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The barren plateau phenomenon, in which cost-function gradients of variational quantum algorithms vanish exponentially, remains a central obstacle for near-term quantum computing. Existing analyses typically depend on t-design or…
Linear layers in neural networks (NNs) trained by gradient descent can be expressed as a key-value memory system which stores all training datapoints and the initial weights, and produces outputs using unnormalised dot attention over the…
We consider a model in which positive and negative particles with equal densities diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and oppositely-charged adjacent…
We study the metastable behaviour of a stochastic system of particles with hard-core interactions in a high-density regime. Particles sit on the vertices of a bipartite graph. New particles appear subject to a neighbourhood exclusion…
We study a class of random processes on $N$ particles which can be interpreted as stochastic model of luminescence. Each particle can stay in one of two states: Excited state or ground state. Any particle at ground state is excited with a…
A deterministic and scalable array of single photon nonlinearities in the solid state holds great potential for both fundamental physics and technological applications, but its realization has proved extremely challenging. Despite…
We use inelastic hard sphere molecular dynamics simulations and laboratory experiments to study patterns in vertically oscillated granular layers. The simulations and experiments reveal that {\em phase bubbles} spontaneously nucleate in the…
The behavior of active matter under confinement poses significant challenges due to the intricate coupling between dynamics near boundaries and those in the bulk. A defining feature of active matter systems is that a substantial portion of…
In this article, we demonstrate that in a transport model of particles with kinetic constraints, long-lived spatial structures are responsible for the blocking dynamics and the decrease of the current at strong driving field. Coexistence…
Neural fields model signals by mapping coordinate inputs to sampled values. They are becoming an increasingly important backbone architecture across many fields from vision and graphics to biology and astronomy. In this paper, we explore…
We study the production of photons in a model of three bosonic atomic modes non-linearly coupled to a cavity mode. In absence of external driving and dissipation, the energy levels at different photon numbers assemble into the steps of an…
We investigate the nonlinear parity-time (PT) symmetric coupler from a dynamical perspective. As opposed to linear PT-coupler where the PT threshold dictates the evolutionary characteristics of optical power in the two waveguides, in a…
The permutation symmetry of the hidden units in multilayer perceptrons causes the saddle structure and plateaus of the learning dynamics in gradient learning methods. The correlation of the weight vectors of hidden units in a teacher…
Many systems exhibit a phase where the order parameter is spatially modulated. These patterns can be the result of a frustration caused by the competition between interaction forces with opposite effects. In all models with local…
We present a computer-assisted approach to coarse-graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph…
We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…
Variational quantum algorithms (VQAs), which classically optimize a parametrized quantum circuit to solve a computational task, promise to advance our understanding of quantum many-body systems and improve machine learning algorithms using…
We propose a scheme to trap and filter electrons, valley dependently, on a scale beyond the diffraction limit, in a gapped Dirac system using a circularly polarized light beam and a microscale metallic resonator. The main mechanism allowing…
In this paper, we propose a general scheme to analyze the gradient vanishing phenomenon, also known as the barren plateau phenomenon, in training quantum neural networks with the ZX-calculus. More precisely, we extend the barren plateaus…
We study the optical response of a binary system of identical atoms in which one of them is excited by an incoherent pump. %We study the properties of photon scattering, absorption and emission, together with the time evolution of the…