17 citations · 85 across the 19 of their papers we have counts for
19 papers
A Hierarchy of Fibonacci Forbidden-Word Hamiltonians: From the Golden Chain to the Plastic Chain and Aperiodic Order
Marcelo Maciel Amaral
We introduce an infinite, scale-aligned hierarchy of one-dimensional, frustration-free Hamiltonians by forbidding the minimal forbidden factors of the Fibonacci word up to length $…
The Lock-In Phase Hypothesis: Identity Consolidation as a Precursor to AGI
Marcelo Maciel Amaral, Raymond Aschheim
Large language models (LLMs) remain broadly open and highly steerable: they imitate at scale, accept arbitrary system prompts, and readily adopt multiple personae. By analogy to hu…
Consistent Simulation of Fibonacci Anyon Braiding within a Qubit Quasicrystal Inflation Code
Marcelo M. Amaral
The simulation of non-Abelian anyon braiding is a critical step towards fault-tolerant quantum computation. We introduce a framework for this task based on a one-dimensional Quasic…
Tiling Spaces and the Expanding Universe: Bridging Quantum Mechanics and Cosmology
Marcelo Maciel Amaral, Aman Yadav
We propose a heuristic model of the universe as a growing quasicrystal projected from a higher-dimensional lattice. This quasicrystalline framework offers a novel perspective on co…
Quasicrystalline Spin Foam with Matter: Definitions and Examples
Marcelo Amaral, Richard Clawson, Klee Irwin
In this work, we define quasicrystalline spin networks as a subspace within the standard Hilbert space of loop quantum gravity, effectively constraining the states to coherent stat…
Exploiting Anyonic Behavior of Quasicrystals for Topological Quantum Computing
Marcelo Amaral, David Chester, Fang Fang +1
We show that quasicrystals exhibit anyonic behavior that can be used for topological quantum computing. In particular, we study a correspondence between the fusion Hilbert spaces o…
Character varieties and algebraic surfaces for the topology of quantum computing
Michel Planat, Marcelo M. Amaral, Fang Fang +3
It is shown that the representation theory of some finitely presented groups thanks to their character variety is related to algebraic surfaces. We make use of t…
Informationally complete characters for quark and lepton mixings
Michel Planat, Raymond Aschheim, Marcelo M. Amaral +1
A popular account of the mixing patterns for the three generations of quarks and leptons is through the characters of a finite group . Here we introduce a -dimensional Hi…
Aspects of aperiodicity and randomness in theoretical physics
Leonardo Ortiz, Marcelo Amaral, Klee Irwin
In this work we explore how the heat kernel, which gives the solution to the diffusion equation and the Brownian motion, would change when we introduce quasiperiodicity in the scen…
Quantum computation and measurements from an exotic space-time R4
Michel Planat, Raymond Aschheim, Marcelo. M. Amaral +1
The authors previously found a model of universal quantum computation by making use of the coset structure of subgroups of a free group with relations. A valid subgroup of…
Holographic Code Rate
Noah Bray-Ali, David Chester, Dugan Hammock +3
Holographic codes grown with perfect tensors on regular hyperbolic tessellations using an inflation rule protect quantum information stored in the bulk from errors on the boundary…
Group geometrical axioms for magic states of quantum computing
Michel Planat, Raymond Aschheim, Marcelo M. Amaral +1
Let be a non trivial subgroup of index of a free group and the normal closure of in . The coset organization in a subgroup of provides a group of…
Quantum Gravity at the Fifth Root of Unity
Marcelo Amaral, Raymond Aschheim, Klee Irwin
We consider quantum transition amplitudes, partition functions and observables for 3D spin foam models within quantum group deformation symmetry, where the deformation para…
Quantum computing, Seifert surfaces and singular fibers
Michel Planat, Raymond Aschheim, Marcelo M. Amaral +1
The fundamental group of a knot or link may be used to generate magic states appropriate for performing universal quantum computation and simultaneously for retrieving…
Quantum computing with Bianchi groups
Michel Planat, Raymond Aschheim, Marcelo M. Amaral +1
It has been shown that non-stabilizer eigenstates of permutation gates are appropriate for allowing -dimensional universal quantum computing (uqc) based on minimal informational…
Anamorphic Quasiperiodic Universes in Modified and Einstein Gravity with Loop Quantum Gravity Corrections
Marcelo M. Amaral, Raymond Aschheim, Laurenţiu Bubuianu +3
The goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theo…
A path-integral approach to the problem of time
M. M. Amaral, Martin Bojowald
Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of…
Quantum walk on a spin network
M. M. Amaral, R. Aschheim, Klee Irwin
We apply a discrete quantum walk from a quantum particle on a discrete quantum spacetime from loop quantum gravity and show that the related Entanglement Entropy can drive a entrop…
Remarks on Gribov mechanism on N=1 Supersymmetric 3D theories and the possibility of obtaining Gribov from one ABJM like Theory
M. M. Amaral, V. E. R. Lemes
Some remarks on Gribov mechanism on N=1 Supersymmetric 3D theories are presented. The two point correlation function is analysed and the possibility of obtaining the confining Grib…