimensional (3D) Weyl Hamiltonian with broken inversion symmetry and in which topological phase transitions can be triggered in situ. We argue that currently available superconducting circuit technology allows experiments that probe topological properties inaccessible in condensed matter systems.

We image equilibrium and nonequilibrium transport through a two-dimensional electronic cavity using scanning gate microscopy. Injecting electrons into the cavity through a quantum point contact close to equilibrium, we raster scan a weakly invasive tip above the cavity region and measure the modulated conductance through the cavity. Varying the electron injection energy between $\pm 2\mathrm{meV}$, we observe that conductance minima turn into maxima beyond an energy threshold of $\pm 0.6\mathrm{meV}$. This observation bears similarity to previous measurements by Jura et al. [Phys. Rev. B 82, 155328 (2010)], who used a strongly invasive tip potential to study electron injection into an open two-dimensional electron gas. This resemblance suggests a similar microscopic origin based on electron-electron interactions.

Significant efforts are being directed toward developing a quantum simulator capable of solving combinatorial optimization problems. The challenges are Hamiltonian programming in terms of high-dimensional qubit connectivities and large-scale implementations. Here, we report a quantum simulation demonstration of Ising Hamiltonians with up to $N=22$ spins mapped on various Cayley-tree graphs. For this, we use three-dimensional arrangements of Rydberg single atoms arranged in such a way that their Rydberg atoms and blockaded strong couplings respectively represent the vertices and edges of each graph. Three different Cayley-tree graphs of $Z=3$ neighbors and of up to $S=4$ shells are constructed, and their many-body ground states and Néel's order formations are experimentally probed. The antiferromagnetic phase in regular Cayley trees and frustrated competing ground states in a dual-center Cayley tree are directly observed, demonstrating the possibilities of high-dimensional qubit connections in quantum simulators.

Localized surface plasmon and Klein tunneling resonances are two phenomena that were previously thought to be unrelated, where the former plays an important role in subwavelength optics while the latter is fundamental to relativistic quantum mechanics and physics of Dirac materials. We develop a rigorous theory for spin-1 Dirac-Weyl particles, which establishes a striking analogy between the two phenomena and unveils a deep connection between the distinct physical contexts, paving the way for gate-controlled surface plasmon mimetic electronics as well as for realizing localized spoof plasmons in a scope wider than previously thought. A possible experimental scheme is articulated.

We describe and benchmark a method to accurately calculate the quantum droplet states that can be produced from a dipolar Bose-Einstein condensate. Our approach also allows us to consider vortex states, where the atoms circulate around the long-axis of the filament-shaped droplet. We apply our approach to determine a phase diagram showing where self-bound droplets are stable against evaporation, and to quantify the energetics related to the fission of a vortex droplet into two nonvortex droplets.