Related papers: Optimization Algorithms Based on Renormalization G…

Optimization by stochastic gradient descent is an important component of many large-scale machine learning algorithms. A wide variety of such optimization algorithms have been devised; however, it is unclear whether these algorithms are…

The advantages of evolutionary algorithms with respect to traditional methods have been greatly discussed in the literature. While particle swarm optimizers share such advantages, they outperform evolutionary algorithms in that they require…

The renormalization group method is a successive integration over the fluctuations which are ordered according to their length scale, a parameter in the external space. A different procedure is described, where the fluctuations are treated…

A new approach to combinatorial optimization based on systematic move-class deflation is proposed. The algorithm combines heuristics of genetic algorithms and simulated annealing, and is mainly entropy-driven. It is tested on two problems…

We introduce a numerical method of the adaptive time-dependent density-matrix renormalization-group to compute one-dimensional quantum spin systems with periodic boundary condition. We check our algorithm to study the dynamic correlation in…

Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this…

This paper argues that the ideas underlying the renormalization group technique used to characterize phase transitions in condensed matter systems could be useful for distinguishing computational complexity classes. The paper presents a…

Finding the ground state of Ising spin glasses is notoriously difficult due to disorder and frustration. Often, this challenge is framed as a combinatorial optimization problem, for which a common strategy employs simulated annealing, a…

A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard approaches, such as variational calculations, consist of writing down a wave function ansatz and minimizing over…

We discuss the formulation of "thermal renormalization group-equations" and their application to the finite temperature phase-transition of scalar O(N)-theories. Thermal renormalization group-equations allow for a computation of both the…

For the last few decades, optimization has been developing at a fast rate. Bio-inspired optimization algorithms are metaheuristics inspired by nature. These algorithms have been applied to solve different problems in engineering, economics,…

While there are various approaches to benchmark physical processors, recent findings have focused on computational phase transitions. This is due to several factors. Importantly, the hardest instances appear to be well-concentrated in a…

We propose a general learning algorithm for solving optimization problems, based on a simple strategy of trial and adaptation. The algorithm maintains a probability distribution of possible solutions (configurations), which is updated…

The numerical realization of the dynamic programming principle for continuous-time optimal control leads to nonlinear Hamilton-Jacobi-Bellman equations which require the minimization of a nonlinear mapping over the set of admissible…

Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…

We propose a new design heuristic to tackle combinatorial optimisation problems, inspired by Hamiltonians for optimal state-transfer. The result is a rapid approximate optimisation algorithm. We provide numerical evidence of the success of…

We study the fully generalized Grover's algorithm to find the optimal phase changes for each step of the iteration to maximize gain in probability of observation of the target, and when phase matching is required. We find that classical…

The use of combinatorial optimization algorithms has contributed substantially to the major progress that has occurred in recent years in the understanding of the physics of disordered systems, such as the random-field Ising model. While…

A quantum thermodynamic system is described by a Hamiltonian and a list of conserved, non-commuting charges, and a fundamental goal is to determine the minimum energy of the system subject to constraints on the charges. Recently, [Liu et…

Incorporating the concept of order parameter of the mean-field theory into the simulated annealing method, we presented a new optimization algorithm, the guided simulated annealing method. In this method mean-field order parameters are…