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There has been a recent surge of interest in physics-based solvers for combinatorial optimization problems. We present a dynamical solver for the Ising problem that is comprised of a network of coupled parametric oscillators and show that…
Oscillator-based Ising/Potts machines (OIMs/OPMs) are promising hardware accelerators for NP-hard combinatorial optimization problems using coupled oscillator synchronization dynamics. Analog OIMs/OPMs offer speed advantages but have…
Grover's database search algorithm is the optimal algorithm for finding a desired object from an unsorted collection of items. Although it was discovered in the context of quantum computation, it is simple and versatile enough to be…
Mathematical optimization is one of the cornerstones of modern engineering research and practice. Yet, throughout all application domains, mathematical optimization is, for the most part, considered to be a numerical discipline.…
Synchronous oscillations in neuronal ensembles have been proposed to provide a neural basis for the information processes in the brain. In this work, we present a neuromorphic computing algorithm based on oscillator synchronization in a…
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…
We introduce a novel approach to solving dynamic programming problems, such as those in many economic models, on a quantum annealer, a specialized device that performs combinatorial optimization. Quantum annealers attempt to solve an…
Synthesizing optimal controllers for dynamical systems often involves solving optimization problems with hard real-time constraints. These constraints determine the class of numerical methods that can be applied: computationally expensive…
A prominent approach to solving combinatorial optimization problems on parallel hardware is Ising machines, i.e., hardware implementations of networks of interacting binary spin variables. Most Ising machines leverage second-order…
This paper deals with an optimal control problem associated to the Kuramoto model describing the dynamical behavior of a network of coupled oscillators. Our aim is to design a suitable control function allowing us to steer the system to a…
Combinatorial optimization problems pose significant computational challenges across various fields, from logistics to cryptography. Traditional computational methods often struggle with their exponential complexity, motivating exploration…
Building oscillator based computing systems with emerging nano-device technologies has become a promising solution for unconventional computing tasks like computer vision and pattern recognition. However, simulation and analysis of these…
Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven…
We study the optimal design of a conductance network as a means for synchronizing a given set of oscillators. Synchronization is achieved when all oscillator voltages reach consensus, and performance is quantified by the mean-square…
An overview is given on two representative methods of dynamical reduction known as center-manifold reduction and phase reduction. These theories are presented in a somewhat more unified fashion than the theories in the past. The target…
Interest in non-algorithmic, unconventional computing is rising in recent years due to more and more apparent short comings of classic stored-program digital computers, such as energy efficiency, degree of parallelism in computations, clock…
We present a method to approximately solve general instances of combinatorial optimization problems using the physical dynamics of 3d rotors obeying Landau-Lifshitz-Gilbert dynamics. Conventional techniques to solve discrete optimization…
In this thesis I discuss combinatorial optimization problems, from the statistical physics perspective. The starting point are the motivations which brought physicists together with computer scientists and mathematicians to work on this…
Combinatorial optimization is a promising application for near-term quantum computers, however, identifying performant algorithms suited to noisy quantum hardware remains as an important goal to potentially realizing quantum computational…
In this paper, we develop a computationally-efficient approach to minimum-time trajectory optimization using input-output data-based models, to produce an end-to-end data-to-control solution to time-optimal planning/control of dynamic…