This working note presents a quantum circuit test of Specular Field Theory (SFT), a geometric framework in which the scrambling rate of a quantum system is linked to the curvature of a temporal manifold. Using a 5-qubit mirror circuit (Loschmidt echo) with a temporal modulation applied to the single-qubit rotation angles,we establish a quantitative mapping between the circuit modulation parameter (omega) and the temporal curvature (A).We analyze the entanglement contribution (E_ent) as an operational interpolation between the fidelity of recovery (F_rec0) in the bulk and the Shannon entropy (S_Shannon) at the boundary, governed by a sigmoidal transition. The study evaluates the model across three main aspects: Circuit Calibration: The mapping A(omega) is calibrated using baseline circuit constants (A_0 and alpha),establishing a consistent linear response in the bulk. Bulk-Boundary Transition: The transition between bulk and boundary regimes is analyzed using a sigmoidal weighting function, yielding a strong coefficient of determination (R^2 = 0.9974). Blind Prediction & Horizon Regularization: Parameters are calibrated exclusively on the linear bulk (omega <= 0.05), and the regularized formula predicts the scrambling rate in the critical regime (omega >= 0.08) with an average error of 7.93%, utilizing a boundary regularization scale (epsilon) that accounts for temporal volume saturation near the informational horizon (A = 1/2). The note also discusses finite-size scaling (showing the bulk intercept beta vanishing in the thermodynamic limit),directional circuit responses under time reversal (comparing forward and rewind evolutions), and the distinction between exact statevector simulations and future empirical validation on quantum hardware.
This working note presents a quantum circuit test of Specular Field Theory (SFT), a geometric framework in which the scrambling rate of a quantum system is linked to the curvature of a temporal manifold. Using a 5-qubit mirror circuit (Loschmidt echo) with a temporal modulation applied to the single-qubit rotation angles,we establish a quantitative mapping between the circuit modulation parameter (omega) and the temporal curvature (A).We analyze the entanglement contribution (E_ent) as an operational interpolation between the fidelity of recovery (F_rec0) in the bulk and the Shannon entropy (S_Shannon) at the boundary, governed by a sigmoidal transition. The study evaluates the model across three main aspects: Circuit Calibration: The mapping A(omega) is calibrated using baseline circuit constants (A_0 and alpha),establishing a consistent linear response in the bulk. Bulk-Boundary Transition: The transition between bulk and boundary regimes is analyzed using a sigmoidal weighting function, yielding a strong coefficient of determination (R^2 = 0.9974). Blind Prediction & Horizon Regularization: Parameters are calibrated exclusively on the linear bulk (omega <= 0.05), and the regularized formula predicts the scrambling rate in the critical regime (omega >= 0.08) with an average error of 7.93%, utilizing a boundary regularization scale (epsilon) that accounts for temporal volume saturation near the informational horizon (A = 1/2). The note also discusses finite-size scaling (showing the bulk intercept beta vanishing in the thermodynamic limit),directional circuit responses under time reversal (comparing forward and rewind evolutions), and the distinction between exact statevector simulations and future empirical validation on quantum hardware.
Six quantum circuit experiments performed on ibm_marrakesh (IBM Quantum, 156 qubits, Heron R2 architecture) are reported, designed to test boundary signatures of the ER=EPR conjecture within the AdS₂/JT gravity framework, with the Sachdev-Ye-Kitaev (SYK) model as the holographic dual of the black hole horizon. The experiments were executed iteratively: each result raised new questions that directly motivated the next protocol. In order of execution they implement: tripartite entanglement certification via the Mermin operator (|⟨M⟩| = 3.885); a traversable wormhole baseline using a Bell-pair thermofield double (F(g=π/2) = 1.000); black hole evaporation unitarity via the Hayden-Preskill protocol (F_rec = 0.9983, with the decoder reduced to zero two-qubit gates by the compiler); a corrected traversable wormhole using genuine SYK scrambling and exact Majorana coupling (F(g=0) = 0.020, F(g=π/2) = 0.953, GJW gain = 0.933); quantum chaos via out-of-time-order correlators (λ_L = 1.975 ± 0.294, 54.8% of the Maldacena-Shenker-Stanford bound); and black hole entropy under information absorption, where the hardware reproduces the entropy growth S(t) of SYK formation on top of a noise floor and the energy response to Alice’s input (correlation 0.998 with simulation), while the predicted area growth consistent with the Bekenstein law is obtained in simulation but is not resolved above noise on hardware. Total QPU time across all experiments: 7 minutes 2 seconds. Five of the six experiments reproduce the boundary predictions of the ER=EPR framework on hardware; the sixth reproduces them in simulation and only partially on hardware. Version 3 corrects Experiments 2 and 3 following the original laboratory reports. Exp. 2 reports the raw F(g=π/2) = 1.01 ± 0.01 instead of the clipped 1.000. In Exp. 3 the fused U†U circuit is identity by construction; its fidelity (0.9983) is reported as a noise-floor control, not as hardware recovery. The hardware scrambling result (F_scr = 0.530 vs. 0.532 in simulation) is kept; recovery is demonstrated in simulation. Experiments 2b, 5 and 6 are unchanged. Code and data: https://github.com/horca17/er-epr-six-protocols
We implement a chiral spin-chain black hole simulator on IBM superconducting quantum hardware and probe, within a common microscopic framework, both semiclassical horizon physics and interacting quantum scrambling. We first measure the dispersion relation across the exterior, horizon and over-tilted interior regimes, reproducing the predicted evolution of the effective light-cone structure. To probe Hawking thermality, we prepare a localised excitation inside the horizon and monitor its density response at an exterior site, observing the predicted inverse relation between the peak arrival time and the surface gravity, thereby establishing a calibrated dynamical estimator of the Hawking temperature. Beyond the semiclassical regime, we continuously tune the interactions and distinguish non-exponential operator spreading in the free-fermion limit from Lyapunov-like OTOC decay in the strongly interacting chiral regime. These measurements use observable-specific Floquet circuits derived from the same parent chiral model, including its mean-field and coordinate-equivalent XY descriptions, to reduce circuit depth while preserving the physics relevant to each probe. Our results provide a unified programmable platform for studying horizon geometry, Hawking thermality and interacting scrambling on quantum hardware.
We report systematic experimental observation of coherent, topology-dependent inter-horizon correlations in thermofield double (TFD) states implemented on IBM quantum processors. Using a 100-qubit ladder geometry mapped onto the heavy-hex topology of ibm_fez (156 qubits, Heron r2 architecture), we demonstrate signal ratios R_fit spanning 1.2–202.7 across runs/seeds, with best single-seed R_fit = 23.93 (Run #11) and record multi-seed median R_fit = 102.7 (Run #2, 5 seeds, range 63.5–202.7), validated by pre-registered GO/NO-GO criteria across 14 experimental runs spanning January 24-30, 2026. Our experimental framework incorporates two rigorous anti-artifact controls (see Fig. 6-7): (1) SCRAMBLE control applies identical circuit depth with incorrect topology, destroying the signal (reduction factor > 10×); (2) ECHO control (Loschmidt reversal) applies the coupling layer twice, annihilating coherent contributions (reduction factor 8.6-50.5×, consistent with expected finite-size echo saturation for N~50 effective subsystems (see Gorin et al. [14] for saturation plateau theory)). Both controls maintain > 95% local fringe retention, confirming they do not trivially destroy coherence. A critical discovery emerged from our January 30, 2026 validation campaign (see Fig. 5): quantum processor calibration drift can cause signal collapse within less than one hour on hardware with identical offline calibration snapshots. Runs #11-#12 achieved R_fit = 23.93 and 18.4 respectively (GO-1 PASS, GO-3 PASS), while Run #13 executed only 53 minutes later on the same backend collapsed to R_fit = 1.20 (GO-1 FAIL). This finding establishes that offline Health Scores do not reliably predict experimental success, and defines an operational envelope requiring Health > 80% (Grade B or better) for empirically associated with high-probability signal stability. The observed second-harmonic (2ω) dominance in the phase-dependent signal (A₂ω/A₁ω > 40×, R² > 0.99, see Fig. 9) is consistent with theoretical predictions for bilinear left-right correlations. A stride sweep (s = 2-5, see Fig. 4) reveals a signal-coherence trade-off, with s = 3 identified as optimal. Total quantum processor time across all 14 runs: approximately 45 minutes. These results establish a validated, falsifiable experimental framework for probing analog quantum gravity signatures on NISQ hardware, with explicit calibration-conditional bounds. The methodology may provide a validated framework applicable to analog Hawking radiation platforms where topology-controlled correlations play a central role (see Section 5.4). Note: Results demonstrated primarily on IBM ibm_fez; multi-device validation on additional backends is recommended to establish cross-platform generalizability.
We propose that quantum critical systems, when collective dynamics dominate over particle-like behavior, can be described by an effective curved geometry. Working within this geometric framework, we derive three testable predictions for quantum chaos near criticality: (1) the Lyapunov exponent saturates to a constant at criti- cality rather than diverging or vanishing; (2) out-of-time-ordered correlators exhibit geometric scrambling with saturation at strong coupling; and (3) the level spacing distribution transitions from Poisson to Wigner-Dyson with a universal crossover function. These predictions are independent of microscopic details and can be tested in cold atom systems, trapped ion chains, and superconducting qubit arrays. Com- plete computational validation is provided in two accompanying SageMath notebooks (DOIs: 10.5281/zenodo.18440342 and 10.5281/zenodo.18720405).
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+αM2),αtheo=42≈0.35355, where α 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 αexp=0.355±0.042 is consistent with this geometric conjecture within 0.03σ. 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 Rvirtual≈0.082fm, consistent with the QCD confinement scale.- **Geometric origin of mixing**: The small mixing angle θ∼2∘–5∘ corresponds to a fiber-bundle overlap Ifiber∼0.1–0.3, quantifying the near-orthogonality between geometric modes and flavor-carrying matter excitations.- **Two testable predictions**: - Strong suppression B(X→γϕ)≪B(X→γω) 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.
We characterize the geometric and algebraic conditions governing noise-induced landscape regularization in Recurrent Quantum Circuits (Q-RNNs). In quantum recurrent models training on sequence parity (temporal XOR), gradient optimization typically encounters a severe topological trap (the parity plateau at accuracy ≈ 0.72–0.75). While physical environmental noise is conventionally viewed as detrimental to quantum information, we provide empirical evidence that the primary boundary separating regularizing and non-regularizing open-system channels is unitality. Specifically: 1. Unital Channels (e.g., Pauli depolarizing, phase-flip, bit-flip, and phase damping) contract the Bloch sphere symmetrically, preserving the loss landscape's up/down parity symmetry and enabling optimizers to escape the topological traps. 2. Non-Unital Channels (e.g., amplitude damping) shift the center of the Bloch sphere; large non-unital origin drift severely disrupts the optimization landscape by breaking the loss landscape's up/down parity symmetry. 3. We map this boundary empirically by conducting a Generalized Amplitude Damping (GAD) sweep over the thermal parameter [0.0, 1.0] across varying damping rates \0.25, 0.35, 0.50, 0.75\ (Sweep 1), and a state-initialization asymmetry sweep (Sweep 2). We show that convergence is restored within a near-unital basin (e.g., [0.42, 0.56] at =0.50). We show that the slight asymmetry of this basin (which is invariant to the initial state of the memory qubit) is consistent with a structural loop asymmetry caused by the recurrent input qubit reset to |0. We also map the parametric scaling of this basin, showing that the critical displacement boundary |v_z, crit| shrinks as increases due to the rapid contraction of the available state space volume. 4. We characterize the fine-grained transition of the bit-flip channel, revealing a sharp degeneracy hole at exactly p=0.50 where the Bloch sphere contracts to a 1D line. 5. We characterize an empirical optimizer-class robustness pattern at this finite experimental depth (2-qubit, T=3): normalized direction-preserving optimizers (Adam, signSGD, Muon, Normalized GD) achieve 6/6 convergence under unital noise, whereas non-normalized gradient descent (SGD, Heavy Ball) fails (2/6) due to recurrent gradient magnitude contraction. We discuss the analogy between this regularization structure and Quantum Error Correction (QEC), noting that the symmetries protecting parity in stabilizer codes appear to play a parallel role in protecting parity classification landscapes under unital noise. All results are from 2-qubit Q-RNN simulations on T=3 parity; generalization to larger circuits and longer sequences is a target for future work.