Large-scale quantum networks with thousands of nodes require scalable network protocols and physical hardware to realize. In this paper, we introduce packet switching as a paradigm for quantum data transmission in both future and near-term quantum networks. We propose a classical-quantum data frame structure and explore methods of frame generation and processing. Further, we present conceptual designs for a quantum reconfigurable optical add-drop multiplexer to realize the proposed transmission scheme. Packet switching allows for a universal design for a next-generation Internet where classical and quantum data share the same network protocols and infrastructure. In this quantum networking paradigm, entanglement distribution, as with quantum key distribution, is an application built on top of the quantum network rather than as a network designed especially for those purposes. For analysis of the network model, we simulate the feasibility of quantum packet switching for some preliminary models of quantum key and entanglement distribution. Finally, we discuss how our model can be integrated with other network models toward a realization of the quantum Internet.

The archetypal magnetoelectric (ME) antiferromagnet ${\mathrm{Cr}}_2{\mathrm{O}}_3$, which has the diagonal components of linear ME tensor, exhibits several different types of nonreciprocal optical effects: the electric field-induced $\left(E\text{−}\mathrm{induced}\right)$ Faraday effect, the electric field-induced magnetic circular dichroism ($E\text{−}\mathrm{induced}$ MCD), and the spontaneous nonreciprocal rotation of reflected light (NRR). In principle, antiferromagnetic (AFM) domains of ${\mathrm{Cr}}_2{\mathrm{O}}_3$ are expected to be distinguished by using these effects. However, such domain observations have never been reported mainly due to the smallness of the effects studied to date. In this study, we demonstrate that all these nonreciprocal optical effects allow the observation of AFM domains in ${\mathrm{Cr}}_2{\mathrm{O}}_3$. We first measured spectra of the $E\text{−}\mathrm{induced}$ Faraday effect and $E\text{−}\mathrm{induced}$ MCD, and found that relatively large effects appear in the visible light region. Then, by imaging spatial distributions of the three nonreciprocal effects via field and light-polarization modulation imaging techniques, we succeeded in visualizing AFM domains. Intriguingly, the domain patterns obtained via the bulk sensitive $E\text{−}\mathrm{induced}$ Faraday effect and MCD and those via the surface-sensitive NRR are identical to each other, revealing that the AFM domains in ${\mathrm{Cr}}_2{\mathrm{O}}_3$ are uniform in the thickness direction. The domain observation methods provided here will be widely applied to various ME antiferromagnets, not only insulators but also metals, with the diagonal components of linear ME tensor.

A generalized Langevin equation with fluctuating diffusivity (GLEFD) is proposed, and it is shown that the GLEFD satisfies a generalized fluctuation-dissipation relation. If the memory kernel is a power law, the GLEFD exhibits subdiffusion, non-Gaussianity, and stretched-exponential relaxation. The case in which the memory kernel is given by a single exponential function is also investigated as an analytically tractable example. In particular, the mean-square displacement and the self-intermediate-scattering function of this system show plateau structures. A numerical scheme to integrate the GLEFD is also presented.

Quantum metrology refers to the use of quantum resources in parameter-estimation protocols, aiming at enhancing its precision. The quantum Fisher information is a key quantity in this context, setting the ultimate achievable precision with respect to available resources, such as the total time of the protocol. In this work, we report a scheme where the quantum Fisher information features an exponential scaling with the protocol duration. This is achieved by performing a periodic modulation of the coupling of a quantum critical system close to the its critical value. This modulation leads to an exponential growth of the excitation number in time. Relying on the precision bound derived by Garbe et al. [L. Garbe et al., Quantum Sci. Technol. 7, 035010 (2022)], we show that the quantum Fisher information inherits this exponential time scaling, which is corroborated by numerical simulations. Finally, the impact of dissipation and finite-size effects are analyzed, showing that the exponential time scaling is robust to dissipation, although its exponent decreases for larger values of the dissipation rate. Therefore, our work illustrates the novel metrological opportunities that quantum critical systems can offer.

We theoretically predict a working principle for optical amplification, based on Weyl semimetals: When a Weyl semimetal is suitably irradiated at two frequencies, electrons close to the Weyl points convert energy between the frequencies through the mechanism of topological frequency conversion from [Martin et al., Phys. Rev. X 7, 041008 (2017)]. Each electron converts energy at a quantized rate given by an integer multiple of Planck's constant multiplied by the product of the two frequencies. In simulations, we show that optimal, but feasible band structures, can support topological frequency conversion in the “THz gap” at intensities down to $2\mathrm{W}/{\mathrm{mm}}^2$; the gain from the effect can exceed the dissipative loss when the frequencies are larger than the relaxation time of the system. Topological frequency conversion forms a paradigm for optical amplification, which further extends Weyl semimetals' promise for technological applications.

An analytic closed form solution is derived for the bound states of a two-dimensional electron gas subject to a static, inhomogeneous ($1/r$ in plane decaying) magnetic field, including the Zeeman interaction. The solution provides access to many-body properties of a two-dimensional, noninteracting, electron gas in the thermodynamic limit. Radially distorted Landau levels can be identified as well as magnetic field induced density and current oscillations close to the magnetic impurity. These radially localized oscillations depend strongly on the coupling of the spin to the magnetic field, which gives rise to nontrivial spin currents. Moreover, the Zeeman interaction introduces a unique flat band, i.e., infinitely degenerate energy level in the ground state, assuming a spin $g_s$-factor of two. Surprisingly, the charge and current densities can be computed analytically for this fully filled flat band in the thermodynamic limit. Numerical calculations show that the total magnetic response of the electron gas remains diamagnetic (similar to Landau levels) independent of the Fermi energy. However, the contribution of certain, infinitely degenerate energy levels may become paramagnetic. Furthermore, numerical computations of the Hall conductivity reveal asymptotic properties of the electron gas, which are driven by the anisotropy of the vector potential instead of the magnetic field, i.e., become independent of spin. Eventually, the distorted Landau levels give rise to negative and positive Hall conductivity phases, with sharp transitions at specific Fermi energies. Overall, our work merges “impurity” with Landau-level physics, which provides novel physical insights, not only locally, but also in the asymptotic limit. This paves the way for a large number of future theoretical as well as experimental investigations, e.g., to include electronic correlations and to investigate two-dimensional systems such as graphene or transition metal dichalcogenides under the influence of inhomogeneous magnetic fields.

We have devised an artificial intelligence algorithm with machine reinforcement learning (Q-learning) to construct remarkable entangled states with four qubits. This way, the algorithm is able to generate representative states for some of the 49 true SLOCC classes of the four-qubit entanglement states. In particular, it is possible to reach at least one true SLOCC class for each of the nine entanglement families. The quantum circuits synthesized by the algorithm may be useful for the experimental realization of these important classes of entangled states and to draw conclusions about the intrinsic properties of our universe. We introduce a graphical tool called the state-link graph (SLG) to represent the construction of the quality matrix (Q-matrix) used by the algorithm to build a given objective state belonging to the corresponding entanglement class. This allows us to discover the necessary connections between specific entanglement features and the role of certain quantum gates, which the algorithm needs to include in the quantum gate set of actions. The quantum circuits found are optimal by construction with respect to the quantum gate-set chosen. These SLGs make the algorithm simple, intuitive, and a useful resource for the automated construction of entangled states with a low number of qubits.

The kinetic energy fluctuation metric ${\mathrm{\Omega }}_{\mathbf{K}}\left(t\right)$ is modified to extract the dynamical friction in non-Markovian scenarios to circumvent Markovian scenarios. Dynamical friction is calculated from the ratio ${\mathrm{\Omega }}_{\mathbf{K}}\left(0\right)/{\mathrm{\Omega }}_{\mathbf{K}}\left(t\right)$, which obeys a universal scaling law. Both analytical and numerical results of a minimal non-Markovian model substantiate the validity of the modified kinetic energy fluctuation metric. We reveal that previous studies on the rates of relaxation in harmonically bounded proteins, which are somewhat larger than those resulting from the experimental fit, may have neglected non-Markovian effects. When applying the metric to a system subjected to thermal broadband colored noise in the harmonic potential, resonance phenomenon occurs. Specifically, dynamical friction varies nonmonotonically with the frequency of the harmonic potential. The optimal frequency inducing the strongest dynamical friction matches well with the peak frequency of power spectrum of thermal broadband colored noise. The system then approaches to equilibrium rapidly. For an acoustic phonon spectrum, the resonance for dynamical friction provides further insight as to why complete thermalization only occurs when the particle frequency of the system is within a certain range of the environment particle frequencies. This is because the closer the potential frequency is to the central value of the range of frequencies, the stronger is the dynamical friction induced.

Quantum parameter estimation promises a high-precision measurement in theory; however, how to design the optimal scheme in a specific scenario, especially under a practical condition, is still a serious problem that needs to be solved case by case due to the existence of multiple mathematical bounds and optimization methods. Depending on the scenario considered, different bounds may be more or less suitable, both in terms of computational complexity and the tightness of the bound itself. At the same time, the metrological schemes provided by different optimization methods need to be tested against realization complexity, robustness, etc. Hence, a comprehensive toolkit containing various bounds and optimization methods is essential for the scheme design in quantum metrology. To fill this vacancy, here we present a Python-Julia-based open-source toolkit for quantum parameter estimation, which includes many well-used mathematical bounds and optimization methods. Utilizing this toolkit, all procedures in the scheme design, such as the optimizations of the probe state, control and measurement, can be readily and efficiently performed.

We provide two inequalities for estimating adiabatic fidelity in terms of two other more handily calculated quantities, i.e., generalized orthogonality catastrophe and quantum speed limit. As a result of considering a two-dimensional subspace spanned by the initial ground state and its orthogonal complement, our method leads to stronger bounds on adiabatic fidelity than those previously obtained. One of the two inequalities is nearly sharp when the system size is large, as illustrated using a driven Rice-Mele model, which represents a broad class of quantum many-body systems whose overlap of different instantaneous ground states exhibits orthogonality catastrophe.

A Kerr nonlinear parametric oscillator (KPO) is one of the promising devices used to realize qubits for universal quantum computing. The KPO can stabilize two coherent states with opposite phases, yielding a quantum superposition called a Schrödinger cat state. Universal quantum computing with KPOs requires three kinds of quantum gates: $R_z,R_x$, and $R_{zz}$ gates. We theoretically propose a two-qubit gate $R_{zz}$ for highly detuned KPOs. In the proposed scheme, we add a parametric drive for the first KPO. This leads to the $R_{zz}$ gate based on the driving of the second KPO depending on the first-KPO state, which we call “conditional driving.” First, we perform simulations using a conventional KPO Hamiltonian derived from a superconducting-circuit model under some approximations and evaluate the gate fidelity. Next, we also perform numerical simulations of the two-qubit gate using the superconducting-circuit model without the approximations. The simulation results indicate that the conditional-driving gates can be implemented with high fidelity ($>99.9\%$) for rotation angles required for universality.

Excited atomic states of neutral einsteinium were investigated by resonant laser ionization using 10 pg $(2\times {10}^{10}$ atoms) of ${}^{254}\mathrm{Es}$. Ten transitions from the ${5f}^{11}7s{}^2{}^{4}I_{15/2}^o$ ground state to even-parity states were investigated in detail, via studies of lifetimes and further excitation steps into higher-lying odd-parity states below and above the first ionization potential. This led to the identification of 37 previously unknown odd-parity energy levels in the region between $37000$ and $42500\mathrm{cm}{}^{-1}$ and a number of autoionizing states, which ensure a high ion yield in resonant ionization. Rydberg states were identified and the corresponding Rydberg series converging either to the ionic ground or an excited state were analyzed to determine the first ionization potential of einsteinium to a value of $E_{\text{IP}}=51364.58{\left(14\right)}_{\mathrm{stat}}{\left(50\right)}_{\mathrm{sys}}\mathrm{cm}{}^{-1}$, improving the previous result by a factor of four.

A powerful feature of stabilizer error correcting codes is the fact that stabilizer measurement projects arbitrary errors to Pauli errors, greatly simplifying the physical error correction process as well as classical simulations of code performance. However, logical non-Clifford operations can map Pauli errors to non-Pauli (Clifford) errors, and while subsequent stabilizer measurements will project the Clifford errors back to Pauli errors the resulting distributions will possess additional correlations that depend on both the nature of the logical operation and the structure of the code. Previous work has studied these effects when applying a transversal $T$ gate to the three-dimensional color code and shown the existence of a nonlocal “linking charge” phenomenon between membranes of intersecting errors. In this paper we generalise these results to the case of a $CCZ$ gate in the three-dimensional surface code and find that many aspects of the problem are much more easily understood in this setting. In particular, the emergence of linking charge is a local effect rather than a nonlocal one. We use the relative simplicity of Clifford errors in this setting to simulate their effect on the performance of a single-shot magic state preparation process and find that their effect on the threshold is largely determined by probability of $X$ errors occurring immediately prior to the application of the gate, after the most recent stabilizer measurement.

Artificial intelligence using neural networks has achieved remarkable success. However, optimization procedures of the learning algorithms require global and synchronous operations of variables, making it difficult to realize neuromorphic hardware, a promising candidate of low-cost and energy-efficient artificial intelligence. The optimization of learning algorithms also fails to explain the recently observed criticality of the brain. Cortical neurons show a critical power law implying the best balance between expressivity and robustness of the neural code. However, the optimization gives less robust codes without the criticality. To solve these two problems simultaneously, we propose a model neural network, dual sampling neural network, in which both neurons and synapses are commonly represented as a probabilistic bit like in the brain. The network can learn external signals without explicit optimization and stably retain memories while all entities are stochastic because seemingly optimized macroscopic behavior emerges from the microscopic stochasticity. The model reproduces various experimental results, including the critical power law. Providing a conceptual framework for computation by microscopic stochasticity without macroscopic optimization, the model will be a fundamental tool for developing scalable neuromorphic devices and revealing neural computation and learning.