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Results for “topological” 29 papers
Anyons & topology. Anyons, braiding and topological order Tagged papers: 43.
Synthetic Vacuum Photonic Lattices: A Quantitative Feasibility Analysis of Room-Temperature, Gauge-Protected Fibonacci Anyon Computing
Large-scale fault-tolerant quantum computation currently requires cryogenic operation and an active error-correction layer whose ancilla, syndrome-extraction and magic-state overheads dominate the resource budget of any scalable processor. A conjectured alternative is a room-temperature solid-state…
Can Finite‑Group Topological Quantum Field Theories Generate Continuous Standard‑Model Gauge Symmetry?
The Standard Model (SM) requires a continuous gauge group $SU(3)\times SU(2)\times U(1)$ with infinitely many charge sectors, while finite‑group Walker‑Wang constructions provide only finitely many superselection sectors. Existing proposals therefore face a gap: no demonstration that a finite‑group…
Exchange Symmetry Is an Involution, Not an Idempotent: A Derivation‑Based Fact‑Check
The claim that particle exchange is idempotent, that the two‑particle configuration space is the three‑sphere $S^{3}$, that the spin‑statistics theorem holds without qualification, and that non‑Abelian anyons are idempotent appears in recent speculative notes. This paper addresses the gap between…
Passive Error Rejection via Cryo-Fluidic Topological Phases: A Feasibility Analysis of the Topological Matter Engine
Active quantum error correction imposes a large and growing overhead of physical qubits, control electronics, and entropy-exporting measurement cycles on every scalable quantum processor. This paper examines a proposed alternative: a "Topological Matter Engine" in which errors are rejected…
Braid Group Representations, Modular Data, and the Classification of Majorana Zero Mode Fusion Rules in Two-Dimensional Topological Superconductors
Majorana zero modes (MZMs) bound to vortices of a two-dimensional topological superconductor (2D TSC) realize non-Abelian anyons whose exchange is described by a projective representation of the braid group $B_N$. The associated anyon theory is encoded in a modular tensor category (MTC) with fusion…
Quantitative Bulk–Boundary Correspondence for Anyon Condensation: Two Computable Indices with Explicit Arithmetic
When a $(2+1)$-dimensional topologically ordered phase terminates at a boundary where a subset of anyons condenses, the boundary becomes gapped, and the bulk–boundary correspondence acquires sharp quantitative content: which boundary phenomena are forced by the bulk condensation data, and which…
Projective Braid Group Representations from a Microscopic Long-Range Kitaev Chain
We construct an explicit projective representation of the braid group from the microscopic Hilbert space of a Kitaev chain extended with algebraically decaying long-range hopping and pairing. The construction proceeds in three steps. First, we identify the topological phase of the long-range Kitaev…
A Two-Index Framework for the Bulk-Boundary Correspondence of Anyon Condensation and Boundary Majorana Statistics
The bulk-boundary correspondence asserts that topological data of a (2+1)-dimensional phase determine the physics of its boundary, but in the setting of anyon condensation the correspondence is usually stated structurally rather than quantitatively. We propose a set of computable indices that…
Braid Group Representations and Modular Data: Non-Uniqueness, Finite Images, and the Ising Test Case
A central question in the theory of topological order asks whether the braid group representation $B_N$ carried by $N$ non-Abelian anyons uniquely determines the modular data — the $S$ and $T$ matrices — of the underlying topological quantum field theory. We reconcile three lines of analysis into a…
Braid Group Representations, Modular Data, and the Classification of Majorana Zero Mode Fusion Rules in 2D Topological Superconductors
Majorana zero modes (MZMs) localized on vortices of a two-dimensional topological superconductor carry a projective representation of the braid group, and the associated anyon theory is encoded in a modular tensor category whose fusion rules and modular data ($S$ and $T$ matrices) determine the…
Braid Group Representations, Modular Data, and the Classification of Majorana Zero Mode Fusion Rules in 2D Topological Superconductors
We investigate whether the braid group representation on $N$ anyons uniquely determines the modular data ($S$ and $T$ matrices) of a non-Abelian topological order, and whether this framework classifies all fusion rules for Majorana zero modes (MZMs) in 2D topological superconductors. We show that…
Majorana Zero‑Mode Parity, the Hexagon Equation, and the Necessity of Chiral Edge Modes in Two‑Dimensional Topological Superconductors
Topological quantum computation requires non‑Abelian anyons whose braiding implements fault‑tolerant logical gates. In two‑dimensional topological superconductors, vortices bind Majorana zero modes (MZMs) that furnish a projective braid‑group representation. A persistent open question is whether the…
Configuration-Space Topology and the Distinction Calculus: The Exchange Scalar, Its ±1 Shadow, and a Pre-Registered Derivation Program
Configuration-space topology (CST) derives exchange statistics from the topology of the space in which identical particles move: the fundamental group pi_1(C_N(M)) is the symmetric group S_N in d >= 3 spatial dimensions (exactly two exchange phases: boson +1, fermion -1) and the braid group B_N in d…
Vanishing ZBW Signal: The ZBW-Majorana Hypothesis as a Unified Framework for Topological Fermion Distinction
The ZBW-Majorana hypothesis, developed across four companion papers (P1--P4), establishes that Zitterbewegung (ZBW) --- the rapid trembling motion of Dirac fermions at the Compton scale --- is a $\mathbb{Z}_2$ topological observable that distinguishes Dirac from Majorana fermions at the hardware…
p-Adic Anyon Fusion and Braiding: Quantum Groups at Roots of Unity, Verma Modules, and Ultrametric Anyon Models
Phases 1–2 established the p-adic braid group $B_n(\mathbb{Q}_p)$ on Bruhat-Tits buildings and identified the Temperley-Lieb parameter $\delta$ as a p-adic cyclotomic unit, yielding a p-adic Markov trace and Jones polynomial $V_L^p(t) \in \mathbb{Z}_p[\zeta_{2p^k}]$. In this third phase, we complete…
p-Adic Braid Groups on Bruhat-Tits Buildings
The standard braid group $B_n$ is defined as the fundamental group of the configuration space of $n$ distinct points in $\mathbb{R}^2$, $\pi_1(\text{Conf}_n(\mathbb{R}^2))$. This construction is inherently archimedean: it relies on the continuous topology of $\mathbb{R}^2$ to define braiding as…
Zitterbewegung as the Physical Realization of p-Adic Anyon Braiding
The p-Adic Anyons program (Phases 1-4) developed the mathematical framework for anyons whose braid statistics are defined on Bruhat-Tits trees rather than in continuous spacetime. The ZBW program (P1-P3) demonstrated that Zitterbewegung — the rapid trembling motion of Dirac fermions at the Compton…
Adelic Synthesis: The Pattern-Particle Correspondence and the Complete Arithmetic Theory of Anyons
The prior three phases of this program constructed p-adic anyon theories at individual finite places: p-adic braid groups on Bruhat-Tits buildings (Phase 1), the Temperley-Lieb parameter as p-adic cyclotomic units with the p-adic Jones polynomial (Phase 2), and anyon fusion and braiding via…
Zitterbewegung as a p-Adic Observable: Ultrametric Readout and Intrinsic Topological Protection
The Zitterbewegung (ZBW) of a Dirac fermion — the rapid oscillatory motion at the Compton frequency arising from interference between positive- and negative-energy states — has resisted direct experimental observation for nearly a century. The standard interpretation attributes this to the Compton…
Majorana Zitterbewegung Current Correlator: Vanishing ZBW Signal as a Z2 Topological Invariant
We compute the Zitterbewegung contribution to the current-current correlator $\langle j^\mu(x) j^\nu(0) \rangle$ for both Dirac and Majorana fermions in (2+1) dimensions. In the Dirac case, the ZBW term oscillates at frequency $2E$ with magnitude comparable to the static vacuum polarization term…
Topological Aliasing and Holographic Readout
URL: https://papers.qnfo.org/papers/topological-aliasing-and-holographic-readout/ Date: 2026-03-23 Version: 1.0 The foundation of modern physical theories relies heavily on the continuous nature of real numbers. This mathematical framework assumes that space and time can be divided infinitely…
Quantum Architectonics
The engineering of robust, decoherence-resistant topological qubits is currently impeded by a fragmented approach to material design that often treats control parameters in isolation. This study introduces and computationally supports the “Superconducting Quadrangle,” a unified framework integrating…
Double Pendulum as a Topological Bridge
The double pendulum serves as the paradigmatic model for the transition from integrability to chaos, yet its potential as a rigorous bridge between classical nonlinear dynamics and quantum open systems remains underutilized. By treating the system’s phase space as a topologically tiled manifold…
Hamiltonian Engineering of Topological Deconfinement in Weyl Semimetals
The theoretical existence of the magnetic monopole has long represented a foundational prediction in physics, with significant implications for technology. However, astrophysical constraints (the Parker Bound) render the extraction of cosmic monopoles physically and economically non-viable. This…
Operationalizing Generalized Symmetries
The experimental realization of Fractional Chern Insulators (FCIs) in twisted moiré superlattices has opened a new frontier for topological physics, yet the classification of their underlying generalized symmetries remains theoretically abstract. This study operationalizes the framework of…
TOPOLOGICAL HYDRODYNAMICS AND THE SPECTRAL GAP
Standard quantum field theory conceptualizes the vacuum as a probabilistic void, yet phenomenological isomorphism with superfluid Helium-3 suggests a deeper hydrodynamic ontology. While this topological substrate theoretically supports analog computation via vorticity, the practical realization is…
Chiral High-Temperature Topological Processing
By replacing active syndrome extraction with passive topological protection derived from the 25 meV spectral gap of 45-degree twisted Bi-2212, the architecture circumvents the cooling power limitations of dilution refrigeration to enable the monolithic integration of classical control logic at 4…
Topological Origins of Number Theory
This establishes a theoretical framework wherein number-theoretic structures, particularly prime factorization, emerge as causal signatures of topological organization in quantum critical systems. We posit a foundational ontological inversion: physical reality, including particles and spacetime, is…
Winding Number as Hidden Variable
This paper proposes that physical reality emerges from a pre-geometric substrate based on the circle \(S^1\), with its integer winding numbers providing a deterministic foundation for physics. A universal computation of pattern writing, evolution, and projection generates spacetime and particles,…
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