arXiv subjects
Publications and source records attributed to Tiago M. L. Veras.
We use a labelled deduction system ( LND$_{ED-}$TRS ) based on the concept of computational paths (sequences of rewrites) as equalities between two terms of the same type, which allowed us to carry out in homotopic theory an approach using the concept of computational paths. From this, we show that the computational paths can be used to perform the proofs of the $LND_{EQ}-TRS_{2}$ rewriting system.
We use a labelled deduction system based on the concept of computational paths (sequences of rewrites) as equalities between two terms of the same type. We also define a term rewriting system that is used to make computations between these computational paths, establishing equalities between equalities. We then proceed to show the main result here: using this system to obtain the calculation of the fundamental group of the circle, of the torus and the real projective plane.
Probabilistic Quantum Memory (PQM) is a data structure that computes the distance from a binary input to all binary patterns stored in superposition on the memory. This data structure allows the development of heuristics to speed up artificial neural networks architecture selection. In this work, we propose an improved parametric version of the PQM to perform pattern classification, and we also present a PQM quantum circuit suitable for Noisy Intermediate Scale Quantum (NISQ) computers. We present a classical evaluation of a parametric PQM network classifier on public benchmark datasets. We also perform experiments to verify the viability of PQM on a 5-qubit quantum computer.