Adaptive Rewiring in Non-Uniform Coupled Oscillators

Structural plasticity of the brain can be represented in a highly simplified form as adaptive rewiring, the relay of connections according to the spontaneous dynamic synchronization in network activity. Adaptive rewiring, over time, leads from initial random networks to brain-like complex networks, i.e., networks with modular small-world structures and a rich-club effect. Adaptive rewiring has only been studied, however, in networks of identical oscillators with uniform or random coupling strengths. To implement information processing functions (e.g., stimulus selection or memory storage), it is necessary to consider symmetry-breaking perturbations of oscillator amplitudes and coupling strengths. We studied whether non-uniformities in amplitude or connection strength could operate in tandem with adaptive rewiring. Throughout network evolution, either amplitude or connection strength of a subset of oscillators was kept different from the rest. In these extreme conditions, subsets might become isolated from the rest of the network or otherwise interfere with the development of network complexity. However, whereas these subsets form distinctive structural and functional communities, they generally maintain connectivity with the rest of the network and allow the development of network complexity. Pathological development was observed only in a small proportion of the models. These results suggest that adaptive rewiring can robustly operate alongside information processing in biological and artificial neural networks.

A Spatiotemporal Chaotic System Based on Pseudo-Random Coupled Map Lattices and Elementary Cellular Automata

The coupled map lattices (CML) is a spatiotemporal chaotic system with complex dynamic behavior. In this paper, we propose a spatiotemporal chaotic system with a novel pseudo-random coupling method based on the elementary cellular automata (ECA), and add different perturbations to lattices in each iteration according to ECA. We investigate the spatiotemporal dynamic properties and chaotic behaviors of the proposed system such as bifurcation diagrams, Kolmogorov-Sinai entropy density, and universality. Moreover, the correlation between any two lattices is discussed. Theory analysis and simulation test indicate that the new system has better performance in complexity, ergodic and unpredictability than conventional CML systems such as adjacent CML and mixed linear-nonlinear CML. Furthermore, the correlation coefficient between any two lattices in proposed system is significantly lower than other systems, and another advantage of the proposed system is utilizing the output of ECA to perturb the chaotic system which can effectively alleviate the dynamical degradation in digital system. The excellent performance of proposed system demonstrates that it has great potential for crypto-system.

Quantum computed moments correction to variational estimates

The variational principle of quantum mechanics is the backbone of hybrid quantum computing for a range of applications. However, as the problem size grows, quantum logic errors and the effect of barren plateaus overwhelm the quality of the results. There is now a clear focus on strategies that require fewer quantum circuit steps and are robust to device errors. Here we present an approach in which problem complexity is transferred to dynamic quantities computed on the quantum processor – Hamiltonian moments, ⟨Hn⟩. From these quantum computed moments, an estimate of the ground-state energy can be obtained using the ``infimum'' theorem from Lanczos cumulant expansions which manifestly corrects the associated variational calculation. With higher order effects in Hilbert space generated via the moments, the burden on the trial-state quantum circuit depth is eased. The method is introduced and demonstrated on 2D quantum magnetism models on lattices up to 5×5 (25 qubits) implemented on IBM Quantum superconducting qubit devices. Moments were quantum computed to fourth order with respect to a parameterised antiferromagnetic trial-state. A comprehensive comparison with benchmark variational calculations was performed, including over an ensemble of random coupling instances. The results showed that the infimum estimate consistently outperformed the benchmark variational approach for the same trial-state. These initial investigations suggest that the quantum computed moments approach has a high degree of stability against trial-state variation, quantum gate errors and shot noise, all of which bodes well for further investigation and applications of the approach.