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Poset Engineering for DAGI on Quantum Hardware: Causal-Cone Mobius Decomposition and Patch-Invariant Context Signatures on IBM Torino

Petr Sramek

Published May 16, 2026• 0 citations
Publisher

Abstract

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 $|S|\leq 3$) and a reachability-defined causal-cone poset (truncated past cones with $r_{\max}=3$). 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 ($P=4$ and $P=8$ 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 $P=4$ and $P=8$, normalized top-region Jaccard stability is $\Jnorm_{\cone}=0.505$ and $0.603$, while $\Jnorm_{\sub}=0.008$ and $-0.001$. Out-of-patch classifiers remain only weakly above chance, but multinomial logistic calibration reduces expected calibration error to $0.035$--$0.079$ 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.

DOI
10.5281/zenodo.20237450

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•Mar 7, 2026•0 citations
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\Jnorm_{\cone}=0.505\Jnorm\cone​=0.505 and 0.6030.6030.603, while \Jnorm⊂=0.008\Jnorm_{\sub}=0.008\Jnorm⊂​=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 belongs to the empirical hardware-validation track of the DAGI (Directed Acyclic Graph Interpretation) research program at Whytics. It provides direct experimental evidence for high-order informational thresholding, a concept central to the framework's treatment of emergent spacetime and black hole information. Abstract: The Directed Acyclic Graph Interpretation (DAGI) framework predicts that certain globally coherent variables are not locally accessible, but instead reside in irreducible high-order information structures (synergy) that become available only when sufficiently many degrees of freedom are jointly accessed. Motivated by Page-time transitions in black-hole information and by entanglement-wedge thresholds in holographic quantum error correction, we design a deliberately minimal "threshold-lock" circuit family whose measurement statistics implement a synergy-only encoding of a binary label KKK: all 1- and 2-bit marginals of the early radiation are (ideally) independent of KKK while the 3-bit prefix jointly reveals KKK. We execute this experiment on IBM Quantum ibm_torino with n=6n=6n=6 measured qubits and 2048 shots per key, alongside a "leaky" control in which low-order information is intentionally present. Using a Möbius/DAGI decomposition of the mutual information over the prefix subset lattice, we observe a sharp Page-like turn-on for the locked variant, with cumulative positive synergy dominated entirely by an intrinsic order-3 term. A bootstrap reliability sweep confirms that the locked order-3 synergy mass is statistically stable, while the leaky order-3 signal remains unstable. These results constitute a compact, falsifiable hardware demonstration that DAGI can detect and distinguish high-order, thresholded information release from low-order leakage in real quantum measurement data, supporting the use of DAGI Möbius diagnostics as experimental probes of Page-like information transitions and as design tools for DAG-inspired QECCs. Key Highlights: Hardware-Verified Thresholds: Demonstrates a distinct Page-curve-like accessibility transition on a superconducting IBM Quantum processor. Synergy vs. Leakage: Proves the efficacy of the DAGI Möbius decomposition in distinguishing true irreducible high-order synergy from low-order hardware leakage. Holographic Analogs: Provides an operational, circuit-level analog for entanglement-wedge reconstruction phenomena utilized in emergent gravity and holographic error correction.
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 nnn-bit registers (u,v)(u,v)(u,v) with n=4n=4n=4 (modulus 16), each key instance kkk induces an ideal relation v≡k⋅u(mod16)v \equiv k \cdot u \pmod{16}v≡k⋅u(mod16), producing a visually distinct ridge in the joint (u,v)(u, v)(u,v) distribution. Executed on ibm\_torino in a single Sampler V2 job (8 keys, 1024 shots/key, N=8192N=8192N=8192 total shots), the ridge persists under hardware noise with ridge-hit probability phit=0.1830p_{hit} = 0.1830phit​=0.1830 (uniform baseline 1/161/161/16), corresponding to a ridge contrast of 2.93×2.93\times2.93× (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;DS)I(K;D_S)I(K;DS​) over detector-bit subsets SSS via a Möbius inversion pipeline and evaluate targeted positive synergy CPSKCPS_KCPSK​ at order kmax=3k_{max}=3kmax​=3. We observe CPSK(k=3)=0.08788CPS_K(k=3) = 0.08788CPSK​(k=3)=0.08788 with significance under label-shuffle permutation tests (accuracy p=0.001996p=0.001996p=0.001996, CPSKCPS_KCPSK​ p=0.004975p=0.004975p=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.
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.
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.
Mid-circuit measurements are essential primitives for dynamic circuits and quantum error correction, yet characterizing their induced disturbance on spectator qubits remains a central practical problem. Device-level benchmarking often compresses this disturbance into low-order proxy metrics such as T1T_1T1​, T2T_2T2​, readout assignment error, and pairwise crosstalk. We argue that these proxies can be operationally incomplete for multiscale dynamic circuits. We introduce a higher-order context-conditioned kernel, Γeff[Y,O]=Γloc[O]+Γproxy[O]+Γrel[Y,O]Γ_{\mathrm{eff}}[Y,O] = Γ_{\mathrm{loc}}[O] + Γ_{\mathrm{proxy}}[O] + Γ_{\mathrm{rel}}[Y,O]Γeff​[Y,O]=Γloc​[O]+Γproxy​[O]+Γrel​[Y,O], where YYY is a global context label and OOO a local observable. The term Γrel[Y,O]Γ_{\mathrm{rel}}[Y,O]Γrel​[Y,O] is a phenomenological compression ansatz isolating residual context dependence unexplained by standard proxies. To avoid impossibility issues of quantum partial-information decompositions on non-commuting algebras, the Möbius weights entering this ansatz are evaluated operationally on classical measurement outcomes. We present evidence in three steps. First, earlier GHZ-versus-clock hardware results motivate an observable-class split. Second, we present dynamical evidence using the A6 synthetic hardware harness. A6 injects a pure higher-order context dependence via a programmed conditional interaction. Because the (C0,C1,C2)(C_0,C_1,C_2)(C0​,C1​,C2​) parity context is invisible to singles and pairs by construction, standard low-order diagnostics are fundamentally blind to the source of the probe's disturbance. Third, we demonstrate coherent controllability through the A6.2 quantum-eraser experiment. Programmable MARK interactions suppress unconditional fringes while eraser-basis conditioning restores them, consistent with complementarity bounds. These results validate a context-conditioned description of backaction over proxy-only null models.
Context: This manuscript provides the empirical hardware foundation for the Emergent Spacetime Geometry (ESG) and Directed Acyclic Graph Interpretation (DAGI) research programs at Whytics. It details the physical extraction of microscopic "informational time dilation" primitives from IBM superconducting qubits, which are subsequently used to parameterize macroscopic gravitational simulations (g₀₀). Abstract: We report an empirical, hardware-defined informational time dilation effect on superconducting quantum processors (ibm_fez, ibm_marrakesh): when an operational quantum clock is locally coupled to irreversible record creation (mid-circuit measurement and reset), its inferred forward progress is drastically reduced relative to a strictly schedule-matched baseline. Conversely, applying a coherent quantum-eraser control at the exact same physical interaction depth successfully uncomputes the record, maintaining the clock near its unperturbed baseline. We define a relative dilation factor D = N_eff / N by inverting a monotone baseline calibration curve. Across strictly schedule-matched sweeps, increasing the density of irreversible records yields a strong monotone decrease in clock progress down to D ≈ 0.2 – 0.3, whereas coherent erasure yields D ≈ 0.93. Rigorous multivariable model selection confirms this effect is governed by informational irreversibility rather than standard physical gate load. Information-aware predictors decisively outperform standard two-qubit crosstalk proxies by a massive margin (ΔBIC = 64.18). Crucially, pilot light-cone (C1-LC) transport experiments reveal a conformal-metric refinement: we observe strong local clock dilation (D ≈ 0.384) while causal-cone transport velocities remain invariant within uncertainty (v_record / v_sham ≈ 1). This indicates that records renormalize proper time without shrinking null cones. Furthermore, we document a severe spatial "split outcome" for remote backaction. A spatially separated k=1 clock remains completely isolated from a remote measurement (ΔD ≈ 0.0015), whereas a distributed k ≥ 3 GHZ coherence witness undergoes massive suppression (Δ_GHZ = −0.1569) that is heavily restored via coherent erasure (R_erase = 0.964). This falsifies a universal scalar mechanism for nonlocal clock slowdown, pointing instead to an observable-selective topological graph-cut. Finally, we map these hardware-calibrated primitives to emergent gravity. The empirical Generalized Record-Rate (GRR) map (r → D) extracted here provides the foundational time-dilation primitive for Emergent Spacetime Geometry (ESG), defining the temporal metric component as g₀₀ ∝ −D². These strict hardware primitives successfully parameterize a 10,000-node classical DAG simulation, spontaneously generating localized macroscopic time-dilation wells that satisfy weak-field Einstein-Poisson closure diagnostics (median relative RMSE ≈ 0.0029). Key Experimental Highlights: Irreversibility-Controlled Time: Empirically proves that local operational clock rates are fundamentally controlled by the density of irreversible record creation, rather than standard thermal/gate noise. The Quantum Eraser Switch: Demonstrates that clock slowdown is a programmable, informational graph-property; applying coherent erasure actively rewinds the thermodynamic boundary and restores normal clock rates. Invariant Light Cones: Empirically verifies a core requirement for emergent relativity: proper time dilates locally, but the maximum speed of causal transport remains invariant. Hardware "Split Outcome": Validates that remote measurement backaction is observable-selective, completely bypassing localized operational clocks while severely suppressing distributed synergistic entanglement. The Microscopic Engine for Gravity: Extracts the exact empirical transfer function needed to parameterize g₀₀, bridging noisy intermediate-scale quantum (NISQ) devices to macroscopic Einstein-Poisson gravitational simulations.