Related papers: Path optimization for $U(1)$ gauge theory with com…
Within the framework of the path-integral formalism we reinvestigate the different methods of removing the unphysical degrees of freedom from spontanously broken gauge theories. These are: construction of the unitary gauge by gauge fixing;…
In theories with topological sectors, such as lattice QCD and four-dimensional SU(N) gauge theories with periodic boundary conditions, conventional update algorithms suffer from topological freezing due to large action barriers separating…
We review our perturbative techniques for improved heavy quark actions. A new procedure for computing improvement coefficients is suggested, where the continuum limit of a lattice-regularized theory provides the matching conditions.We also…
This paper presents a novel phase-field-based methodology for solving minimum compliance problems in topology optimization under fixed external loads and body forces. The proposed framework characterizes the optimal structure through an…
In this paper, we present an automated parameter optimization method for trajectory generation. We formulate parameter optimization as a constrained optimization problem that can be effectively solved using Bayesian optimization. While the…
We present a framework wherein the trajectory optimization problem (or a problem involving calculus of variations) is formulated as a search problem in a discrete space. A distinctive feature of our work is the treatment of discretization…
We consider the possibility of gauge coupling unification within the simplest realizations of the $\mathrm{SU(3)_c \times SU(3)_L \times SU(3)_R \times U(1)_{X}}$ gauge theory. We present a first exploration of the renormalization group…
We consider a suboptimal solution path algorithm for the Support Vector Machine. The solution path algorithm is an effective tool for solving a sequence of a parametrized optimization problems in machine learning. The path of the solutions…
Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter, and quantum information science. Their local symmetries enforce the charge conservation observed in the laws of physics. Impressive…
We analyze approaches to the partial or complete unification of gauge symmetries in theories with dynamical symmetry breaking. Several types of models are considered, including those that (i) involve sufficient unification to quantize…
Gauge functions significantly generalize the notion of a norm, and gauge optimization, as defined by Freund (1987}, seeks the element of a convex set that is minimal with respect to a gauge function. This conceptually simple problem can be…
The quantum approximate optimization algorithm (QAOA) has numerous promising applications in solving the combinatorial optimization problems on near-term Noisy Intermediate Scalable Quantum (NISQ) devices. QAOA has a quantum-classical…
In this paper, we investigate a digitised SU$(2)$ lattice gauge theory in the Hamiltonian formalism. We use partitionings to digitise the gauge degrees of freedom and show how to define a penalty term based on finite element methods to…
In this paper, we investigate the complexity of the central path of semidefinite optimization through the lens of real algebraic geometry. To that end, we propose an algorithm to compute real univariate representations describing the…
A thesis submitted for the degree of Doctor of Philosophy of The Australian National University. In this work we introduce several new optimisation methods for problems in machine learning. Our algorithms broadly fall into two categories:…
The Landau gauge fixing algorithm in the new definition of gauge fields is presented. In this algorithm a new solver of the Poisson equations based on the Green's function method is used. Its numerical performance of the gauge fixing…
For a wide variety of regularization methods, algorithms computing the entire solution path have been developed recently. Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but…
A generalization of Wilsonian lattice gauge theory may be obtained by considering the possible self-adjoint extensions of the electric field operator in the Hamiltonian formalism. In the special case of 3D $\mathrm{U}(1)$ gauge theory these…
We discuss the interpretation of path integral optimization as a uniformization problem in even dimensions. This perspective allows for a systematical construction of the higher-dimensional path integral complexity in holographic conformal…
We discuss a gauged XY model a $\theta$-term on an arbitrary lattice in 1+1 dimensions, and show that the theory reduces exactly to the 2d Ising model on the dual lattice in the limit of the strong gauge coupling, provided that the…