Overview This paper proposes a geometric interpretation of the recent landmark experiment by Biswas *et al.* (arXiv:2607.12047), who implemented the HaPPY holographic quantum error-correcting code on the IonQ Forte trapped-ion quantum computer and observed gravity-like signatures — proto-area entropy dependence on bulk entanglement that increases with injected magic. The experimental group identified three outstanding theoretical questions:1. Stochastic noise models alone cannot fully fit the data;2. The physical mechanism by which the slope increases with magic is unclear;3. The double-sided experiment has no first-principles prediction for the proto-area entropy. Contribution This work addresses all three questions through the **Holographic Information Stiffness (HIS-GR)** framework. The central result is a geometric relationship between the slope \(|m|\) and the injected magic \(M\): \[|m|(M) = |m|_0(1 + \alpha M^2), \qquad \alpha_{\mathrm{theo}} = \frac{\sqrt{2}}{4} \approx 0.35355,\] where \(\alpha\) is conjectured to originate from the intrinsic curvature \(K = 1\) of the qubit Bloch sphere projected onto the local stiffness response. The experimentally calibrated value \(\alpha_{\mathrm{exp}} = 0.355 \pm 0.042\) is consistent with this geometric conjecture within \(0.03\sigma\). The framework provides a unified geometric interpretation of the three experimental phenomena — structural deviation from noise models, slope increase with magic, and the double-sided proto-area entropy — as manifestations of a single underlying mechanism: the stiffness response of virtual space to information perturbations. Key Results - **Mass–curvature correspondence**: The glueball mass maps to a virtual-space curvature radius \(R_{\text{virtual}} \approx 0.082\ \mathrm{fm}\), consistent with the QCD confinement scale.- **Geometric origin of mixing**: The small mixing angle \(\theta \sim 2^\circ\text{--}5^\circ\) corresponds to a fiber-bundle overlap \(I_{\text{fiber}} \sim 0.1\text{--}0.3\), quantifying the near-orthogonality between geometric modes and flavor-carrying matter excitations.- **Two testable predictions**: - Strong suppression \(\mathcal{B}(X \to \gamma\phi) \ll \mathcal{B}(X \to \gamma\omega)\) in radiative decays; - Monotonic increase of the flavor-suppression ratio \(R(s)\) with local entropy density \(s\) in nuclear matter. Scope and Positioning This is a **high-level interpretive framework** — analogous to a high-level programming language that compiles to the same machine code as assembly language, but provides a fundamentally different abstraction layer. It does not replace AdS/CFT or lattice QCD calculations; rather, it offers a unified geometric language for otherwise disconnected phenomena and generates testable predictions for next-generation experiments.
Overview This paper proposes a geometric interpretation of the recent landmark experiment by Biswas et al. (arXiv:2607.12047), who implemented the HaPPY holographic quantum error-correcting code on the IonQ Forte trapped-ion quantum computer and observed gravity-like signatures — proto-area entropy dependence on bulk entanglement that increases with injected magic. The experimental group identified three outstanding theoretical questions:1. Stochastic noise models alone cannot fully fit the data;2. The physical mechanism by which the slope increases with magic is unclear;3. The double-sided experiment has no first-principles prediction for the proto-area entropy. Contribution This work addresses all three questions through the Holographic Information Stiffness (HIS-GR) framework. The central result is a geometric relationship between the slope (|m|) and the injected magic (M): [|m|(M) = |m|0(1 + \alpha M^2), \qquad \alpha{\mathrm{theo}} = \frac{\sqrt{2}}{4} \approx 0.35355,] where (\alpha) is conjectured to originate from the intrinsic curvature (K = 1) of the qubit Bloch sphere projected onto the local stiffness response. The experimentally calibrated value (\alpha_{\mathrm{exp}} = 0.355 \pm 0.042) is consistent with this geometric conjecture within (0.03\sigma). The framework provides a unified geometric interpretation of the three experimental phenomena — structural deviation from noise models, slope increase with magic, and the double-sided proto-area entropy — as manifestations of a single underlying mechanism: the stiffness response of virtual space to information perturbations. Key Results - Mass–curvature correspondence: The glueball mass maps to a virtual-space curvature radius (R_{\text{virtual}} \approx 0.082\ \mathrm{fm}), consistent with the QCD confinement scale.- Geometric origin of mixing: The small mixing angle (\theta \sim 2^\circ\text{--}5^\circ) corresponds to a fiber-bundle overlap (I_{\text{fiber}} \sim 0.1\text{--}0.3), quantifying the near-orthogonality between geometric modes and flavor-carrying matter excitations.- Two testable predictions: - Strong suppression (\mathcal{B}(X \to \gamma\phi) \ll \mathcal{B}(X \to \gamma\omega)) in radiative decays; - Monotonic increase of the flavor-suppression ratio (R(s)) with local entropy density (s) in nuclear matter. Scope and Positioning This is a high-level interpretive framework — analogous to a high-level programming language that compiles to the same machine code as assembly language, but provides a fundamentally different abstraction layer. It does not replace AdS/CFT or lattice QCD calculations; rather, it offers a unified geometric language for otherwise disconnected phenomena and generates testable predictions for next-generation experiments.
The unification of quantum mechanics and general relativity remains one of the major open problems of theoretical physics. The Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence provides a valuable theoretical framework for this effort via a holographic duality between a theory of quantum gravity in asymptotically AdS spacetime and a conformal quantum field theory on the lower-dimensional boundary. Here, we implement a toy model of this duality called the HaPPY code, a quantum error-correcting code in the form of a tensor network with hyperbolic entanglement patterns, on a trapped-ion quantum computer. We present the first experimental confirmation of the Faulkner-Lewkowycz-Maldacena formula in this model - a key test of the holographic correspondence. We then enrich it with non-stabilizerness, or magic, and observe entropic precursors expected of emergent gravity. Finally, we present and measure a code construction whose entropic behavior is reminiscent of a highly quantum wormhole. Our experiments illustrate how quantum computers can serve as testbeds for modeling the emergence of spacetime.
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-correcting codes provide a powerful framework for emergent spacetime, yet existing subsystem erasure-correcting holographic code models describe only quantum fields on a fixed background: in such codes, the entropic area term is state independent and cannot capture gravitational backreaction. We argue that this limitation is intrinsic to exact subsystem complementary recovery and that incorporating backreaction naturally leads to approximate quantum error correction. We introduce a Ryu-Takayanagi-like entropy decomposition for approximate subsystem erasure-correcting codes, defining bulk matter entropy via optimal recovery and a complementary proto-area entropy as the difference between boundary entropy and recoverable bulk entropy. For a broad class of skewed quantum codes obtained by small nonlocal perturbations of exact codes, the proto-area increases monotonically with bulk entropy, closely aligning with the changes in extremal surface areas in gravitational systems. We identify the origin of this response as a form of tripartite non-local magic in the Choi state of the encoding map, which vanishes in stabilizer codes and controls the leading matter-geometry coupling in approximate subsystem erasure-correcting codes.
Abstract The wave-particle duality, delayed-choice paradox, quantum entanglement, black hole information paradox, and cosmic holography in quantum mechanics have long been regarded as independent fundamental puzzles. Based on a discrete geometric framework (Cantor set topological gluing and recursive folding), this paper derives their unified origin——higher-order noise correlations. We demonstrate that the higher-order correlations of defect points, , constitute a universal geometric carrier of information encoding: In double-slit interference, it naturally resolves the "future determining the past" paradox of delayed-choice experiments, reveals entangled states as macroscopic manifestations of inseparable higher-order correlations, and leaves behind an entanglement residue --- under strong measurement; on the black hole event horizon, it forms a classical-quantum duality with the Heisenberg algebra of soft hair, providing a microscopic statistical interpretation for the Bekenstein-Hawking entropy and naturally truncating the infinite soft degrees of freedom; in the holographic universe, it serves as the boundary condition for generational memory, enabling information transfer across generations through bounce-surface freezing. This unified framework places quantum phenomena, black hole thermodynamics, and cosmic evolution under the same geometric language, proposes four core predictions testable through tabletop experiments, and establishes the quantitative relationship between higher-order correlation entropy and horizon area . If the predictions are confirmed, it will establish discrete geometry as the underlying origin of quantum information and provide the first empirically testable physical support for the holographic universe. 摘要 量子力学中的波粒二象性、延迟选择悖论、量子纠缠、黑洞信息悖论与宇宙全息性,长期被视为相互独立的根本谜题。本文基于离散几何框架(康托尔集拓扑粘合与递归折叠),推导了它们的统一根源——高阶噪声关联。我们论证,瑕疵点的高阶关联 构成信息编码的普适几何载体:在双缝干涉中,它自然消解延迟选择实验的“未来决定过去”悖论,揭示纠缠态为不可分离的高阶关联的宏观表现,并在强测量下留下纠缠残留量 —;在黑洞视界上,它与软毛发的海森堡代数构成经典-量子对偶,为贝肯斯坦-霍金熵 提供微观统计诠释并自然截断无穷多软自由度;在全息宇宙中,它作为世代记忆的边界条件,通过反弹面冻结实现信息跨代传递。这一统一框架将量子现象、黑洞热力学与宇宙演化置于同一几何语言之下,提出四项可通过桌面实验检验的核心预言,并建立了高阶关联熵与视界面积的定量关系 。若预言被证实,将确立离散几何为量子信息的底层起源,为全息宇宙提供首个可实证的物理支撑。
Information Dynamics provides a novel response to the Einstein-Bohr debate: quantum nonlocality is not superluminal signaling, but rather the projection of global coherence in virtual space; no parallel universes are required—measurement is merely a unidirectional projection from the virtual to the real component of information; the geometric constant 0.25 in Bell inequality violations originates from the intrinsic curvature of the two-dimensional virtual space (SU(2)). The violation of the Clauser-Horne (CH) inequality is a core result in the experimental verification of Bell's theorem. In 2025, the BESIII experiment measured the CHSH parameter S = 2.800 ± 0.010 for entangled ΛΛ¯ pairs with exceptional precision, unambiguously violating classical local realism. Within the Information Dynamics framework, we treat quantum systems as Information Superconductors—featuring global coherence in virtual space, information conservation, and a dynamic real-virtual coupling matrix K(x). Starting from two primitive axioms, we rigorously prove that virtual space possesses constant curvature K = 1/4, from which we derive in a unified manner: The Tsirelson bound for the CH inequality: (√2−1)/2 ≈ 0.2071 (projection of one-dimensional geodesic arc length); The quantum upper bound for the I3322 inequality: 0.25 (projection of two-dimensional spherical area). More importantly, we propose a novel testable prediction: for partially entangled pure states, the Information Dynamics prediction for the CH violation, S^ID_CH(η) = (√(1+sin 2η)−1)/2, is systematically larger than the standard quantum mechanical prediction, S^QM_CH(η) = (√(1+sin² 2η)−1)/2, with the two converging only at maximal entanglement. Taking η=30° as an example, the relative deviation exceeds 13%, well within the resolution of current photonic entanglement experiments, thereby providing a direct falsification pathway for Information Dynamics. First-Principles Numerical Verification: We further perform first-principles numerical simulations starting from the generalized Ginzburg-Landau equation, using FFT spectral methods on 2D lattices (up to 128×128). The results show that in the information superconducting phase (ρ_target ≳ 0.85), the effective curvature K_eff(C) ∝ C emerges naturally from the dynamics with ΔAIC = -5.67 and 91% Monte Carlo support, and the fitted exponent α = 1.02 ± 0.06, in excellent agreement with the geometric prediction α = 1. A quick version (64×64, 10 seeds, running in ~25 seconds on a personal computer) also strongly favors the linear model (ΔAIC < -60) across all tested parameter sets. These results provide strong first-principles numerical support for the linear projection hypothesis of Information Dynamics. This work not only answers "why" the geometric scale is 0.25, but also elevates imaginary space from a mathematical tool to a physical entity with measurable curvature, offering a new information-theoretic perspective on the century-old Einstein-Bohr debate.
In this work, we investigate some applications of quantum information theory motivated by high-energy physics. There is strong evidence suggesting that entanglement is deeply connected with the geometry of spacetime, which leads to surprising applications of quantum information theory in the AdS/CFT correspondence and holography. We start by reviewing the fundamental concepts of the AdS/CFT correspondence which play a key role in bulk-boundary reconstruction, in particular, we explore some features which suggest that one must interpret the encoding of information in the correspondence as a quantum errorcorrecting code. We discuss the fundamentals of error correction, exploring the formalisms of operator algebra and stabilizer codes. Then, we establish the concrete connection between the two main concepts by showing examples of quantum error-correcting codes that serve as a toy model for AdS/CFT. We illustrate how the 3-qutrit code and the HaPPY code can be powerful tools to explore the correspondence analytically and to solve apparent paradoxes. Following recent results, using quantum error correction, that suggest an intrinsic incompatibility of quantum gravity with global symmetries, we explore approximate error-correcting codes and asymmetric codes as a way to better understand the consequences in a quantum resource-theoretic way. Finally, we discuss our original contribution: geometric bounds for approximate quantum error correction. We calculate our bounds for three typical quantum channels that model the lack of exactness in error correction, namely, dephasing, depolarizing, and amplitude damping channels. The implications of our bounds for AdS/CFT are somewhat elusive; nonetheless, we provide a new approach to benchmark approximations in error correction performance, which may be of high interest for AdS/CFT and its corresponding absence of global symmetries.