cond-mat.stat-mech

arXiv:2412.18624v2 Announce Type: replace-cross Abstract: Explanation of grokking (delayed generalization) in learning is given by modeling grokking by the stochastic gradient Langevin dynamics (Brownian motion) and applying the ideas of thermodynamics.

arXiv:2412.18290v1 Announce Type: cross Abstract: Quantum reservoir computing (QRC) has emerged as a promising paradigm for harnessing near-term quantum devices to tackle temporal machine learning tasks. Yet identifying the mechanisms that underlie enhanced performance remains challenging, particularly in many-body open systems where nonlinear interactions and dissipation intertwine in complex ways. Here, we investigate a minimal model of a driven-dissipative quantum reservoir described by two coupled Kerr-nonlinear oscillators, an experimentally realizable platform that features controllable coupling, intrinsic nonlinearity, and tunable photon loss. Using Partial Information Decomposition (PID), we examine how different dynamical regimes encode input drive signals in terms of redundancy (information shared by each oscillator) and synergy (information accessible only through their joint observation). Our key results show that, near a critical point marking a dynamical bifurcation, the system transitions from predominantly redundant to synergistic encoding. We further demonstrate that synergy amplifies short-term responsiveness, thereby enhancing immediate memory retention, whereas strong dissipation leads to more redundant encoding that supports long-term memory retention. These findings elucidate how the interplay of instability and dissipation shapes information processing in small quantum systems, providing a fine-grained, information-theoretic perspective for analyzing and designing QRC platforms.

arXiv:2412.17183v1 Announce Type: cross Abstract: We present the design for a thermodynamic computer that can perform arbitrary nonlinear calculations in or out of equilibrium. Simple thermodynamic circuits, fluctuating degrees of freedom in contact with a thermal bath and confined by a quartic potential, display an activity that is a nonlinear function of their input. Such circuits can therefore be regarded as thermodynamic neurons, and can serve as the building blocks of networked structures that act as thermodynamic neural networks, universal function approximators whose operation is powered by thermal fluctuations. We simulate a digital model of a thermodynamic neural network, and show that its parameters can be adjusted by genetic algorithm to perform nonlinear calculations at specified observation times, regardless of whether the system has attained thermal equilibrium. This work expands the field of thermodynamic computing beyond the regime of thermal equilibrium, enabling fully nonlinear computations, analogous to those performed by classical neural networks, at specified observation times.

arXiv:2404.02216v2 Announce Type: replace-cross Abstract: What happens when an infinite number of players play a quantum game? In this tutorial, we will answer this question by looking at the emergence of cooperation, in the presence of noise, in a one-shot quantum Prisoner's dilemma (QuPD). We will use the numerical Agent-based model (ABM), and compare it with the analytical Nash equilibrium mapping (NEM) technique. To measure cooperation, we consider five indicators, i.e., game magnetization, entanglement susceptibility, correlation, player's payoff average and payoff capacity, respectively. In quantum social dilemmas, entanglement plays a non-trivial role in determining the behaviour of the quantum players (or, \textit{qubits}) in the thermodynamic limit, and for QuPD, we consider the existence of bipartite entanglement between neighbouring quantum players. For the five indicators in question, we observe \textit{first}-order phase transitions at two entanglement values, and these phase transition points depend on the payoffs associated with the QuPD game. We numerically analyze and study the properties of both the \textit{Quantum} and the \textit{Defect} phases of the QuPD via the five indicators. The results of this tutorial demonstrate that both ABM and NEM, in conjunction with the chosen five indicators, provide insightful information on cooperative behaviour in an infinite-player one-shot quantum Prisoner's dilemma.