Related papers: A simple approach towards the sign problem using p…
The complex Langevin approach is a promising method for the numerical treatment of systems with a sign problem, for which conventional lattice field theory techniques based on importance sampling cannot be applied. However, complex Langevin…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
A method is proposed to handle the sign problem in the simulation of systems having indefinite or complex-valued measures. In general, this new approach, which is based on renormalisation blocking, is shown to yield statistical errors…
The properties of strongly-coupled lattice gauge theories at finite density as well as in real time have largely eluded first-principles studies on the lattice. This is due to the failure of importance sampling for systems with a complex…
A possible method to solve the sign problem is developed by modifying the original theory. Considering several modifications of the partition function, the observable in the original theory is reconstructed from the identity connecting the…
We discuss how a lattice Schwinger model can be realized in a linear ion trap, allowing a detailed study of the physics of Abelian lattice gauge theories related to one-dimensional quantum electrodynamics. Relying on the rich…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the…
We investigate the efficiency of a gauge invariant input to a neural network for the path optimization method. While the path optimization with a completely gauge-fixed link-variable input has successfully tamed the sign problem in a simple…
Polynomial optimization problems represent a wide class of optimization problems, with a large number of real-world applications. Current approaches for polynomial optimization, such as the sum of squares (SOS) method, rely on large-scale…
We present a method to design parallel algorithms for constrained combinatorial optimization problems. Our method solves and generalizes many classical combinatorial optimization problems including the stable marriage problem, the shortest…
We consider a separation problem where the observation consists of the sum of a high amplitude smooth signal and a low amplitude transient signal. We propose a method for decomposition that relies on solving instances of a `constrained…
Exact diagonalization techniques are a powerful method for studying many-body problems. Here, we apply this method to systems of few bosons in an optical lattice, and use it to demonstrate the emergence of interesting quantum phenomena like…
We present a solution to the sign problem in a class of particle-hole symmetric Hamiltonian lattice fermion models on bipartite lattices using the idea of fermion bags. The solution remains valid when the particle-hole symmetry is broken…
Lattice models with complex actions are important for the understanding of matter at finite densities, but not accessible by the standard Monte Carlo techniques due to the sign problem. Here we derive a new approach for avoiding the complex…
The Lefschetz thimble method, i.e., the integration along the steepest descent cycles, is an idea to evade the sign problem by complexifying the theory. We discuss that such steepest descent cycles can be identified as ground-state…
A non-conventional shape optimization approach is introduced to address the identification of an obstacle immersed in a fluid described by the Stokes equation within a larger bounded domain, relying on boundary measurements on the…
In this article a topology optimization method is developed, which is aware of material uncertainties. The uncertainties are handled in a worst-case sense, i.e. the worst possible material distribution over a given uncertainty set is taken…
We present a new approach to Bayesian inference that entirely avoids Markov chain simulation, by constructing a map that pushes forward the prior measure to the posterior measure. Existence and uniqueness of a suitable measure-preserving…
In Monte Carlo simulation, lattice field theory with a $\theta$ term suffers from the sign problem. This problem can be circumvented by Fourier-transforming the topological charge distribution $P(Q)$. Although this strategy works well for…