In this paper, we propose the geometric mean of bipartite concurrences as a genuine multipartite entanglement measure. This measure achieves the maximum value for absolutely maximally entangled states and has desirable properties for quantifying potential quantum resources. The simplicity and symmetry in the definition facilitates its computation for various multipartite entangled states including the GHZ states and the $W$ states. With explicit examples, we show that our measure results in distinct entanglement orderings from other measures and can detect differences in certain types of genuine multipartite entanglement while other measures cannot. These results justify the potential application of our measure for tasks involving genuine multipartite entanglement.

We study a quantum stochastic neural network (QSNN) based on quantum stochastic walks on a graph, and use gradient descent to update the network parameters. We apply a toy model of QSNN with a few neurons to the problems of function approximation, two-dimensional data classification, and sequence classification. A simple QSNN with five neurons is trained to determine whether a sequence of words is a sentence or not, and we find that a QSNN can reduce the number of training steps. A QSNN with 11 neurons shows a quantum advantage in improving the accuracy of recognizing new types of inputs like verses. Moreover, with our toy model, we find the coherent QSNN is more robust against both label noise and device noise, compared with the decoherent QSNN. These results show that quantum stochastic walks may be a useful resource to implement a quantum neural network.

Previous simulation studies on human connectomes suggested that critical dynamics emerge subcritically in the so-called Griffiths phases. Now we investigate this on the largest available brain network, the 21662 node fruit-fly connectome, using the Kuramoto synchronization model. As this graph is less heterogeneous, lacking modular structure and exhibiting high topological dimension, we expect a difference from the previous results. Indeed, the synchronization transition is mean-field-like, and the width of the transition region is larger than in random graphs, but much smaller than as for the KKI-18 human connectome. This demonstrates the effect of modular structure and dimension on the dynamics, providing a basis for better understanding the complex critical dynamics of humans.

The frustrated magnet ${\mathrm{Nd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, where strong correlations together with spin-orbit coupling play a crucial role, is predicted to be a Weyl semimetal and to host topological pairs of bulk Dirac-like valleys. Here we use an external magnetic field to manipulate the localized rare-earth 4f moments coupled to the 5d electronic bands. Low-energy optical spectroscopy reveals that a field of only a few teslas suffices to create charge-compensating pockets of holes and electrons in different regions of momentum space, thus introducing a valley population shift that can be tuned with the field.

Finite-temperature Kohn-Sham density functional theory (KS-DFT) is a widely-used method in warm dense matter (WDM) simulations and diagnostics. Unfortunately, full KS-DFT-molecular dynamics models scale unfavourably with temperature and there remains uncertainty regarding the performance of existing approximate exchange-correlation (XC) functionals under WDM conditions. Of particular concern is the expected explicit dependence of the XC functional on temperature, which is absent from most approximations. Average-atom (AA) models, which significantly reduce the computational cost of KS-DFT calculations, have therefore become an integral part of WDM modeling. In this paper, we present a derivation of a first-principles AA model from the fully-interacting many-body Hamiltonian, carefully analyzing the assumptions made and terms neglected in this reduction. We explore the impact of different choices within this model—such as boundary conditions and XC functionals—on common properties in WDM, for example equation-of-state data, ionization degree and the behavior of the frontier energy levels. Furthermore, drawing upon insights from ground-state KS-DFT, we discuss the likely sources of error in KS-AA models and possible strategies for mitigating such errors.

In continuous-variable quantum computing with qubits encoded in the infinite-dimensional Hilbert space of bosonic modes, it is a difficult task to realize strong and on-demand interactions between the qubits. One option is to engineer a beamsplitter interaction for photons in two superconducting cavities by driving an intermediate superconducting circuit with two continuous-wave drives, as demonstrated in a recent experiment [Gao et al., Phys. Rev. X 8, 021073 (2018)]. Here we show how quantum optimal control theory (OCT) can be used in a systematic way to improve the beamsplitter interaction between the two cavities. We find that replacing the two-tone protocol by a three-tone protocol accelerates the effective beamsplitter rate between the two cavities. The third tone's amplitude and frequency are determined by gradient-free optimization and make use of cavity-transmon sideband couplings. We show how to further improve the three-tone protocol via gradient-based optimization while keeping the optimized drives experimentally feasible. Our work exemplifies how to use OCT to systematically improve practical protocols in quantum information applications.

On a daily commute, the shortest route from home to work rarely overlaps completely the shortest way back. We analyze this asymmetry for several cities and show that it exists even without traffic, due to a non-negligible fraction of one-way streets. For different pairs of origin-destination $\left(\mathrm{OD}\right)$, we compute the log-ratio $r=ln({\ell }_{\mathrm{D}}/{\ell }_{\mathrm{O}})$, where ${\ell }_{\mathrm{O}}$ and ${\ell }_{\mathrm{D}}$ are the lengths of the shortest routes from $\mathrm{O}$ to $\mathrm{D}$ and from $\mathrm{D}$ to $\mathrm{O}$, respectively. While its average is zero, the amplitude of the fluctuations decays as a power law of the $\mathrm{OD}$ shortest path length $r\sim {\ell }_{\mathrm{O}}^{-\beta }$. Similarly, the fraction of one-way streets in a shortest route also decays as ${\ell }_{\mathrm{O}}^{-\alpha }$. Based on semianalytic arguments, we show that $\beta =(1+\alpha )/2$. Thus, the value of the exponent $\beta$ is related to correlations in the structure of the underlying street network.

The time-resolved physical spectrum of luminescence is theoretically studied for a standard cavity quantum electrodynamics system. In contrast to the power spectrum for the steady state, the correlation functions up to the present time are crucial for the construction of the time-resolved spectrum, while the correlations with future quantities are inaccessible because of the causality, i.e., the future quantities cannot be measured until the future comes. We find that this causality plays a key role in understanding the time-resolved spectrum, in which the Rabi doublet can never be seen during the time of the first peak of the Rabi oscillation. Furthermore, the causality can influence the transient magnitude of the Rabi doublet in some situations. We also study the dynamics of the Fano antiresonance, where the difference from the Rabi doublet can be highlighted.

Entropy production (EP) is a central measure in nonequilibrium thermodynamics, as it can quantify the irreversibility of a process as well as its energy dissipation in special cases. Using the time-reversal asymmetry in a system's path probability distribution, many methods have been developed to estimate EP from only trajectory data. However, for systems with odd-parity variables that prevail in nonequilibrium systems, EP estimation via machine learning has not been covered. In this study, we develop a machine-learning method for estimating the EP in a stochastic system with odd-parity variables through multiple neural networks, which enables us to measure EP with only trajectory data and parity information. We demonstrate our method with two systems, an underdamped bead-spring model and a one-particle odd-parity Markov jump process.

We investigate several fundamental characteristics of the multiloop functional renormalization group (mfRG) flow by hands of its application to a prototypical many-electron system: the Anderson impurity model (AIM). We first analyze the convergence of the algorithm in the different parameter regions of the AIM. As no additional approximation is made, the multiloop series for the local self-energy and response functions converge perfectly to the corresponding results of the parquet approximation (PA) in the weak- to intermediate-coupling regime. Small oscillations of the mfRG solution as a function of the loop order gradually increase with the interaction, hindering a full convergence to the PA in the strong-coupling regime, where perturbative resummation schemes are no longer reliable. By exploiting the converged results, we inspect the fulfillment of (i) sum rules associated to the Pauli principle and (ii) Ward identities related to conservation laws. For the Pauli principle, we observe a systematic improvement by increasing the loop order and including the multiloop corrections to the self-energy. This is consistent with the preservation of crossing symmetries and two-particle self-consistency in the PA. For the Ward identities, we numerically confirm a visible improvement by means of the Katanin substitution. At weak coupling, violations of the Ward identity are further reduced by increasing the loop order in mfRG. In this regime, we also determine the precise scaling of the deviations of the Ward identity as a function of the electronic interaction. For larger interaction values, the overall behavior becomes more complex, and the benefits of the higher-loop terms are mostly present in the contributions at large frequencies.

Higher-order topological insulators have attracted great interest for their unconventional bulk-boundary correspondence especially gapless corner states. Here, we realize topological biphoton corner states in two-dimensional lattices. In addition to the striking state localization, the correlations in topologically nontrivial cases are more than 60 times higher than those in trivial cases and the visibility of Hong-Ou-Mandel interference for output topological corner-entangled states is higher than 90.3%. We confirm that the second-order photonic topological insulators support stable biphoton states that can maintain spatial distributions in high-dimensional Hilbert space, which have potential applications in quantum algorithms, simulation, and computation.

The prototypical system constituted by a two-level atom interacting with a quantized single-mode electromagnetic field is described by the quantum Rabi model (QRM). The QRM is potentially valid at any light-matter interaction regime, ranging from the weak (where the decay rates exceeds the coupling rate) to the deep strong coupling (where the interaction rate exceeds the bare transition frequencies of the subsystems). However, when reaching the ultrastrong coupling regime, several theoretical issues may prevent the correct description of the observable dynamics of such a system: (i) the standard quantum optics master equation fails to correctly describe the interaction of this system with the reservoirs; (ii) the correct output photon rate is no longer proportional to the intracavity photon number; and (iii) they appear to violate gauge invariance. Here, we study the photon flux emission rate of this system under the incoherent excitation of the two-level atom for any light-matter interaction strength and consider different effective temperatures. The dependence of the emission spectra on the coupling strength is the result of the interplay between energy levels, matrix elements of the observables, and the density of states of the reservoirs. Within this approach, we also study the occurrence of light-matter decoupling in the deep strong-coupling regime and show how all of the obtained results are gauge invariant.

Recently, the gapless Dirac/Weyl nodal semimetals with linear dispersion and topologically protected modes degeneracy have been rapidly growing frontiers of topological physics. Especially, type-I, type-II, and critical type-III nodal semimetals are discovered according to the tilt angles of the Dirac/Weyl cones. Here, by introducing hyperbolic metamaterials into one-dimensional photonic crystals, we design the “hypercrystal” and study the photonic fourfold degenerate Dirac nodal-line semimetals (DNLSs) with two types of perpendicularly polarized waves. Moreover, the flexibly controlled photonic DNLSs using the phase compensation effect of hyperbolic dispersion are studied. Our results not only demonstrate a platform to realize the various photonic DNLSs, where the optical polarization plays the role of electron spin in electronic DNLSs, but also may pave a way to explore the abundant Dirac/Weyl physics in the simple classical wave systems.

Pressure-induced structural transformation of known compounds has become an effective routine to obtain new materials. The sulfur motifs that are present in compounds have a considerable effect on their crystal structures and electronic properties. Here, we focus on exploring the evolution of S motifs in the $\mathrm{Ba}{\mathrm{S}}_3$ compound under high pressure. A novel $P{3}_{1}21\text{−}\mathrm{Ba}{\mathrm{S}}_3$, consisting of an equivalent V-shape ${\mathrm{S}}_3$ unit and quasi-hexagon Ba ring, is identified through the combination of first-principles swarm-intelligence search and phonon softening calculations. The bond angle in the ${\mathrm{S}}_3$ unit decreases, accompanied by pressure-induced structural phase transition. $P{3}_{1}21\text{−}\mathrm{Ba}{\mathrm{S}}_3$ shows a semiconducting character, mainly originating from the contribution of S $3p\text{−}\mathrm{electron}$ states. Along with the newly proposed $\mathrm{Ba}{\mathrm{S}}_3$ structure, the temperature effect on stability is estimated using the temperature-dependent effective potential method. For another S-rich $\mathrm{Ba}{\mathrm{S}}_2$, the disappearance of the ${\mathrm{S}}_2$ unit induced by pressure ($>150\mathrm{GPa}$) is mainly responsible for structural instability.

We describe how a coherent optical drive that is near resonant with the upper rungs of a three-level ladder system, in conjunction with a short-pulse excitation, can be used to provide a frequency-tunable source of on-demand single photons. Using an intuitive master equation model, we identify two distinct regimes of device operation: (i) for a resonant drive, the source operates using the Autler-Townes effect, and (ii) for an off-resonant drive, the source exploits the ac Stark effect. The former regime allows for a large frequency-tuning range but coherence suffers from timing jitter effects, while the latter allows for high indistinguishability and efficiency, but with a restricted tuning bandwidth due to high required drive strengths and detunings. We show how both these negative effects can be mitigated by using an optical cavity to increase the collection rate of the desired photons. We apply our general theory to semiconductor quantum dots, which have proven to be excellent single-photon sources, and find that scattering of acoustic phonons leads to excitation-induced dephasing and increased population of the higher-energy level which limits the bandwidth of frequency tuning achievable while retaining high indistinguishability. Despite this, for realistic cavity and quantum dot parameters, indistinguishabilities of over $90\%$ are achievable for energy shifts of up to hundreds of $\mu \mathrm{eV}$, and near-unity indistinguishabilities for energy shifts up to tens of $\mu \mathrm{eV}$. Additionally, we clarify the often-overlooked differences between an idealized Hong-Ou-Mandel two-photon interference experiment and its usual implementation with an unbalanced Mach-Zehnder interferometer, pointing out the subtle differences in the single-photon visibility associated with these different setups.

In this paper, we study wave propagation in generic Hermitian local periodic baths and investigate the effects of anisotropy and quasibreaking of periodicity on resonant emission into the band of the bath. We asymptotically decompose the Green's function into long-range traveling waves composed of all wave vectors (near) resonant at the emitter frequency and rapidly decaying evanescent waves. Our approximation then converges exponentially with increasing source-receiver separation $\mathit{\rho }$ when resonant wave packets with group velocity parallel to $\mathit{\rho }$ exist. In hyperbolic media this condition may not be satisfied, and we find that the exponential decay length of oscillating evanescent waves locally around caustics generally depends as a power law with exponent 3/2 on the angle made between $\mathit{\rho }$ and the caustic. For $\mathit{\rho }$ beyond the caustic we observe that the Green's function can become almost imaginary, which results in exclusively incoherent emitter-emitter interactions and allows the simulation of purely dissipative systems with short-range interactions. Here the interaction length is tunable via the separation vector of the emitters. We finally probe the hyperbolic dispersion beyond the previous regimes by applying an artificial gauge field on the lattice. We find that emission resonant with the corresponding open orbits in the Brillouin zone is quasi one dimensional, in contrast to an isotropic environment. The quasi-one-dimensional emission is further topologically protected against local and global lattice perturbations and periodically refocusing, offering a robust bidirectional transport of excitations in higher-dimensional media.

The coherent superposition of position states in a quantum walk (QW) can be precisely engineered towards the desired distributions to meet the need of quantum information applications. The coherent distribution can make full use of quantum parallel in computation and simulation. Particularly, the uniform superposition provides the robust nonlocality, which has wide applications such as the generation of genuine multibit random numbers without postprocessing. We experimentally demonstrate that the rich dynamics featured with arbitrary coherent distributions can be obtained by introducing different sets of the time- and position-dependent operations. Such a QW is realized by a resource-constant and flexible optical circuit, in which the variable operation is executed based on a Sagnac interferometer in an intrinsically stable and precisely controlled way. Our results contribute to the practical realization of quantum-walk-based quantum computation, quantum simulations, and quantum information protocols.