Related papers: A Universal Construction for Unique Sink Orientati…
Polynomial optimization encompasses a broad class of problems in which both the objective function and constraints are polynomial functions of the decision variables. In recent years, a substantial body of research has focused on…
Mutually unbiased bases (MUBs) are a primitive used in quantum information processing to capture the principle of complementarity. While constructions of maximal sets of d+1 such bases are known for systems of prime power dimension d, it is…
We present modular and optimal architectures for implementing arbitrary discrete unitary transformations on light. These architectures are based on systematically combining smaller M-mode linear optical interferometers together to implement…
Universal cycles are generalizations of de Bruijn cycles and Gray codes that were introduced originally by Chung, Diaconis, and Graham in 1990. They have been developed by many authors since, for various combinatorial objects such as…
We construct an informationally complete set of mutually unbiased - like bases for N ququarts. These bases are used in an explicit tomographic protocol which performance is analyzed by estimating quadratic errors and compared to other…
The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of…
The formalization of process algebras usually starts with a minimal core of operators and rules for its transition system, and then relax the system to improve its usability and ease the proofs. In the calculus of communicating systems…
We give a conceptual explanation of universal deformation formulas for unital associative algebras and prove some results on the structure of their moduli spaces. We then generalize universal deformation formulas to other types of algebras…
In this paper we develop methods to extend the minimal hypersurface approach to positive scalar curvature problems to all dimensions. This includes a proof of the positive mass theorem in all dimensions without a spin assumption. It also…
Sequence prediction methods for dynamical systems with long memory, i.e. marginally stable systems, typically achieve regret that grows polynomially with the hidden dimension of the underlying generative model. Universal Sequence…
Analysis of small angle scattering (SAS) data requires intensive modelling to infer and characterize the structures present in a sample. This iterative improvement of models is a time consuming process. Here we present the Scattering…
We construct universal mixers, incompressible flows that mix arbitrarily well general solutions to the corresponding transport equation, in all dimensions. This mixing is exponential in time (i.e., essentially optimal) for any initial…
The universal object oriented languages made programming more simple and efficient. In the article is considered possibilities of using similar methods in computer algebra. A clear and powerful universal language is useful if particular…
For numerous applications of quantum theory it is desirable to be able to apply arbitrary unitary operations on a given quantum system. However, in particular situations only a subset of unitary operations is easily accessible. This raises…
This short note highlights the most prominent mathematical problems and physical questions associated with the existence of the maximum sets of mutually unbiased bases (MUBs) in the Hilbert space of a given dimension
Data storage in Distributed Storage Systems (DSSs) is a multidimensional optimization problem. Using network coding, one wants to provide reliability, scalability, security, reduced storage overhead, reduced bandwidth for repair and minimal…
UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a…
We propose a deterministic SWAP gate for spatially encoded qubits. The gate is constructed from waveguide crossings, Mach Zender Interferometers and phase shifters providing the gate reconfigurability. Through manipulating the phase of the…
The dynamics of many-body systems spanning condensed matter, cosmology, and beyond is hypothesized to be universal when the systems cross continuous phase transitions. The universal dynamics is expected to satisfy a scaling symmetry of…
We concretely construct an extension of the controlled-U gate in qudit from some elementary gates. We also construct unitary transformation in two-qudit by means of the extended controlled-U gate and show the universality of it.