We propose a simple and generic construction of the variational tensor network operators to study the quantum spin systems by the synergy of ideas from the imaginary-time evolution and the variational optimization of trial wave functions. By applying these operators to simple initial states, accurate variational ground-state wave functions with extremely few parameters can be obtained. Furthermore, the framework can be applied to spontaneously study symmetry-breaking, symmetry-protected topological, and intrinsic topologically ordered phases, and we show that symmetries of the local tensors associated with these phases can emerge directly after the optimization without any gauge fixing. This provides a universal way to identify quantum phase transitions without prior knowledge of the system.

Many biological tissues feature a heterogeneous network of fibers whose tensile and bending rigidity contribute substantially to these tissues' elastic properties. Rigidity percolation has emerged as an important paradigm for relating these filamentous tissues' mechanics to the concentrations of their constituents. Past studies have generally considered tuning of networks by spatially homogeneous variation in concentration, while ignoring structural correlation. We introduce here a model in which dilute fiber networks are built in a correlated manner that produces alternating sparse and dense regions. Our simulations indicate that structural correlation consistently allows tissues to attain rigidity with less material. We further find that the percolation threshold varies nonmonotonically with the degree of correlation, such that it decreases with moderate correlation and once more increases for high correlation. We explain the eventual reentrance in the dependence of the rigidity percolation threshold on correlation as the consequence of large, stiff clusters that are too poorly coupled to transmit forces across the network. Our study offers deeper understanding of how spatial heterogeneity may enable tissues to robustly adapt to different mechanical contexts.

Studies of twisted moiré systems have been mainly focused on two-dimensional (2D) materials such as graphene with Dirac points and transition-metal dichalcogenides so far. Here we propose a twisted bilayer of 2D systems which feature stable quadratic-band-touching points and find exotic physics different from previously studied twisted moiré systems. Specifically, we show that exactly flat bands can emerge at magic angles and, more interestingly, each flat band exhibits a high Chern number ($C=\pm 2$). We further consider the effect of Coulomb interactions in such magic-angle twisted systems and find that the ground state supports the quantum anomalous Hall effect with quantized Hall conductivity $2\frac{e^2}{hc}$ at certain filling. Furthermore, the possible physical realization of such twisted bilayer systems will be briefly discussed.

We investigate a multiqubit quantum battery-charger model, focusing on its potential emulation on a superconducting qubit chip. Using a large-spin representation, we first obtain the analytical form of the energy $E_B\left(t\right)$ and power $P_B\left(t\right)$, and their maximum values $E_B^{\max }$ and $P_B^{\max }$, of the battery part by means of the antiferromagnetic Holstein-Primakoff transformation within the low-energy approximation. In this case, our results show that superextensive scaling behavior of $P_B^{\max }$ ensues. By further combining these with the ones obtained via exact diagonalization, we classify the dynamics of various physical quantities, including the entanglement between the battery and charger parts for system sizes encompassing over 10 000 qubits. Finally, by checking a diverse set of system configurations, including either a fixed battery size with a growing number of charger qubits or when both parts simultaneously grow, we classify the system size scalings of $E_B^{\max }$ and $P_B^{\max }$, relating it with the entanglement entropy in the system. In agreement with the analytical results, robust superextensive behavior of $P_B^{\max }$ is also observed in this case. Our work provides an overall guide for expected features in experiments of quantum batteries emulated in superconducting qubit platforms, in particular ones that exhibit long-range couplings.

Quantum communication channels and quantum memories are the fundamental building blocks of large-scale quantum communication networks. Estimating their capacity to transmit and store quantum information is crucial in order to assess the performance of quantum communication systems and to detect useful communication paths among the nodes of future quantum networks. However, the estimation of quantum capacities is a challenging task for continuous-variable systems, such as the radiation field, for which a complete characterization via quantum tomography is practically unfeasible. Here we introduce a method for detecting the quantum capacity of continuous-variable communication channels and memories without performing a full process tomography. Our method works in the general scenario where the devices are used a finite number of times, can exhibit correlations across multiple uses, and can change dynamically under the control of a malicious adversary. The method is experimentally friendly and can be implemented using only finitely squeezed states and homodyne measurements.

Organoids are in vitro cellular collectives from which, for example, brain-like, or gut-like, or kidney-like structures emerge. To make quantitative predictions regarding the morphology and rheology of a cellular collective in its initial stages of development, we construct and study a three-dimensional vertex model. In such a model, the cells are represented as deformable polyhedrons with cells sharing faces such that there are no gaps between them, otherwise known as confluent. In a bulk model with periodic boundary conditions, we find a rigidity transition as a function of the target cell shape index $s_0$ with a critical value $s_0^{*}=5.39\pm 0.01$. For a confluent cellular collective with a finite boundary, and in the presence of lateral extensile and in-plane, radial extensile deformations, we find a significant boundary-bulk effect that is one-cell layer thick. More specifically, for lateral extensile deformations, the cells in the bulk are much less aligned with the direction of the lateral deformation than the cells at the boundary. For in-plane, radial deformations, the cells in the bulk exhibit much less reorientation perpendicular to the radial direction than the cells at the boundary. In other words, for both deformations, the bulk, interior cells are topologically protected from the deformations, at least over time scales much slower than the timescale for cellular rearrangements and up to reasonable amounts of strain. Our results provide an underlying mechanism for some observed cell shape patterning in organoids and in in vivo settings. Finally, we discuss the use of a cellular-based approach to designing organoids with new types of morphologies to study the intricate relationship between structure and function at the multicellular scale.

We provide a detailed comparison between the dynamics of high-temperature spatiotemporal correlation functions in quantum and classical spin models. In the quantum case, our large-scale numerics are based on the concept of quantum typicality, which exploits the fact that random pure quantum states can faithfully approximate ensemble averages, allowing the simulation of spin-$1/2$ systems with up to 40 lattice sites. Due to the exponentially growing Hilbert space, we find that for such system sizes even a single random state is sufficient to yield results with extremely low noise that is negligible for most practical purposes. In contrast, a classical analog of typicality is missing. In particular, we demonstrate that to obtain data with a similar level of noise in the classical case, extensive averaging over classical trajectories is required, no matter how large the system size. Focusing on (quasi-)one-dimensional spin chains and ladders, we find remarkably good agreement between quantum and classical dynamics. This applies not only to cases where both the quantum and classical models are nonintegrable but also to cases where the quantum spin-$1/2$ model is integrable and the corresponding classical $s\to \infty$ model is not. Our analysis is based on the comparison of space-time profiles of the spin and energy correlation functions, where the agreement is found to hold not only in the bulk but also in the tails of the resulting density distribution. The mean-squared displacement of the density profiles reflects the nature of emerging hydrodynamics and is found to exhibit similar scaling for quantum and classical models.

A bright source of fiber-coupled, polarized single photons is an essential component of any realistic quantum network based on today's existing fiber infrastructure. Here, we develop a Purcell-enhanced, polarized source of single photons at room temperature by coupling single colloidal quantum dots to the localized surface plasmon-polariton modes of single gold nanorods, combined on the surface of an optical nanofiber. A maximum enhancement of the photon emission rate of 62 times was measured corresponding to a degree of polarization of $85\%$, and a brightness enhancement of four times in the fiber mode. Evanescent coupling of photons to the nanofiber guided modes ensures automatic coupling to a single mode fiber. Our technique opens the way to realizing bright sources of polarized single photons connected to fiber networks using a simple composite technique.

Magic-angle twisted bilayer graphene exhibits quasiflat low-energy bands with Van Hove singularities close to the Fermi level. These singularities play an important role in the exotic phenomena observed in this material, such as superconductivity and magnetism, by amplifying electronic correlation effects. In this work, we study the correspondence of four-terminal conductance and the Fermi surface topology as a function of the twist angle, pressure, and energy in mesoscopic, ballistic samples of small-angle twisted bilayer graphene. We establish a correspondence between features in the wide-junction conductance and the presence of Van Hove singularities in the density of states. Moreover, we identify additional transport features, such as a large, pressure-tunable minimal conductance, conductance peaks coinciding with nonsingular band crossings, and unusually large conductance oscillations as a function of the system size. Our results suggest that twisted bilayer graphene close the magic angle is a unique system featuring simultaneously large conductance due to the quasiflat bands, strong quantum nonlinearity due to the Van Hove singularities, and high sensitivity to external parameters, which could be utilized in high-frequency device applications and sensitive detectors.

The study of non-Hermitian systems has attracted more and more attention, because physical properties in many real systems should be described by non-Hermitian Hamiltonians. Due to the existence of absorption and dissipation, transmission and transformation of entangled states with high fidelity are very difficult to realize in the non-Hermitian systems. How to realize transmission and transformation of entangled states with high fidelity in these dissipative systems becomes an open problem. Here we provide an inverse design scheme for topologically protected channels to solve such a problem. From our scheme, topologically protected channels can be designed according to the requirements for the overlap integrals among the initial states, target states, and eigenstates of the system. As a result, robust transmission and transformation of entangled states with high fidelity can be achieved in the non-Hermitian systems. Our proposed scheme has been demonstrated experimentally using the constructed non-Hermitian quantum walk platform. This work interconnects topology, quantum physics, and non-Hermitian systems, and opens up an avenue for quantum engineering in real systems.

Understanding the functional principles of information processing in deep neural networks continues to be a challenge, in particular for networks with trained and thus nonrandom weights. To address this issue, we study the mapping between probability distributions implemented by a deep feed-forward network. We characterize this mapping as an iterated transformation of distributions, where the nonlinearity in each layer transfers information between different orders of correlation functions. This allows us to identify essential statistics in the data, as well as different information representations that can be used by neural networks. Applied to an XOR task and to MNIST, we show that correlations up to second order predominantly capture the information processing in the internal layers, while the input layer also extracts higher-order correlations from the data. This analysis provides a quantitative and explainable perspective on classification.

Cellular ATP plays an important role in the calcium oscillation signal transduction pathway of pancreatic $\beta$ cells. It triggers oscillation by binding the ATP-sensitive ${\text{K}}^{+}$ channels $\left({\text{K}}_{\mathrm{ATP}}\right)$, and maintains the oscillation by providing ATP hydrolysis free energy for the normal function of ion pumps on the plasma membrane. To reveal how cellular ATP level and ATP hydrolysis free energy affect calcium oscillation, we first constructed a simplified kinetic model of ${\text{K}}_{\mathrm{ATP}}$ and calcium pumps, then analyzed their thermodynamic characteristics. Bifurcation of calcium oscillation is determined by both cellular ATP concentration and ATP hydrolysis free energy such that an insufficient ATP energy supply would result in dysfunctional calcium oscillation. Second, to investigate the glucose sensing in $\beta$ cells, we developed a glycolysis-calcium model that considers the dynamics of ATP and free energy levels. The model simulated three calcium patterns in wild type cells and impaired calcium response of ${\text{K}}_{\mathrm{ATP}}$ mutant cells, allowing the use of the ATP-free energy phase plane to explore the underlying mechanism. Our results reveal the thermodynamics of calcium oscillation and provide a framework for understanding the thermodynamics of other ion transport systems.

Quantum information scrambling has received tremendous attention owing to its key concept in the fields of quantum chaos and quantum gravity. Here, with exploiting a fully controllable superconducting quantum processor, we study the verified scrambling in a 1D spin chain by an analog superconducting quantum simulator with the signs and values of individual driving and coupling terms fully controllable. By engineering opposite Hamiltonians on two subsystems, we measure the temporal and spatial patterns of out-of-time ordered correlators (OTOC), with the Hamiltonian mismatch and the decoherence extracted quantitatively from the scrambling dynamics, providing a benchmarking tool for probing not only the spatial but the temporal patterns of scrambling dynamics in many-body systems. Our work demonstrates the superconducting system with strong controllability as a powerful quantum simulator.

Deep-circuit quantum computation, like Shor's algorithm, is undermined by error accumulation, and near-future quantum techniques are far from adequate for full-fledged quantum error correction. Instead of resorting to shallow-circuit quantum algorithms, recent theoretical research suggests that digital quantum simulation (DQS) of closed quantum systems are robust against the accumulation of Trotter errors, as long as local observables are concerned. In this paper, we investigate the error-mitigation problem of open systems via DQS. First, we prove that the deviation in the steady state obtained from digital quantum simulation depends only on the error in a single Trotter step, which indicates that error accumulation may not be disastrous. By numerical simulation of the quantum circuits for the DQS of the dissipative XYZ model, we then show that the correct results can be recovered by quantum error mitigation as long as the error rate in the DQS is below a sharp threshold. We explain this threshold behavior by the existence of a dissipation-driven quantum phase transition. Finally, we propose a error-mitigation technique based on the scaling behavior in the vicinity of the critical point of a quantum phase transition. Our results expand the territory of near-future available quantum algorithms and stimulate further theoretical and experimental efforts in practical quantum applications.

We study the ratio between the variances of work output and heat input, ${\eta }^{\left(2\right)}$, for a class of four-stroke heat engines, which covers various typical cycles. Recent studies on the upper and lower bounds of ${\eta }^{\left(2\right)}$ are based on the quasistatic limit and the linear response regime, respectively. We extend these relations to the finite-time regime within the endoreversible approximation. We consider the ratio ${\eta }_{\text{MP}}^{\left(2\right)}$ at maximum power and find that the square of the Curzon-Ahlborn efficiency, ${\eta }_{\mathrm{CA}}^2$, gives a good estimate of ${\eta }_{\text{MP}}^{\left(2\right)}$ for the class of heat engines considered, i.e., ${\eta }_{\text{MP}}^{\left(2\right)}\simeq {\eta }_{\mathrm{CA}}^2$. This resembles the situation where the Curzon-Ahlborn efficiency gives a good estimate of the efficiency at maximum power for various kinds of finite-time heat engines. Taking an overdamped Brownian particle in a harmonic potential as an example, we can realize such endoreversible small heat engines and give an expression of the cumulants of work output and heat input. The approximate relation ${\eta }_{\text{MP}}^{\left(2\right)}\simeq {\eta }_{\mathrm{CA}}^2$ is verified by numerical simulations. This relation also suggests a trade-off between the efficiency and the stability of finite-time heat engines at maximum power.

We investigate several control strategies for the transport of an excitation along a spin chain. We demonstrate that fast high-fidelity transport can be achieved using protocols designed with differentiable programming. Building on this, we then show how this approach can be effectively adapted to control a disordered quantum system. We consider two settings: optimal control for a known unwanted disorder pattern, i.e., a specific disorder realisation, and optimal control where only the statistical properties of disorder are known, i.e., optimizing for high average fidelities. In the former, disorder effects can be effectively mitigated for an appropriately chosen control protocol. However, in the latter setting the average fidelity can only be marginally improved, suggesting the presence of a fundamental lower bound.

${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ represents a unique example in the family of B20 cubic helimagnets with a tilted spiral and a low-temperature skyrmion phase arising for magnetic fields applied along the easy crystallographic $\langle 100\rangle$ axes. Although the stabilization mechanism of these phases can be accounted for by cubic magnetic anisotropy, the skyrmion nucleation process is still an open question, since the stability region of the skyrmion phase displays strongly hysteretic behavior with different phase boundaries for increasing and decreasing magnetic fields. Here, we address this important point using micromagnetic simulations and come to the conclusion that skyrmion nucleation is underpinned by the reorientation of spiral domains occurring near the critical magnetic fields of the phase diagrams: $H_{C1}$, the critical field of the transition between the helical and conical/tiled spiral phase, and $H_{C2}$, the critical field between the conical/tiled spiral and the homogenous phase. By studying a wide variety of cases we show that domain walls may have a 3D structure. Moreover, they can carry a finite topological charge stemming from half-skyrmions (merons) also permitting along-the-field and perpendicular-to-the-field orientation. Thus, domain walls may be envisioned as nucleation source of skyrmions that can form thermodynamically stable and metastable lattices as well as skyrmion networks with misaligned skyrmion tubes. The results of numerical simulations are discussed in view of recent experimental data on chiral magnets, in particular, for the bulk cubic helimagnet ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$.