Related papers: Complexity continuum within Ising formulation of N…
A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level…
A degenerate optical parametric oscillator network is proposed to solve the NP-hard problem of finding a ground state of the Ising model. The underlying operating mechanism originates from the bistable output phase of each oscillator and…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
Many spin systems affected by critical slowing down can be efficiently simulated using cluster algorithms. Where such systems have long-range interactions, suitable formulations can additionally bring down the computational effort for each…
Paper: cond-mat/9311033 The Hubbard model of interacting electrons, like the Ising model of spin-spin interactions, is the simplest possible model displaying many ``real world'' features, but it is much more difficult to analyze…
In the well-known complexity class NP are combinatorial problems, whose optimization counterparts are important for many practical settings. These problems typically consider full knowledge about the input. In practical settings, however,…
We propose an algorithm to compute the dynamics of articulated rigid-bodies with different sensor distributions. Prior to the on-line computations, the proposed algorithm performs an off-line optimisation step to simplify the computational…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
The last decade has seen the rise of neuromorphic architectures based on artificial spiking neural networks, such as the SpiNNaker, TrueNorth, and Loihi systems. The massive parallelism and co-locating of computation and memory in these…
The coherent Ising machine (CIM) is a quantum-inspired computing platform that leverages optical parametric oscillation dynamics to solve combinatorial optimization problems by searching for the ground state of an Ising Hamiltonian.…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables…
The exact solution of Schrodinger equation for atoms, molecules and extended systems continues to be a "Holy Grail" problem that the entire field has been striving to solve since its inception. Recently, breakthroughs have been made in the…
Many combinatorial optimization problems (COPs) are naturally expressed using variables that take on more than two discrete values. To solve such problems using Ising machines (IMs) - specialized analog or digital devices designed to solve…
We study the complexity of approximating the partition function of dense Ising models in the critical regime. Recent work of Chen, Chen, Yin, and Zhang (FOCS 2025) established fast mixing at criticality, and even beyond criticality in a…
We introduce a novel criterion in clustering that seeks clusters with limited range of values associated with each cluster's elements. In clustering or classification the objective is to partition a set of objects into subsets, called…
We study the problem of computing the minimum adversarial perturbation of the Nearest Neighbor (NN) classifiers. Previous attempts either conduct attacks on continuous approximations of NN models or search for the perturbation by some…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…
Oscillator Ising machines (OIMs) represent an exemplar case of using physics-inspired non-linear dynamical systems to solve computationally challenging combinatorial optimization problems (COPs). The computational performance of such…
In recent years, hardware implementations of Ising machines have emerged as a viable alternative to quantum computing for solving hard optimization problems among other applications. Unlike quantum hardware, dense connectivity can be…