Solving independent set problems with photonic quantum circuits.

An independent set (IS) is a set of vertices in a graph such that no edge connects any two vertices. In adiabatic quantum computation [E. Farhi, et al., Science 292, 472-475 (2001); A. Das, B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061-1081 (2008)], a given graph G(V, E) can be naturally mapped onto a many-body Hamiltonian [Formula: see text], with edges [Formula: see text] being the two-body interactions between adjacent vertices [Formula: see text]. Thus, solving the IS problem is equivalent to finding all the computational basis ground states of [Formula: see text]. Very recently, non-Abelian adiabatic mixing (NAAM) has been proposed to address this task, exploiting an emergent non-Abelian gauge symmetry of [Formula: see text] [B. Wu, H. Yu, F. Wilczek, Phys. Rev. A 101, 012318 (2020)]. Here, we solve a representative IS problem [Formula: see text] by simulating the NAAM digitally using a linear optical quantum network, consisting of three C-Phase gates, four deterministic two-qubit gate arrays (DGA), and ten single rotation gates. The maximum IS has been successfully identified with sufficient Trotterization steps and a carefully chosen evolution path. Remarkably, we find IS with a total probability of 0.875(16), among which the nontrivial ones have a considerable weight of about 31.4%. Our experiment demonstrates the potential advantage of NAAM for solving IS-equivalent problems.

Contrastive voxel clustering for multiscale modeling of brain network.

Resting-state functional magnetic resonance imaging (fMRI) provides an efficient way to analyze the functional connectivity between brain regions. A comprehensive understanding of brain functionality requires a unified description of multi-scale layers of neural structure. However, existing brain network modeling methods often simplify this property by averaging Blood oxygen level dependent (BOLD) signals at the brain region level for fMRI-based analysis with the assumption that BOLD signals are homogeneous within each brain region, which ignores the heterogeneity of voxels within each Region of Interest (ROI). This study introduces a novel multi-stage self-supervised learning framework for multiscale brain network analysis, which effectively delineates brain functionality from voxel to ROIs and up to sample level. A Contrastive Voxel Clustering (CVC) module is proposed to simultaneously learn the voxel-level features and clustering assignments, which ensures the retention of informative clustering features at the finest voxel-level and concurrently preserves functional connectivity characteristics. Additionally, based on the extracted features and clustering assignments at the voxel level by CVC, a Brain ROI-based Graph Neural Network (BR-GNN) is built to extract functional connectivity features at the brain ROI-level and used for sample-level prediction, which integrates the functional clustering maps with the pre-established structural ROI maps and creates a more comprehensive and effective analytical tool. Experiments are performed on two datasets, which illustrate the effectiveness and generalization ability of the proposed method by analyzing voxel-level clustering results and brain ROIs-level functional characteristics. The proposed method provides a multiscale modeling framework for brain functional connectivity analysis, which will be further used for other brain disease identification. Code is available at https://github.com/yanliugroup/fmri-cvc.

The regulatory function of the d-orbital structure in TM@g-t-C4N3 for bifunctional catalysis of the oxygen evolution/reduction reaction.

Highly efficient catalysts for the oxygen evolution/reduction reaction (OER/ORR) have attracted great attention in research for energy devices with high conversion efficiency. Herein, systematic first-principles investigations are performed to explore the catalytic performance of graphitic C4N3 loaded with single transition metal atoms (TM@g-t-C4N3) for the OER/ORR. The results show that Fe, Co, Ni and Rh@g-t-C4N3 exhibit fascinating bifunctional catalytic activities for both the OER and ORR. Moreover, it is observed that better activities are easily achieved when the valence d orbitals of doped TM atoms are nearly fully occupied. Further analysis reveals the volcano relationship between the OER/ORR performance and the adsorption Gibbs free energy. The adsorption free energy of intermediates in the OER/ORR process is also found to highly correlate with the electronic structures of TM@g-t-C4N3, which are mainly characterized by two quantities, one is the descriptor φ related to the electronegativity and the number of valence electrons in d orbitals, and the other is the projected d band center. The results indicate that it is possible to predict the catalytic performance of TM@g-t-C4N3 by a detailed examination of the electronic properties of the doped TM atoms to some extent. This research not only provides several highly active g-t-C4N3-based single-atom catalysts (SACs) for the OER/ORR, but also reveals some potential regularities of SAC systems.

An Underwater Acoustic Network Positioning Method Based on Spatial-Temporal Self-Calibration.

The emergence of underwater acoustic networks has greatly improved the potential capabilities of marine environment detection. In underwater acoustic network applications, node location is a basic and important task, and node location information is the guarantee for the completion of various underwater tasks. Most of the current underwater positioning models do not consider the influence of the uneven underwater medium or the uncertainty of the position of the network beacon modem, which will reduce the accuracy of the positioning results. This paper proposes an underwater acoustic network positioning method based on spatial-temporal self-calibration. This method can automatically calibrate the space position of the beacon modem using only the GPS position and depth sensor information obtained in real-time. Under the asynchronous system, the influence of the inhomogeneity of the underwater medium is analyzed, and the unscented Kalman algorithm is used to estimate the position of underwater mobile nodes. Finally, the effectiveness of this method is verified by simulation and sea trials.

Self-similarity among energy eigenstates.

In a quantum system, different energy eigenstates have different properties or features, allowing us to define a classifier to divide them into different groups. We find that the ratio of each type of energy eigenstate in an energy shell [E_{c}-ΔE/2,E_{c}+ΔE/2] is invariant with changing width ΔE or Planck constant ℏ as long as the number of eigenstates in the shell is statistically large enough. We give an argument that such self-similarity in energy eigenstates is a general feature for all quantum systems, which is further illustrated numerically with various quantum systems, including circular billiard, double top model, kicked rotor, and Heisenberg XXZ model.

Quantum chaos and physical distance between quantum states.

We show that there is genuine chaos in quantum dynamics by introducing a physical distance between two quantum states. Qualitatively different from existing distances for quantum states, for example, the Fubini-Study distance, the physical distance between two mutually orthogonal quantum states, can be very small. As a result, two quantum states, which are initially very close by physical distance, can diverge from each other during the ensuing quantum dynamical evolution. We are able to use physical distance to define the quantum Lyapunov exponent and the quantum chaos measure. The latter leads to a quantum analog of the classical Poincaré section, which maps out the regions where quantum dynamics is regular and the regions where it is chaotic. Three different systems-a kicked rotor, the three-site Bose-Hubbard model, and the spin-1/2 XXZ model-are used to illustrate our results.

Generalized Wigner-von Neumann entropy and its typicality.

We propose a generalization of the quantum entropy introduced by Wigner and von Neumann [Z. Phys. 57, 30 (1929)10.1007/BF01339852]. Our generalization is applicable to both quantum pure states and mixed states. When the dimension N of the Hilbert space is large, this generalized Wigner-von Neumann (GWvN) entropy becomes independent of the choices of basis and is asymptotically equal to lnN in the sense of typicality. The dynamic evolution of our entropy is also typical, and is reminiscent of quantum H theorem proved by von Neumann. For a composite system, the GWvN entropy is typically additive; for the microcanonical ensemble, it is equivalent to the Boltzmann entropy; and for a system entangled with environment, it is consistent with the familiar von Neumann entropy, which is zero for pure states. In addition, the GWvN entropy can be used to derive the Gibbs ensemble.