Active Self-Assembly of Algorithmic Shapes and Patterns in Polylogarithmic Time

We describe a computational model for studying the complexity of self-assembled structures with active molecular components. Our model captures notions of growth and movement ubiquitous in biological systems. The model is inspired by biology's fantastic ability to assemble biomolecules that form systems with complicated structure and dynamics, from molecular motors that walk on rigid tracks and proteins that dynamically alter the structure of the cell during mitosis, to embryonic development where large-scale complicated organisms efficiently grow from a single cell. Using this active self-assembly model, we show how to efficiently self-assemble shapes and patterns from simple monomers. For example, we show how to grow a line of monomers in time and number of monomer states that is merely logarithmic in the length of the line. Our main results show how to grow arbitrary connected two-dimensional geometric shapes and patterns in expected time that is polylogarithmic in the size of the shape, plus roughly the time required to run a Turing machine deciding whether or not a given pixel is in the shape. We do this while keeping the number of monomer types logarithmic in shape size, plus those monomers required by the Kolmogorov complexity of the shape or pattern. This work thus highlights the efficiency advantages of active self-assembly over passive self-assembly and motivates experimental effort to construct general-purpose active molecular self-assembly systems

Subgraph adaptive structure-aware graph contrastive learning

Graph contrastive learning (GCL) has been subject to more attention and been widely applied to numerous graph learning tasks such as node classification and link prediction. Although it has achieved great success and even performed better than supervised methods in some tasks, most of them depend on node-level comparison, while ignoring the rich semantic information contained in graph topology, especially for social networks. However, a higher-level comparison requires subgraph construction and encoding, which remain unsolved. To address this problem, we propose a subgraph adaptive structure-aware graph contrastive learning method (PASCAL) in this work, which is a subgraph-level GCL method. In PASCAL, we construct subgraphs by merging all motifs that contain the target node. Then we encode them on the basis of motif number distribution to capture the rich information hidden in subgraphs. By incorporating motif information, PASCAL can capture richer semantic information hidden in local structures compared with other GCL methods. Extensive experiments on six benchmark datasets show that PASCAL outperforms state-of-art graph contrastive learning and supervised methods in most cases

Quantum simulation of artificial Abelian gauge field using nitrogen-vacancy center ensembles coupled to superconducting resonators

We propose a potentially practical scheme to simulate artificial Abelian gauge field for polaritons using a hybrid quantum system consisting of nitrogen-vacancy center ensembles (NVEs) and superconducting transmission line resonators (TLR). In our case, the collective excitations of NVEs play the role of bosonic particles, and our multiport device tends to circulate polaritons in a behavior like a charged particle in an external magnetic field. We discuss the possibility of identifying signatures of the Hofstadter "butterfly" in the optical spectra of the resonators, and analyze the ground state crossover for different gauge fields. Our work opens new perspectives in quantum simulation of condensed matter and many-body physics using hybrid spin-ensemble circuit quantum electrodynamics system. The experimental feasibility and challenge are justified using currently available technology.Comment: 6 papes+supplementary materia