We propose a sampling-based simulation for fault-tolerant quantum error correction under coherent noise. A mixture of incoherent and coherent noise, possibly due to over-rotation, is decomposed into Clifford channels with a quasiprobability distribution. Then, an unbiased estimator of the logical error probability is constructed by sampling Clifford channels with an appropriate postprocessing. We characterize the sampling cost via the channel robustness and find that the proposed sampling-based method is feasible even for planar surface codes with relatively large code distances intractable for full state-vector simulations. As a demonstration, we simulate repetitive faulty syndrome measurements on the planar surface code of distance 5 with 81 qubits. We find that the coherent error increases the logical error rate. This is a practical application of the quasiprobability simulation for a meaningful task and would be useful to explore experimental quantum error correction on the near-term quantum devices.

A novel metasurface comprised of capped helices arranged as a hexagonal array that supports a broadband near-isotropic negative-index microwave surface-wave is designed, manufactured, and experimentally characterized. The surface-mode dispersion is studied both numerically and experimentally with the operational band more than double the bandwidth of structures previously reported in the literature. Hence, it is shown how one may provide a structured surface that supports just a negative-index mode over a wide operational band with no forward wave being simultaneously excited.

We study the impact of beyond Lee-Huang-Yang (LHY) physics, especially due to intercomponent correlations, in the ground state and the quench dynamics of one-dimensional quantum droplets with an ab initio nonperturbative approach. It is found that the droplet Gaussian-shaped configuration arising for intercomponent attractive couplings becomes narrower for stronger intracomponent repulsion and transits towards a flat-top structure either for larger particle numbers or weaker intercomponent attraction. Additionally, a harmonic trap prevents the flat-top formation. At the balance point where mean-field interactions cancel out, we show that a correlation hole is present in the few-particle limit of LHY fluids as well as for flat-top droplets. Introducing mass imbalance, droplets experience intercomponent mixing and excitation signatures are identified for larger masses. Monitoring the droplet expansion (breathing motion) upon considering interaction quenches to stronger (weaker) attractions, we explicate that beyond LHY correlations result in a reduced velocity (breathing frequency). Strikingly, the droplets feature two-body anticorrelations (correlations) at the same position (longer distances). Our findings pave the way for probing correlation-induced phenomena of droplet dynamics in current ultracold-atom experiments.

From soft polymeric gels to hardened cement paste, amorphous solids under constant load exhibit a pronounced time-dependent deformation called creep. The microscopic mechanism of such a phenomenon is poorly understood in amorphous materials and constitutes an even greater challenge in densely packed and chemically reactive granular systems. Both features are prominently present in hydrating cement pastes composed of calcium silicate hydrate (C-S-H) nanoparticles, whose packing density increases as a function of time, while cement hydration is taking place. Performing nanoindentation tests and porosity measurements on a large collection of samples at various stages of hydration, we show that the creep response of hydrating cement paste is mainly controlled by the interparticle distance and results from slippage between (C-S-H) nanoparticles. Our findings provide a unique insight into the microscopic mechanism underpinning the creep response in aging granular materials, thus paving the way for the design of concrete with improved creep resistance.

We propose a general framework for finding the ground state of many-body fermionic systems by using feed-forward neural networks. The anticommutation relation for fermions is usually implemented to a variational wave function by the Slater determinant (or Pfaffian), which is a computational bottleneck because of the numerical cost of $O\left(N^3\right)$ for $N$ particles. We bypass this bottleneck by explicitly calculating the sign changes associated with particle exchanges in real space and using fully connected neural networks for optimizing the rest parts of the wave function. This reduces the computational cost from $O\left(N^3\right)$ to $O\left(N^2\right)$ or less, while the overall cost depends on the number of Monte Carlo samples and the number of parameters in neural networks. We show that the accuracy of the approximation can be improved by optimizing the “variance” of the energy simultaneously with the energy itself. We also find that a reweighting method in Monte Carlo sampling can stabilize the calculation. These improvements can be applied to other approaches based on variational Monte Carlo methods. Moreover, we show that the accuracy can be further improved by using the symmetry of the system, the representative states, data preprocessing, and an additional neural network implementing a generalized Gutzwiller-Jastrow factor. We demonstrate the efficiency of the method by applying it to a two-dimensional Hubbard model.

One of the most widely discussed features of the cuprate high-$T_c$ superconductors is the presence of a pseudogap in the normal state. Recent transport and specific heat measurements have revealed an abrupt transition at the pseudogap critical point, denoted $p^{*}$, characterized by a drop in carrier density and a strong mass enhancement. In order to give more details about this transition at $p^{*}$, we performed low-temperature infrared spectroscopy in the normal state of cuprate superconductors ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (LSCO) and ${\mathrm{La}}_{1.8-x}{\mathrm{Eu}}_{0.2}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (Eu-LSCO) for doping contents across the pseudogap critical point $p^{*}$ (from $p=0.12$ to 0.24). Through the complex optical conductivity $\sigma$, we can extract the spectral weight $K^{*}$ of the narrow Drude peak due the coherent motion of the quasiparticles, and the spectral weight enclosed inside the mid-infrared (MIR) band $K_{\mathrm{MIR}}$ caused by coupling of the quasiparticles to collective excitations of the many-body system. $K^{*}$ is smaller than a third of the value predicted by band calculations, and $K_{\mathrm{MIR}}$ forms a dome as a function of doping. We observe a smooth doping dependence of $K^{*}$ through $p^{*}$, and demonstrate that this is consistent with the observed doping dependence of the carrier density and the mass enhancement. We argue that the superconducting dome is the result of the confluence of two opposite trends, namely the increase of the density of the quasiparticles and the decrease of their coupling to the collective excitations as a function of doping.

Weights and directionality of the edges carry a large part of the information we can extract from a complex network. However, many network measures were formulated initially for undirected binary networks. The necessity to incorporate information about the weights led to the conception of multiple extensions, particularly for definitions of the local clustering coefficient discussed here. We uncover that not all of these extensions are fully weighted; some depend on the degree and thus change a lot when an infinitely-small-weight edge is exchanged for the absence of an edge, a feature that is not always desirable. We call these methods “hybrid” and argue that, in many situations, one should prefer fully weighted definitions. After listing the necessary requirements for a method to analyze many various weighted networks properly, we propose a fully weighted continuous clustering coefficient that satisfies all the previously proposed criteria while also being continuous with respect to vanishing weights. We demonstrate that the behavior and meaning of the Zhang-Horvath clustering and our proposed continuous definition provide complementary results and significantly outperform other definitions in multiple relevant conditions. We demonstrate, using synthetic and real-world networks, that when the network is inferred, noisy, or very heterogeneous, it is essential to use the fully weighted clustering definitions.

We develop a model-independent reduction method of chemical reaction systems based on the stoichiometry, which determines their network topology. A subnetwork can be eliminated systematically to give a reduced system with fewer degrees of freedom. This subnetwork removal is accompanied by rewiring of the network, which is prescribed by the Schur complement of the stoichiometric matrix. Using homology and cohomology groups to characterize the topology of chemical reaction networks, we can track the changes of the network topology induced by the reduction through the changes in those groups. We prove that, when certain topological conditions are met, the steady-state chemical concentrations and reaction rates of the reduced system are ensured to be the same as those of the original system. This result holds regardless of the modeling of the reactions, namely, chemical kinetics, since the conditions only involve topological information. This is advantageous because the details of reaction kinetics and parameter values are difficult to identify in many practical situations. The method allows us to reduce a reaction network while preserving its original steady-state properties, thereby complex reaction systems can be studied efficiently. We demonstrate the reduction method in hypothetical networks and the central carbon metabolism of Escherichia coli.

The quantum Fisher information (QFI) represents a fundamental concept in quantum physics. It quantifies the metrological potential of quantum states in quantum parameter estimation measurements, and is intrinsically related to quantum geometry and multipartite entanglement of many-body systems. Using a nitrogen-vacancy center spin in diamond, we experimentally demonstrate a randomized-measurement method to extract the QFI of the qubit, for both pure and mixed states. We then apply this scheme to a 4-qubit state, using a superconducting quantum computer, and show that it provides access to the sub-QFI, which sets a lower bound on the QFI for general mixed states. We numerically study the scaling of statistical error, considering $N$-qubit states, to illustrate the advantage of our randomized-measurement approach in estimating the QFI and multipartite entanglement. Our results highlight the general applicability of our method to different quantum platforms, including solid-state spin systems, superconducting quantum computers, and trapped ions.

A programmable quantum device that has a large number of qubits without fault-tolerance has emerged recently. Variational quantum eigensolver (VQE) is one of the most promising ways to utilize the computational power of such devices to solve problems in condensed matter physics and quantum chemistry. As the size of the current quantum devices is still not large for rivaling classical computers at solving practical problems, Fujii et al. proposed a method called “Deep VQE”, which can provide the ground state of a given quantum system with the smaller number of qubits by combining the VQE and the technique of coarse graining [K. Fujii, K. Mitarai, W. Mizukami, and Y. O. Nakagawa, arXiv:2007.10917]. In this paper, we extend the original proposal of Deep VQE to obtain the excited states and apply it to quantum chemistry calculation of a periodic material, which is one of the most impactful applications of the VQE. We first propose a modified scheme to construct quantum states for coarse graining in Deep VQE to obtain the excited states. We also present a method to avoid a problem of meaningless eigenvalues in the original Deep VQE without restricting variational quantum states. Finally, we classically simulate our modified Deep VQE for quantum chemistry calculation of a periodic hydrogen chain as a typical periodic material. Our method reproduces the ground-state energy and the first-excited-state energy with the errors up to $O\left(1\right)\%$ despite the decrease in the number of qubits required for the calculation by two or four compared with the naive VQE. Our result will serve as a beacon for tackling quantum chemistry problems with classically-intractable sizes by smaller quantum devices in the near future.

Entangled systems in experiments may be lost or off-line in distributed quantum information processing. This inspires a general problem to characterize quantum operations, which result in breaking of entanglement or not. Our goal in this paper is to solve this problem both in single entanglement and network scenarios. We firstly propose a local model for characterizing all entangled states that are breaking for losing particles. This implies a simple criterion for witnessing single entanglement such as generalized GHZ states and Dicke states. It further provides an efficient witness for entangled quantum networks depending on its connectivity such as $k$-independent quantum networks, completely connected quantum networks, and $k$-connected quantum networks. These networks are universal resources for measurement-based quantum computations. The strong nonlocality can be finally verified by using nonlinear inequalities. These results show distinctive features of both single entangled systems and entangled quantum networks.

We report on the numerically exact simulation of the dissipative dynamics governed by quantum master equations that feature fractional quantum Hall states as unique steady states. In particular, for the paradigmatic Hofstadter model, we show how Laughlin states can be to good approximation prepared in a dissipative fashion from arbitrary initial states by simply pumping strongly interacting bosons into the lowest Chern band of the corresponding single-particle spectrum. While pure (up to topological degeneracy) steady states are only reached in the low-flux limit or for extended hopping range, we observe a certain robustness regarding the overlap of the steady state with fractional quantum Hall states for experimentally well-controlled flux densities. This may be seen as an encouraging step towards addressing the long-standing challenge of preparing strongly correlated topological phases in quantum simulators.

Measurement-based quantum computing is an alternative paradigm to the circuit-based model. This approach can be advantageous in certain scenarios, such as when read-out is fast and accurate, but two-qubit gates realized via inter-particle interactions are slow and can be parallelized to efficiently create a cluster state. However, understanding how two-qubit errors impact algorithm accuracy and developing experimentally viable approaches to characterize cluster-state fidelity are outstanding challenges. Here, we consider one-dimensional cluster states built from controlled phase, Ising, and XY interactions with slow two-qubit error in the interaction strength, consistent with error models of interactions found in a variety of qubit architectures. We detail an experimentally viable teleportation fidelity that offers a measure of the impact of these errors on the cluster state. Our fidelity calculations show that the error has a distinctly different impact depending on the underlying interaction used for the two-qubit entangling gate. In particular, the Ising and XY interactions can allow perfect teleportation through the cluster state even with large errors, but the controlled phase interaction does not. Nonetheless, we find that teleportation through cluster state chains of size $N$ has a maximum two-qubit error for teleportation along a quantum channel that decreases as $N^{-1/2}$. To enable the construction of larger cluster states, we design lowest-order refocusing pulses for correcting these slow errors in the interaction strength. Our work generalizes to higher-dimensional cluster states and sets the stage for experiments to monitor the growth of entanglement in cluster states built from error-prone interactions.

In 2015, the Gamma-Ray Observation of Winter Thunderstorms (GROWTH) collaboration launched a mapping observation campaign for high-energy atmospheric phenomena related to thunderstorms and lightning discharges. This campaign has developed a detection network of gamma rays with up to 10 radiation monitors installed in the cities of Kanazawa and Komatsu, Ishikawa Prefecture, Japan, where low-charge-center winter thunderstorms frequently occur. During four winter seasons from October 2016 to April 2020, a total of 70 gamma-ray glows, i.e., minute-lasting bursts of gamma rays originating from thunderclouds, were detected. Their average duration is 58.9 s. Among the detected events, 77% were observed at night. The gamma-ray glows can be classified into temporally symmetric, temporally asymmetric, and lightning-terminated types based on their count-rate histories. An averaged energy spectrum of the gamma-ray glows is well fitted with a power-law function with an exponential cutoff, whose photon index, cutoff energy, and flux are $0.613\pm 0.009$ MeV, $4.68\pm 0.04$ MeV, and $(1.013\pm 0.003)\times {10}^{-5}$ erg ${\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$ (0.2–20.0 MeV), respectively. The present paper provides a catalog of gamma-ray glows and their statistical analysis detected during winter thunderstorms in the Kanazawa and Komatsu areas.

While negativity in phase space is a well-known signature of nonclassicality, a wide variety of nonclassical states require their characterization beyond negativity. We establish a framework of nonclassicality in phase space that addresses nonclassical states comprehensively with a direct experimental evidence. This includes the negativity of phase-space distribution as a special case and further analyzes quantum states with positive distributions effectively. We prove that it detects all nonclassical Gaussian states and all non-Gaussian states of arbitrary dimension remarkably by examining three phase-space points only. Our formalism also provides an experimentally accessible lower bound for a nonclassicality measure based on trace distance. Importantly, this foundational approach can be further adapted to constitute practical tests in two directions looking into particle and wave nature of bosonic systems, via an array of nonideal on-off detectors and coarse-grained homodyne measurement, respectively. All these tests are practically powerful in characterizing nonclasssical states reliably against noise, making a versatile tool for a broad range of quantum systems in quantum technologies.

We report an experimental study of quench dynamics across the superfluid transition temperature $T_{\mathrm{c}}$ in a strongly interacting Fermi gas by ramping down the trapping potential. The nonzero quasicondensate number $N_0$ at temperatures significantly above $T_{\mathrm{c}}$ in the unitary and the BEC regimes is consistent with the pseudogap physics via preformed pairs. Below $T_{\mathrm{c}}$, a rapid growth of $N_0$ is accompanied by the spontaneous generation of tens of vortices. We observe a power-law scaling of the vortex density versus the quasicondensate formation time, consistent with the Kibble-Zurek theory. Our work provides an example of studying emerged many-body physics by quench dynamics and paves the way for studying the quantum turbulence in a strongly interacting Fermi gas.