Version: v1.0 DESCRIPTION: We introduce Coherence Field Dynamics (CFD), a theoretical framework that extends holographic quantum gravity by promoting quantum coherence — the off-diagonal density matrix elements — to an independent geometric degree of freedom. While standard holographic frameworks (AdS/CFT, Ryu-Takayanagi) encode bulk geometry through entanglement entropy alone, CFD posits that coherence parameterizes effective bulk depth, complementary to entanglement's encoding of connectivity. The coherence field φ(p,γ) satisfies a wave equation in information-geometric parameter space, generating a Lorentzian metric that degenerates at a critical decoherence threshold γ_c. The framework predicts the existence of such a threshold from geometric stability analysis; its specific numerical value is system-dependent. Connections are established between information geometry, MERA tensor networks, and holographic entropy. The variational principle coupling coherence to an effective gravitational action is presented as an analogue gravity model (c and G are effective parameters), not a claim about physical 4D spacetime. Key results: Theoretical framework: coherence field equation, information-geometric metric, variational principle, and five testable predictionsCompanion experimental work demonstrates a fidelity threshold at γ ≈ 0.535 on IonQ Forte-1 (F = 0.988 baseline, collapse to F ≈ 0 under dephasing) and consistency with the dephasing response on Pasqal FRESNEL_CAN1 QPU (noise ratio 1.13×). These results are consistent with CFD's predicted critical behavior, though they do not uniquely distinguish CFD from standard noise models. The specific threshold value (0.535) is determined by the experimental circuit geometry, not derived from CFD aloneFour predictions remain open and experimentally accessible on current NISQ hardware: coherence-depth complementarity, MERA-decoherence correspondence, coherence-modulated entropy scaling, and hardware demonstration of non-trivial reversibilityThis paper presents the theoretical framework. The detailed experimental protocols and hardware data are reported in the companion publication "Cross-Platform Noise Thresholds in Quantum Teleportation: Trapped-Ion and Neutral-Atom Architectures" (see Related Identifiers).
Quantum error correction (QEC) relies on redundancy to combat decoherence, yet resource overhead remains the primary barrier to scalability—leading surface-code architectures require O(10³) physical qubits per logical qubit. We propose a complementary approach inspired by Radial Coherential Dynamics (RCD), where decoherence suppression emerges from geometric coupling to a coherential substrate rather than brute isolation. Leveraging the RCD principle that effective coupling strengths scale with √α (where α ≈ 1.3×10⁻⁴ is the universal coherential parameter), we model a "coherential qubit" whose effective dephasing rate is topologically suppressed by √α ≈ 0.0114. Numerical simulation using QuTiP confirms an **87.7× improvement in coherence time** compared to a standard qubit under equivalent environmental coupling. For typical trapped-ion or superconducting qubits with T₂ = 10 μs, RCD predicts **T₂(RCD) ≈ 877 μs**. This constitutes a **falsifiable prediction testable on current hardware platforms**. We present this as a minimal toy model under pure dephasing conditions, intended as an upper-bound estimate rather than a complete QEC protocol. Nevertheless, the results suggest that topological quantum codes (surface codes, color codes) may approximate natural coherential attractors, offering a geometric pathway toward passive fault tolerance with reduced overhead. Framework: Radial Coherential Dynamics (RCD)Author: Arturo Cerezo García (ORCID: 0009-0007-4739-4990)
Holographic quantum error-correcting codes have been proposed as toy models that describe key aspects of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. In this work, we introduce a versatile framework of Majorana dimers capturing the intersection of stabilizer and Gaussian Majorana states. This picture allows for an efficient contraction with a simple diagrammatic interpretation and is amenable to analytical study of holographic quantum error-correcting codes. Equipped with this framework, we revisit the recently proposed hyperbolic pentagon code (HyPeC). Relating its logical code basis to Majorana dimers, we efficiently compute boundary-state properties even for the non-Gaussian case of generic logical input. The dimers characterizing these boundary states coincide with discrete bulk geodesics, leading to a geometric picture from which properties of entanglement, quantum error correction, and bulk/boundary operator mapping immediately follow. We also elaborate upon the emergence of the Ryu-Takayanagi formula from our model, which realizes many of the properties of the recent bit thread proposal. Our work thus elucidates the connection among bulk geometry, entanglement, and quantum error correction in AdS/CFT and lays the foundation for new models of holography.
This study extends the framework of non-equilibrium Hamiltonian field theory and algebraic coset partitioning established in preceding architectures to holographic quantum information manifold sectors, providing an explicit formulation for the macroscopic emergence of anti-de Sitter (AdS) spacetimes driven by the variational minimization of codimension-two entangling surfaces inside boundary conformal field theories (CFT). By embedding the Helfrich elastic bending grammar into the generalized Ryu-Takayanagi entropy functional, the spontaneous emergence of localized bulk horizons coupled to quantum error-correcting stabilizer codes is formalized. Partitioning the total configuration space under tensor network constraints demonstrates that non-local entanglement geometries undergo algebraic degeneration into exactly three universal holographic cosets.
The De Giuseppe Multi-Sheet Topological Qubit: Emergent Quantum Computation from Space-Time Geometry Abstract We introduce the De Giuseppe Qubit (DGQ), a novel quantum computational unit that leverages multi-sheet topological structures of space-time predicted by the Topological Phase Signalling Theorem (TPST). Unlike conventional qubits confined to a single space-time sheet, the DGQ exists simultaneously across multiple topologically connected sheets, providing emergent entanglement, intrinsic decoherence suppression, and super-parallel computation. This framework formalizes multi-sheet Hilbert spaces, sheet-symmetric operators, Hamiltonian dynamics, energy-momentum coupling, and holographic regularization of entanglement divergences. We present key equations underpinning the DGQ, demonstrating how computation can emerge from the geometry of space-time itself. ( I also added the other my articles: "Holographic Extension as a Dynamic Mechanics for Bulk Geometry CTC with Topological Phase Signalling Theorem" And "Worldline Non-Injectivity as a Necessary and Sufficient Condition for the Emergence of Holographic Spacetime" And "Quantum Mechanics as Topological Intersection Theory: The Born Rule, Wavefunction Collapse, and Planck's Constant from Worldline Non-Injectivity" to help better understand the multisheet DGQ paper. I hope it is appreciated.) 1. Introduction Quantum computation traditionally relies on coherent manipulation of qubits, often represented as[|\psi\rangle = \alpha |0\rangle + \beta |1\rangle, \quad \alpha, \beta \in \mathbb{C}, \quad |\alpha|^2 + |\beta|^2 = 1.]Topological qubits improve resilience to decoherence by encoding information in non-local degrees of freedom, but still require explicit entangling operations. The DGQ generalizes this approach: a single qubit is embedded across N topologically connected sheets, generating intrinsic entanglement and enabling parallel computation without conventional gates. This document introduces the DGQ framework, including: Multi-sheet Hilbert space formalism and operators; Hamiltonian dynamics with topological correlations; Observer-state gravitational coupling and emergent cosmological constant; Master TPST equation unifying bulk entanglement and geometry; Holographic regularization and decoherence suppression. 2. Topological Phase Signalling Theorem (TPST) The DGQ relies fundamentally on TPST, which formalizes how state-dependent global unitaries induce correlated changes across subsystems without explicit entangling gates. Consider a tripartite system:[\mathcal{H} = \mathcal{H}_A \otimes \mathcal{H}_B \otimes \mathcal{H}_F,]with
A the control subsystem,
B the target, and
F an auxiliary system. A state-dependent global unitary is defined as[U(\rho) = \exp\big(-i \phi[\rho] \hat{G}\big),]where
G^ acts nontrivially on
BF, and
ϕ[ρ] depends on the global state. TPST states that distinct operations on
A induce distinct reduced states on
B:[\rho_B^{(V)} \neq \rho_B^{(V')}, \quad \text{for suitable } V_A \neq V'_A.] Constructive Example For qubits (
C2) with Pauli operators
X^,Y^,Z^:[\phi[\rho] = g, \mathrm{Tr}[\hat{X}_A \rho], \quad \hat{G} = \hat{Z}_B \otimes \hat{X}_F, \quad \rho_0 = |0\rangle\langle 0|_A \otimes |+\rangle\langle +|_B \otimes |0\rangle\langle 0|_F,]and local operations
VA=I,
VA′=H (Hadamard). Then:[\rho_B^{(V)} = |+\rangle\langle +|_B, \quad\rho_B^{(V')} = \frac{1}{2}(\mathbb{I}_B + \cos(2g) \hat{X}_B),]demonstrating emergent correlation without direct entangling gates. 3. Multi-Sheet DGQ Formalism Let each sheet
i=1,…,N have Hilbert space
Hi. Define the global DG Hilbert space:[\mathcal{H}\text{DG} := \bigotimes_{i=1}^N \mathcal{H}_i.] Sheet-Symmetric Operators [\hat{\Sigma}\alpha := \frac{1}{N} \sum{i=1}^{N} \sigma_\alpha^{(i)}, \quad \alpha \in {x,y,z}.]Eigenstates of
Σ^α encode emergent entanglement, enforcing synchronized evolution across sheets. Intrinsic Entanglement For
N=2:[|\Psi_\text{DG}\rangle = \frac{1}{\sqrt{2}}\big(|0\rangle_1 |0\rangle_2 + |1\rangle_1 |1\rangle_2\big),]without explicit gates. 4. Hamiltonian Dynamics Global Hamiltonian:[H_\text{DG} = \sum_{i=1}^{N} H^{(i)}, \quad H^{(i)} = H^{(j)} \ \forall i,j.] Time evolution:[U_\text{DG}(t) = e^{-i H_\text{DG} t} = \bigotimes_{i=1}^{N} e^{-i H^{(i)} t}.] Energy-momentum coupling enforces:[T_{\mu\nu}^{(i)} = T_{\mu\nu}^{(j)}, \quad \forall i,j.] 5. Observer-State Gravitational Coupling When the observer’s quantum state $\rho^$ is included, the gravitational dynamics yield a dynamical cosmological constant:[G_{\mu\nu} + \Lambda[\rho^] g_{\mu\nu} = 8 \pi G_N T_{\mu\nu}, \quad\Lambda[\rho^] = 4 \pi G_N \lambda^2 \langle T_{00} \rangle_A [\rho^].] 6. Master Equation of TPST The unified TPST master equation captures quadratic entropy response, observer-dependent cosmological constant, and bulk-state coupling:[G_{\mu\nu} + 4\pi G_N \lambda^2 \langle T_{00} \rangle_A [\rho^*] g_{\mu\nu} =8 \pi G_N T_{\mu\nu} + \frac{8 \pi R_B^2}{L_A} K(a, R_B) \frac{(\delta E)^2}{\epsilon_d} h_{\mu\nu} \Big|_{\gamma_B}.] This reduces to classical general relativity in the limit
δE→0, while formalizing emergent interplay between topology, entanglement, and spacetime geometry. 7. Holographic Entropy Response A local boundary perturbation
δE induces quadratic bulk entanglement:[\delta S_B = \left( 1 + \frac{1}{\pi} \arctan \frac{R_B}{a} \right) (\delta E)^2.] Multi-sheet structure regularizes divergences:[\hat{A}\text{total} = \sum{n=1}^{N} \int_{\gamma_n} f_n(x) \sqrt{h_n} , d^d x, \quad\lim_{a \to R_B} \sum_n \int_{\gamma_n} f_n(x) \sqrt{h_n} , d^d x < \infty.] 8. Decoherence Suppression For Lindblad operators
L(i):[\mathcal{L}\text{DG} = \frac{1}{N} \sum{i=1}^N \mathcal{L}^{(i)}, \quad\Gamma_\text{decoherence}^\text{DG} \sim \frac{\Gamma_\text{single}}{N}.] 9. Implementation Strategies Dynamic (motion-based): ultra-relativistic trajectories create multiple sheet intersections. Static (metric-engineered): local metric
gμν(x) ensures
f(x)=1 across sheets, realizable via holographic lattices or photonic crystals. 10. Computational Paradigm Shift The DGQ framework demonstrates that computation can emerge directly from space-time topology, with intrinsic fault-tolerance and super-parallelism. This suggests a new generation of quantum devices where geometry itself encodes logical operations. 11. Technology Description This work introduces the De Giuseppe Qubit (DGQ) and its physical implementation via the De Giuseppe Photonic Crystal (DGPC) — a room-temperature quantum computing architecture that operates on a fundamentally different principle from all existing platforms. Standard quantum computers encode information in isolated physical qubits that must be explicitly connected through quantum gates, maintained at temperatures near absolute zero, and protected from decoherence through massive error-correction overhead. The number of control lines, the cooling infrastructure, and the gate complexity all scale with the number of qubits, making large-scale integration extraordinarily difficult and expensive. The DGQ eliminates these constraints at the architectural level. The core idea is that at sufficiently high Lorentz factors (γ ≥ 21,915), the worldline of a massive body folds relative to any observer's simultaneity surface, producing multiple simultaneous spatial intersections — not multiple particles, but a single physical entity appearing N times across N topologically connected sheets of spacetime. This multi-sheet structure is not postulated: it is a direct, causality-preserving consequence of Special Relativity, proven within the framework of this paper. The DGQ encodes quantum information across all N sheets simultaneously. Correlations between sheets emerge automatically from the topology — no entangling gates are required. Operating on one sheet propagates coherently to all others, so a single control input drives the entire N-sheet system. Decoherence suppresses as 1/N: adding sheets reduces the error rate rather than increasing it. Holographic divergences regularize automatically through the same multi-sheet averaging. The physical implementation — the DGPC — translates this spacetime structure into a two-dimensional silicon photonic crystal fabricated on a standard silicon-on-insulator wafer. The unit cell carries a C_N rotational symmetry that forces N photonic modes into exact degeneracy, reproducing the N-sheet Hilbert space in hardware. The device operates at room temperature (300 K), requires no cryogenic infrastructure, integrates at a density of 10⁶ DGQ units per cm² on a 200mm SOI wafer using standard CMOS-compatible processes, and achieves a single-gate fidelity above 99.5%. The three properties that distinguish this architecture from every existing quantum computing platform — entanglement without gates, decoherence suppression without error-correction overhead, and room-temperature operation — are not engineering optimizations. They are direct geometric consequences of the multi-sheet topological structure. They cannot be simultaneously achieved by any combination of existing qubit technologies. The central experimental prediction is a fourfold-degenerate flat photonic band at normalized frequency ωa/2πc = 0.312 in the fabricated DGPC, measurable via standard near-field scanning optical microscopy. Verification of this band structure, together with a nonzero off-diagonal De Giuseppe Chern vector, constitutes the first experimental confirmation of the DGQ framework. This manuscript is current in Official Peer Review. Not final version.Copyright©2026 Alex De Giuseppe.All rights reserved. This work is protected by copyright. Any form of plagiarism, unauthorized reproduction, or misappropriation of ideas, mathematica
The core of quantum error correction lies in how to isolate local errors to prevent them from contaminating the global system. Within the framework of connectivity engineering, this paper proposes a holographic quantum error correction mechanism based on pure geometric decoupling. Numerical results show that in a locally connected network (k=1), local errors rapidly diffuse globally through the increase of entanglement entropy; while in the decoupled network (k=3), long-range hopping constructs a graph-topological barrier, strictly locking the error within the isolated sub-chain where it was injected, and the mutual entanglement entropy between A and B remains strictly at its initial zero value. Since the physical hopping between subsystems is cut off, the injected error state cannot trigger global chaos, and the purity of boundary information remains stable. This mechanism does not rely on traditional redundant encoding, but rather utilizes the intrinsic graph-topological isolation property of geometric connectivity to achieve "physical-layer" fault tolerance. It provides a minimal discrete dynamical benchmark for understanding Bulk Locality in holographic duality and points the way for designing redundancy-free quantum memories.