Related papers: Canonical Forms and Automorphisms in the Projectiv…
This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within…
Classical coding theory contains several techniques to obtain new codes from other codes, including puncturing and shortening. For quantum codes, a form of puncturing is known, but its description is based on the code space rather than its…
The aim of this paper is to present a symbolic computational algorithm that will allow us to deal with the feedback stabilization problem for continuous nonlinear polynomial systems. The overall approach is based on a methodology that…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…
We consider the distributed optimization problem in which a network of agents aims to minimize the average of local functions. To solve this problem, several algorithms have recently been proposed where agents perform various combinations…
The stabilizer formalism for quantum error-correcting codes has been, without doubt, the most successful at producing examples of quantum codes with strong error-correcting properties. In this paper, we discuss strong automorphism groups of…
Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good…
We present an algorithm for manipulating quantum information via a sequence of projective measurements. We frame this manipulation in the language of stabilizer codes: a quantum computation approach in which errors are prevented and…
Enormous activity in the Quantum Computing area has resulted in considering them to solve different difficult problems, including those of applied nature, together with classical computers. An attempt is made in this work to nail down a…
A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…
Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…
We present a systematic canonical quantization procedure for lumped-element superconducting networks by making use of a redundant configuration-space description. The algorithm is based on an original, explicit, and constructive…
In this paper, we further investigate and refine the subspace-constrained preconditioning technique to enhance the theoretical and numerical convergence properties of randomized iterative methods for solving linear systems. In particular,…
Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…
Robotic manipulation systems are increasingly deployed across diverse domains. Yet existing multi-modal learning frameworks lack inherent guarantees of geometric consistency, struggling to handle spatial transformations such as rotations…
A practical version of the polynomial canonical formalism is developed for normal mesoscopic systems consisting of N independent electrons. Drastic simplification of calculations is attained by means of proper ordering excited states of the…
Canonicalization is a widely used strategy in equivariant machine learning, enforcing symmetry in neural networks by mapping each input to a standard form. Yet, it often introduces discontinuities that can affect stability during training,…
We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in system analysis and verification. Coalgebraic generality allows us to cover not only classical…
This paper is concerned with structures of general graphs with perfect matchings. We first reveal a partially ordered structure among factor-components of general graphs with perfect matchings. Our second result is a generalization of…
As a key step towards a complete automation of the finite element method, we present a new algorithm for automatic and efficient evaluation of multilinear variational forms. The algorithm has been implemented in the form of a compiler, the…