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arXiv:2604.15051

Hardware Validation of DAGI via a Modular "Ridge" Signature and High-Order Synergistic Information

Petr Sramek

quant-phSubmitted Apr 16, 2026• Announced Apr 17, 2026• 0 citations
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Abstract

We report a hardware validation of the DAGI (Directed Acyclic Graph Information) framework on IBM Quantum hardware using a small, controlled experiment whose ideal output distribution is constrained to a low-dimensional modular manifold (a "ridge"). For two $n$-bit registers $(u,v)$ with $n=4$ (modulus 16), each key instance $k$ induces an ideal relation $v \equiv k \cdot u \pmod{16}$, producing a visually distinct ridge in the joint $(u, v)$ distribution. Executed on ibm\_torino in a single Sampler V2 job (8 keys, 1024 shots/key, $N=8192$ total shots), the ridge persists under hardware noise with ridge-hit probability $p_{hit} = 0.1830$ (uniform baseline $1/16$), corresponding to a ridge contrast of $2.93\times$ (95\% bootstrap CI [2.80, 3.06]). Key recovery exceeds chance: per-shot accuracy 0.1689 (chance 0.125, 95\% Wilson CI [0.1610, 0.1772]), and per-group dictionary recovery 0.375 (chance 0.125). To test the central DAGI hypothesis -- that recoverable key information is predominantly high-order/synergistic rather than visible in low-order marginals -- we compute a Möbius-based information decomposition of $I(K;D_S)$ over detector-bit subsets $S$ via a Möbius inversion pipeline and evaluate targeted positive synergy $CPS_K$ at order $k_{max}=3$. We observe $CPS_K(k=3) = 0.08788$ with significance under label-shuffle permutation tests (accuracy $p=0.001996$, $CPS_K$ $p=0.004975$). Uniformity diagnostics show near-uniform single-bit marginals while correlation concentrates in specific low-order pairs, and a bootstrap reliability sweep confirms order-3 targeted synergy remains statistically reliable at the full 1024-shot target budget. These results support the claim that DAGI detects and quantifies nontrivial, hardware-resilient, higher-order information structure associated with a known global algebraic constraint.

Comments
10 pages, 5 figures. Hardware execution performed on the 133-qubit IBM Quantum 'ibm_torino' processor. Part of the DAGI Research Program (Empirical Validation Track). Companion dataset and evaluation suite available on Zenodo (DOI: 10.5281/zenodo.18891561)

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Context: This manuscript belongs to the computational validation track of the DAGI (Directed Acyclic Graph Interpretation) research program at Whytics. It provides a mathematically exact confirmation of holographic entanglement wedge reconstruction using multiscale information theory. Abstract: We validate the entanglement wedge reconstruction property in a holographic stabilizer code using a multiscale information-theoretic approach. In a 16-qubit stabilizer graph code, we identify a bulk qubit whose information can only be recovered from a specific minimum set of five boundary qubits (its "entanglement wedge"). We employ the Directed Acyclic Graph Interpretation (DAGI) framework and a Möbius inversion-based decomposition of mutual information to quantify how information about the bulk is distributed among boundary subsets. Our analysis confirms that no information about the bulk qubit is accessible from any proper subset of its five-qubit wedge or from disjoint outside regions. Only when all five qubits in the entanglement wedge are present does the mutual information rise to its maximum (2 bits), corresponding to a perfect quantum correlation. Moreover, a Möbius decomposition reveals that this 2-bit mutual information is an irreducible five-party correlation: all lower-order contributions (one-body, two-body, etc.) are zero. We thus explicitly confirm that the bulk qubit's information is encoded entirely in a five-body entanglement, providing a quantitative, multiscale verification of entanglement wedge reconstruction in the code. Key Highlights: Exact Holographic Validation: Quantitatively confirms the entanglement wedge threshold in a 16-qubit hyperbolic graph code using exact algebraic rank methods. Synergy Verification: Proves via Möbius inversion that bulk information manifests entirely as an irreducible 5-body synergistic correlation, with strictly zero information present in lower-order marginals. Open Source Framework: The complete Python computational pipeline—including graph-state generation, Möbius inversion, and visualization routines—is included in this release to guarantee reproducibility.
Context: This manuscript serves as the empirical Quantum Darwinism validation track for the Directed Acyclic Graph Interpretation (DAGI) framework at Whytics. It bridges Wojciech Zurek's paradigm of decoherence with DAGI's topological mereology, providing the rigorous mathematical derivation of the "Redundancy Plateau" utilized throughout the broader research program. Abstract: Recent advances in quantum experiments allow rigorous tests of how classical reality emerges from quantum systems. Here we present an experimental validation of the Directed Acyclic Graph Interpretation (DAGI) theoretical framework using a multiscale information decomposition applied to a state-of-the-art quantum Darwinism experiment on superconducting circuits (Zhu et al., 2025). We analyze the mutual information between a quantum system and fragments of its environment, decomposing it via a Möbius inversion technique into irreducible kkk-body informational contributions. Our results confirm a unique prediction of the DAGI framework: we observe a "Redundancy Plateau" where higher-order synergistic information (involving three or more environmental subsystems, k≥3k \ge 3k≥3) is strongly suppressed for partial environment fragments. First-order redundant information (f1f_1f1​) heavily dominates, second-order overlaps (f2f_2f2​) are strictly negative, and higher-order terms (k≥3k \ge 3k≥3) nearly perfectly cancel out. Synergy becomes significant only when the entire environment is accessed, successfully isolating the system's residual quantum entanglement as an irreducible NNN-body secret. This pattern cannot be reproduced by standard decoherence models without DAGI’s information-theoretic perspective. The validation of this prediction bolsters the falsifiability of the DAGI framework and provides the exact kinematic mechanism for how objective classical reality emerges from the quantum substrate.
The DAGI program uses M\"obius inversion on partially ordered sets to decompose an information observable into irreducible contributions. A central methodological question is whether the Boolean powerset is merely a convenient default, or whether the poset should be engineered to match the physical accessibility structure of the experiment. We report a hardware validation of the latter claim on IBM Quantum hardware (\texttt{ibm\_torino}). In repetition-code memory circuits with mid-circuit measurement and reset, we compare two decompositions computed on exactly the same detector-window data: a truncated subset lattice (all detector subsets with ∣S∣≤3|S|\leq 3∣S∣≤3) and a reachability-defined causal-cone poset (truncated past cones with rmax⁡=3r_{\max}=3rmax​=3). Controlled contexts increase two-qubit exposure using barrier-separated canceling two-qubit operations while preserving the ideal logical circuit. Across a single-patch pilot and two multi-patch extensions (P=4P=4P=4 and P=8P=8P=8 far-separated parallel patches), the detector windows contain measurable context signal. The strongest positive result is not raw classification accuracy but \emph{region stability}: top cone-poset regions selected by M\"obius magnitude are highly patch-invariant, whereas subset-lattice top terms are nearly random-like across patches. For P=4P=4P=4 and P=8P=8P=8, normalized top-region Jaccard stability is $\Jnorm_{\cone}=0.505$ and 0.6030.6030.603, while $\Jnorm_{\sub}=0.008$ and −0.001-0.001−0.001. Out-of-patch classifiers remain only weakly above chance, but multinomial logistic calibration reduces expected calibration error to 0.0350.0350.035--0.0790.0790.079 and removes a large Naive-Bayes calibration artifact. This weak classification is expected: predicting a global two-qubit-load context from one local 12-detector window is a low-SNR domain-generalization task. The mutual information statistic in this experiment is interpreted as an operational proxy for the context-modulated correlated-error footprint, not as a direct measurement of pure topological synergy. We therefore state a conservative conclusion: causal-cone posets expose reusable, patch-invariant macro-region signatures in this repetition-code hardware setting; they are not yet shown to improve logical decoding or to dominate arbitrary subsets in all predictive tasks. The accompanying dataset bundle contains raw detector windows, QPY circuits, explicit poset definitions, fold outputs, and paper-ready tables.
Context: This manuscript provides the rigorous mathematical and information-theoretic toolkit for the DAGI research program at Whytics, bridging abstract mereology with effective field theory and macroscopic observables. Abstract: We extend the Directed Acyclic Graph Informational (DAGI) framework by integrating a rigorous mereological decomposition based on Möbius inversion on partially ordered sets. The central output is a multiscale expansion that decomposes a macroscopic informational observable g(X)g(X)g(X) on node-sets XXX into unique, irreducible contributions f(Y)f(Y)f(Y) across all sub-configurations Y⊆XY \subseteq XY⊆X. To bridge this abstract mereology with physical kinematics, we apply the formalism to total correlation (multi-information). Its Möbius inversion isolates order-resolved kkk-body dependency atoms that can be positive (synergy) or negative (redundancy). We introduce the positive-tail truncation f+(X)=max⁡{f(X),0}f^+(X) = \max\{f(X),0\}f+(X)=max{f(X),0} to rigorously isolate active, irreducible synergistic constraints; this "f+f^+f+ tail" yields the exact geometric source terms employed in the companion Emergent Spacetime Geometry (ESG) framework. We also show how the same decomposition can be coupled back into dynamics via a coarse-grained effective field theory (EFT) Lagrangian. Finally, we summarize computational pathways and modern experimental status, including superconducting-qubit demonstrations that extract irreducible 3-body and thresholded high-order synergies from IBM quantum processors using Möbius/HOIC diagnostics. Key Highlights: Order-Resolved Information: Deploys Möbius inversion on subset lattices to cleanly separate multi-partite redundancy from irreducible synergy. Effective Dynamics: Proposes a method to couple higher-order informational constraints back into an effective Lagrangian, providing a concrete mathematical basis for context-dependent dynamics ("downward causation") while avoiding double-counting via connected-cluster normalizations. Hardware Extraction: Details the analytical foundation used to isolate multiscale High-Order Information Content (HOIC) in real quantum circuits (e.g., IBM Torino benchmarks). Companion Toolkit: Serves as the mathematical prerequisite for defining the discrete curvature sources used in the DAGI Emergent Spacetime Geometry (ESG) mapping.
This manuscript reframes a series of IBM superconducting-qubit experiments as a targeted validation study for the Directed Acyclic Graph Interpretation (DAGI), with emphasis on the operational distinction between \emph{record creation} and \emph{record erasure}, and on how that distinction manifests in different classes of observables. DAGI models quantum processes as a directed acyclic graph of informational events: branching is permitted only when an interaction produces a durable record at the relevant coarse-graining scale, while coherent erasure can restore interference by removing the distinguishing record. We consolidate three falsifier-friendly hypotheses: (H1) remote record activity need not produce a universal ``clock slowdown'' for arbitrary local probes; (H2) remote influence is expected to appear preferentially in observables supported by a relational/entangled substrate; and (H3) the record/eraser distinction should be directly visible in distributed witnesses under strictly pulse-matched controls. Using the C1 ``informational time dilation'' series as the local benchmark, and the T4 remote-closure suite as the nonlocal stress test, we report a split outcome: clock-side remote slowdown remains bounded and proxy-dominated in tested geometries, yet a GHZ-class distributed coherence witness exhibits a large, replicated record-creation (REC) versus reversible sham (SHAM) separation on both ibm_fez and ibm_marrakesh, and is strongly restored by coherent erasure (ERASE). We position this pattern as evidence for observable-selective remote sensitivity that is consistent with DAGI's record/eraser mechanism while remaining conservative about hardware backaction channels.