Related papers: Q-curvature and Path Integral Complexity
We consider some important computational aspects of the long-step path-following algorithm developed in our previous work and show that a broad class of complicated optimization problems arising in quantum information theory can be solved…
Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…
We consider an ``integral'' extension of the classical notion of affine connection providing a correspondence between paths in the manifold and diffeomorphisms of the manifold. These path-diffeomorphisms are a generalization of parallel…
The quadratic unconstrained binary optimization (QUBO) problem arises in diverse optimization applications ranging from Ising spin problems to classical problems in graph theory and binary discrete optimization. The use of preprocessing to…
Quantum variational optimization has been posed as an alternative to solve optimization problems faster and at a larger scale than what classical methods allow. In this paper we study systematically the role of entanglement, the structure…
Since quantum spatial searches on complex networks have a strong network dependence, the question arises whether the universal perspective exists in this quantum algorithm for complex networks. Here, we uncover the universal scaling laws of…
In this work we deal with the so-called path convexities, defined over special collections of paths. For example, the collection of the shortest paths in a graph is associated with the well-known geodesic convexity, while the collection of…
This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the…
The algebraic path problem provides a general setting for shortest path algorithms in optimization and computer science. This work extends the algebraic path problem to networks equipped with input and output boundaries. We show that the…
Convex optimization encompasses a wide range of optimization problems that contain many efficiently solvable subclasses. Interior point methods are currently the state-of-the-art approach for solving such problems, particularly effective…
In the foreseeable future, toolchains for quantum computing should offer automatic means of transforming a high level problem formulation down to a hardware executable form. Thereby, it is crucial to find (multiple) transformation paths…
We introduce a quantum algorithm for computing the Ollivier Ricci curvature, a discrete analogue of the Ricci curvature defined via optimal transport on graphs and general metric spaces. This curvature has seen applications ranging from…
One of several possibilities to construct a quantum theory of gravity is employing the Feynman path integral. This approach is plagued by some problems: the integration measure is not uniquely defined, the Einstein-Hilbert action unbounded,…
Gauge invariance of systems whose Hamilton-Jacobi equation is separable is improved by adding surface terms to the action fuctional. The general form of these terms is given for some complete solutions of the Hamilton-Jacobi equation. The…
Quantum circuit complexity has played a central role in recent advances in holography and many-body physics. Within quantum field theory, it has typically been studied in a Lorentzian (real-time) framework. In a departure from standard…
We solve robot trajectory planning problems at industry-relevant scales. Our end-to-end solution integrates highly versatile random-key algorithms with model stacking and ensemble techniques, as well as path relinking for solution…
Sparse parametric models are of great interest in statistical learning and are often analyzed by means of regularized estimators. Pathwise methods allow to efficiently compute the full solution path for penalized estimators, for any…
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…
We study different aspects the worldline path integrals with gauge fields using quantum computing. We use the Variational Quantum Eigensolver (VQE) and Evolution of Hamiltonian (EOH) quantum algorithms and IBM QISKit to perform our…
We develop the structure theory for transformations of weakly geometric rough paths of bounded $1 < p$-variation and their controlled paths. Our approach differs from existing approaches as it does not rely on smooth approximations. We…