arXiv subjects

Abir Hasan

Publications and source records attributed to Abir Hasan.

4 recordsLinked to original sources

arXiv2026

Breakdown of Gradient-Flow Dynamics in Oscillator Ising Machines from Harmonic Misalignment

Oscillator Ising machines (OIMs) are often viewed as physical systems that perform gradient descent on an energy landscape encoding Ising solutions. Here, we show that this interpretation is not generic and breaks down in a broad class of oscillator implementations. We establish that gradient-flow dynamics require a harmonic-by-harmonic quadrature relation between the oscillator waveform and its phase response. Deviations from this condition, which we term harmonic misalignment, introduce even components in the pairwise interaction function, leading to non-conservative phase dynamics and precluding a gradient-flow description. We introduce a normalized metric for this non-gradient contribution and evaluate it across representative oscillator models relevant to OIMs. This metric reveals substantial non-gradient contributions in ring oscillators and across other hardware-realistic oscillator models. These findings identify harmonic misalignment as a fundamental mechanism for the breakdown of energy-based dynamics in OIMs and motivate nonequilibrium analysis and algorithms that explicitly account for and potentially exploit non-gradient behavior.

physics.comp-ph↗

arXiv2026

How Physical Dynamics Shape the Properties of Ising Machines: Evaluating Oscillators vs. Bistable Latches as Ising Spins

Ising machines exploit the natural dynamics of physical systems to minimize the Ising Hamiltonian and thereby address computationally hard combinatorial optimization problems. This paradigm has motivated a range of physical implementations. In the electronic domain, coupled networks of oscillators and bistable latches have emerged as two prominent realizations of Ising machines and are the focus of the present work. Despite this common abstraction, we demonstrate that differences in the underlying physical dynamics of oscillators and latches lead to fundamentally different stability properties of the resulting dynamical systems. Specifically, we show analytically that in Bistable Latch Ising Machines (BLIMs) all discrete Ising configurations possess identical linear stability, whereas in Oscillator Ising Machines (OIMs) the Jacobian spectrum depends explicitly on the spin configuration, enabling selective destabilization of higher-energy states. We further corroborate this analysis using finite-noise perturbation experiments initialized near prescribed Ising configurations. These results highlight how the characteristics of the device nonlinearity directly shape the local dynamical properties of Ising machine implementations.

physics.comp-ph↗

arXiv2026

At the Top of the Mountain, the World can Look Boltzmann-Like: Sampling Dynamics of Noisy Double-Well Systems

The success of the transistor as the cornerstone of digital computation motivates analogous efforts to identify an equivalent hardware primitive, the probabilistic bit or p-bit, for the emerging paradigm of probabilistic computing. Here, we uncover a fundamental ubiquity in the stochastic dynamics of double well energy systems when initialized near the barrier top. Using a topological framework grounded in Morse theory and singularity theory, we make use of the result that all smooth, even double well potentials reduce near the saddle point to a canonical quartic normal form. Within this regime, the interplay of noise, synaptic bias, and potential curvature produces a topologically robust short time evolution characterized by a tanh like response. This enables Boltzmann like sampling that is largely independent of the detailed shape of the potential, apart from its effective temperature scaling. Analytical derivations and numerical simulations across multiple representative systems corroborate this behavior. Our work provides a unifying foundation for assessing and engineering a broad class of physical platforms, including oscillators, bistable latches, and magnetic devices, as p-bits operating within a synchronous framework for stochastic sampling and probabilistic computation.

physics.comp-ph↗

arXiv2024

Designing a K-state P-bit Engine

Probabilistic bit (p-bit)-based compute engines utilize the unique capability of a p-bit to probabilistically switch between two states to solve computationally challenging problems. However, when solving problems that require more than two states (e.g., problems such as Max-3-Cut, verifying if a graph is K-partite (K>2) etc.), additional pre-processing steps such as graph reduction are required to make the problem compatible with a two-state p-bit platform. Moreover, this not only increases the problem size by entailing the use of auxiliary variables but can also degrade the solution quality. In this work, we develop a unique framework for implementing a K-state (K>2) p-bit engine. Furthermore, from an implementation standpoint, we show that such a K-state p-bit engine can be implemented using N traditional (2-state) p-bits, and one multi-state p-bit -- a novel concept proposed here. Augmenting traditional p-bit platforms, our approach enables us to solve an archetypal combinatoric problem class requiring multiple states, namely Max-K-Cut (K=3, 4 shown here), without using any additional auxiliary variables. Thus, our work fundamentally advances the functional capability of p-bit engines, enabling them to solve a broader class of computationally challenging problems more efficiently.

cs.ET↗