Dilute superconductivity survives in bulk strontium titanate when the Fermi temperature falls well below the Debye temperature. Here, we show that the onset of the superconducting dome is dopant dependent. When mobile electrons are introduced by removing oxygen atoms, the superconducting transition survives down to $2\times {10}^{17}{\mathrm{cm}}^{-3}$, but when they are brought by substituting Ti with Nb, the threshold density for superconductivity is an order of magnitude higher. Our study of quantum oscillations reveals a difference in the band dispersion between the dilute metals made by these doping routes and our band calculations demonstrate that the rigid band approximation does not hold when mobile electrons are introduced by oxygen vacancies. We identify the band sculpted by these vacancies as the exclusive locus of superconducting instability in the ultradilute limit.

Kinetic approaches are generally accurate in dealing with microscale plasma physics problems but are computationally expensive for large-scale or multiscale systems. One of the long-standing problems in plasma physics is the integration of kinetic physics into fluid models, which is often achieved through sophisticated analytical closure terms. In this paper, we successfully construct a multimoment fluid model with an implicit fluid closure included in the neural network using machine learning. The multimoment fluid model is trained with a small fraction of sparsely sampled data from kinetic simulations of Landau damping, using the physics-informed neural network (PINN) and the gradient-enhanced physics-informed neural network (gPINN). The multimoment fluid model constructed using either PINN or gPINN reproduces the time evolution of the electric field energy, including its damping rate, and the plasma dynamics from the kinetic simulations. In addition, we introduce a variant of the gPINN architecture, namely, $\mathrm{gPINN}p$, to capture the Landau damping process. Instead of including the gradients of all the equation residuals, $\mathrm{gPINN}p$ only adds the gradient of the pressure equation residual as one additional constraint. Among the three approaches, the $\mathrm{gPINN}p$-constructed multimoment fluid model offers the most accurate results. This work sheds light on the accurate and efficient modeling of large-scale systems, which can be extended to complex multiscale laboratory, space, and astrophysical plasma physics problems.

We introduce a general numerical method to compute the dynamics and multitime correlations of chains of quantum systems, where each system may couple strongly to a structured environment. The method combines the process tensor formalism for general (possibly non-Markovian) open quantum systems with time-evolving block decimation for one-dimensional chains. It systematically reduces the numerical complexity originating from system-environment correlations before integrating them into the full many-body problem, making a wide range of applications numerically feasible. We illustrate the power of this method by studying two examples. First, we study the thermalization of individual spins of a short XYZ Heisenberg chain with strongly coupled thermal leads. Our results confirm the complete thermalization of the chain when coupled to a single bath, and they reveal distinct effective temperatures in low-, mid-, and high-frequency regimes when the chain is placed between a hot and a cold bath. Second, we study the dynamics of diffusion in a longer XY chain, when each site couples to its own bath.

Currently most progress on quantum secret sharing suffers from rate-distance bound, and thus the key rates are limited. In addition to the limited key rate, the technical difficulty and the corresponding cost together prevent large-scale deployment. Furthermore, the performance of most existing protocols is analyzed in the asymptotic regime without considering participant attacks. Here we report a measurement-device-independent quantum secret-sharing protocol with improved key rate and transmission distance. Based on spatial multiplexing, our protocol shows it can break rate-distance bounds over network under at least ten communication parties. Compared with other protocols, our work improves the secret key rate by more than two orders of magnitude and has a longer transmission distance. We analyze the security of our protocol in the composable framework considering participant attacks and evaluate its performance in the finite-size regime. In addition, we investigate applying our protocol to digital signatures where the signature rate is improved more than ${10}^7$ times compared with existing protocols. We anticipate that our quantum secret-sharing protocol will provide a solid future for multiparty applications on the quantum network.

Superposing multiple plane waves can generate helicity lattices in which the optical helicity varies regularly in space. Here we propose an inverse design method for constructing arbitrary helicity structures based on placing a digital object consisting of dielectric inclusions in three-dimensional space. We apply the method to design structures that reproduce two-dimensional lattices embedded within a three-dimensional region using only a single plane wave as an input. In order to demonstrate the power and flexibility of our method, we go beyond the paradigm of a regular lattice and propose structures which can create arbitrary images consisting of regions of varying helicity, again using only a single plane wave as an input.

We propose a method to engineer repulsive long-range interactions between ultracold ground-state molecules using optical fields, thus preventing short-range collisional losses. It maps the microwave coupling recently used for collisional shielding onto a two-photon transition and takes advantage of optical control techniques. In contrast to one-photon optical shielding [Xie et al., Phys. Rev. Lett. 125, 153202 (2020)], this scheme avoids heating of the molecular gas due to photon scattering. The proposed protocol, exemplified for ${}^{23}\mathrm{Na}{}^{39}\mathrm{K}$, should be applicable to a large class of polar diatomic molecules.

The Fermi sea topology is characterized by the Euler characteristic ${\chi }_F$. In this paper, we examine how ${\chi }_F$ of the metallic state is inherited by the topological invariant of the superconducting state. We establish a correspondence between the Euler characteristic and the Chern number $C$ of $p$-wave topological superconductors without time-reversal symmetry in two dimensions. By rewriting the pairing potential ${\mathrm{\Delta }}_{\mathbf{k}}={\mathrm{\Delta }}_1-i{\mathrm{\Delta }}_2$ as a vector field $\mathbf{u}=({\mathrm{\Delta }}_1,{\mathrm{\Delta }}_2)$, we found that ${\chi }_F=C$ when $\mathbf{u}$ and fermion velocity $\mathbf{v}$ can be smoothly deformed to be parallel or antiparallel on each Fermi surface. We also discuss a similar correspondence between the Euler characteristic and three-dimensional winding number of time-reversal-invariant $p$-wave topological superconductors in three dimensions.

Quantum spin systems may offer the first opportunities for beyond-classical quantum computations of scientific interest. While general quantum simulation algorithms likely require error-corrected qubits, there may be applications of scientific interest prior to the practical implementation of quantum error correction. The variational quantum eigensolver (VQE) is a promising approach to finding energy eigenvalues on noisy quantum computers. Lattice models are of broad interest for use on near-term quantum hardware due to the sparsity of the number of Hamiltonian terms and the possibility of matching the lattice geometry to the hardware geometry. Here, we consider the Kitaev spin model on a hardware-native square-octagon qubit connectivity map, and examine the possibility of efficiently probing its rich phase diagram with VQE approaches. By benchmarking different choices of variational Ansatz states and classical optimizers, we illustrate the advantage of a mixed optimization approach using the Hamiltonian variational Ansatz (HVA) and the potential of probing the system's phase diagram using VQE. We further demonstrate the implementation of HVA circuits on Rigetti's Aspen-9 chip with error mitigation.

Computation of the Green's function is crucial to study the properties of quantum many-body systems such as strongly correlated systems. Although the high-precision calculation of the Green's function is a notoriously challenging task on classical computers, the development of quantum computers may enable us to compute the Green's function with high accuracy even for classically-intractable large-scale systems. Here, we propose an efficient method to compute the real-time Green's function based on the local variational quantum compilation (LVQC) algorithm, which simulates the time evolution of a large-scale quantum system using a low-depth quantum circuit constructed through optimization on a smaller-size subsystem. Our method requires shallow quantum circuits to calculate the Green's function and can be utilized on both near-term noisy intermediate-scale and long-term fault-tolerant quantum computers depending on the computational resources we have. We perform a numerical simulation of the Green's function for the one- and two-dimensional Fermi-Hubbard model up to $4\times 4$ sites lattice (32 qubits) and demonstrate the validity of our protocol compared to a standard method based on the Trotter decomposition. We finally present a detailed estimation of the gate count for the large-scale Fermi-Hubbard model, which also illustrates the advantage of our method over the Trotter decomposition.

Despite spectacular successes, deep neural networks (DNNs) with a huge number of adjustable parameters remain largely black boxes. To shed light on the hidden layers of DNNs, we study supervised learning by a DNN of width $N$ and depth $L$ consisting of $NL$ perceptrons with $c$ inputs by a statistical mechanics approach called the teacher-student setting. We consider an ensemble of student machines that exactly reproduce $M$ sets of $N$-dimensional input/output relations provided by a teacher machine. We show that the statistical mechanics problem becomes exactly solvable in a high-dimensional limit which we call a “dense limit”: $N\gg c\gg 1$ and $M\gg 1$ with fixed $\alpha =M/c$ using the replica method developed by Yoshino [SciPost Phys. Core 2, 005 (2020)] In conjunction with the theoretical study, we also study the model numerically performing simple greedy Monte Carlo simulations. Simulations reveal that learning by the DNN is quite heterogeneous in the network space: configurations of the teacher and the student machines are more correlated within the layers closer to the input/output boundaries, while the central region remains much less correlated due to the overparametrization in qualitative agreement with the theoretical prediction. We evaluate the generalization error of the DNN with various depths $L$ both theoretically and numerically. Remarkably, both the theory and the simulation suggest that the generalization ability of the student machines, which are only weakly correlated with the teacher in the center, does not vanish even in the deep limit $L\gg 1$, where the system becomes heavily overparametrized. We also consider the impact of the effective dimension $D(\le N)$ of data by incorporating the hidden manifold model [Goldt, Mézard, Krzakala, and Zdevorová, Phys. Rev. X 10, 041044 (2020)] into our model. Replica theory implies that the loop corrections to the dense limit, which reflect correlations between different nodes in the network, become enhanced by either decreasing the width $N$ or decreasing the effective dimension $D$ of the data. Simulation suggests that both lead to significant improvements in generalization ability.

Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterizing quantum materials. Recently, a series of quantum algorithms employing block encoding of Hamiltonians have succeeded in providing efficient simulation of time-evolution operators on quantum computers. While time-independent Hamiltonians can be simulated by the quantum eigenvalue transformation (QET) or quantum singular value transformation with the optimal query complexity in time $t$ and desirable accuracy $\varepsilon$, generic time-dependent Hamiltonians face at larger query complexity and more complicated oracles due to the difficulty of handling time-dependency. In this paper, we establish a QET-based approach for simulating time-dependent Hamiltonians with multiple time periodicity. Such time-dependent Hamiltonians involve a variety of nonequilibrium systems such as time-periodic systems (Floquet systems) and time-quasiperiodic systems. Overcoming the difficulty of time dependency, our protocol can simulate the dynamics under multiperiodic time-dependent Hamiltonians with optimal and nearly optimal query complexity both in time $t$ and desirable accuracy $\varepsilon$, and simple oracles as well as the optimal algorithm for time-independent cases.

We use quantum entanglement witnesses derived from Gaussian operators to study the separable criteria of continuous variable states. For bipartite system, we transform the validity of a Gaussian witness to a bosonic Gaussian channel problem. It follows that the maximal means of two-mode and some four-mode Gaussian operators over product pure states are achieved by vacuum (or coherent states and squeezed states) according to the properties of bosonic Gaussian channels. We demonstrate necessary and sufficient criteria of separability for two-mode and some four-mode Gaussian quantum states. We also propose multipartite Gaussian witnesses based on numeric evidence. The entanglement and multipartite entanglement detecting powers of the Gaussian witness criteria are illustrated by the mixture of two Gaussian states. We apply the Gaussian witness criterion to a Gaussian Fock state, which is prepared by passing a product Fock state through bosonic Gaussian channel. We show that the necessary criterion of separability for a Gaussian Fock state does not rely on the initial product Fock state, it relies on the channel.

Epidemic spreading and awareness diffusion are typically driven by information exchange and physical contact generated by activities, respectively, evolving in a synergistic manner. In response to this reality, we propose a dynamic model of information-awareness-epidemic-activity coevolution on a four-layer network. Our findings reveal the presence of an optimal coupling between information contact preference and activity contact preference, which efficiently suppresses epidemic spreading. Specifically, the disease-related information should be targeted towards individuals who engage in more activities, enhancing their awareness and resistance to infection. Examining the epidemic situation, we observe that the epidemic threshold can be moderately increased with higher information levels but significantly decreased with increased activity frequency. Quantitatively, we establish that the epidemic threshold is strictly inversely proportional to the activity frequency. By integrating the microscopic Markov chain approach with the mean-field method, we provide theoretical insights into the system's state size and epidemic threshold. We derive an explicit expression for the critical combination of information level and activity frequency required to prevent epidemic outbreaks. These results are consistently supported by extensive Monte Carlo simulations on both heterogeneous scale-free multiplex networks and homogeneous Erdős-Rényi multiplex networks. This research emphasizes the crucial importance of reducing physical contact through activities as a key preventive measure against epidemics, complementing the focus on information dissemination to raise awareness.

Information about the internal properties of a system can only be obtained through interactions of the system with an external meter. However, such interactions generally result in entanglement between the system and the meter, making it difficult to trace the measurement result back to a specific value of the physical property in the system. It is therefore possible that the outcomes of quantum measurements depend in a nontrivial manner on the dynamics of the measurement interaction, possibly providing a physical explanation for the role of measurement contexts in quantum mechanics. Here we show that the effects of the measurement interaction on the meter can be described entirely in terms of the quantum coherent system dynamics associated with the back-action on the system. For sufficiently small back-action uncertainties, the physical property of the system is described by a weak value obtained from the Hamilton-Jacobi equation of the back-action dynamics. At higher measurement resolutions, the observed values are determined by quantum interferences between different amounts of back-action. Eigenvalues emerge when the quantum interferences between different back-actions correspond to a Fourier transform in the back-action parameter. We conclude that the values of physical properties obtained in quantum measurements originate from the quantum coherent properties of the back-action dynamics generated by that physical property during an interaction. Measurement outcomes represent elements of the dynamics and cannot be explained by measurement independent elements of reality.

We present real-time time-dependent density-functional-theory calculations of the electronic stopping power for negative and positive projectiles (electrons, protons, antiprotons, and muons) moving through liquid water. After correction for finite mass effects, the nonlinear stopping power obtained in this paper is significantly different from the previously known results from semiempirical calculations based on the dielectric response formalism. Linear-nonlinear discrepancies are found both in the maximum value of the stopping power and the Bragg peak's position. Our results indicate the importance of the nonlinear description of electronic processes, particularly, for electron projectiles, which are modeled here as classical point charges. Our findings also confirm the expectation that the quantum nature of the electron projectile should substantially influence the stopping power around the Bragg peak and below.

Low-density neutron matter is characterized by fascinating emergent quantum phenomena, such as the formation of Cooper pairs and the onset of superfluidity. We model this density regime by capitalizing on the expressivity of the hidden-nucleon neural-network quantum states combined with variational Monte Carlo and stochastic reconfiguration techniques. Our approach is competitive with the auxiliary-field diffusion Monte Carlo method at a fraction of the computational cost. Using a leading-order pionless effective field theory Hamiltonian, we compute the energy per particle of infinite neutron matter and compare it with those obtained from highly realistic interactions. In addition, a comparison between the spin-singlet and triplet two-body distribution functions indicates the emergence of pairing in the ${}^1{S}_0$ channel.