Random circuit sampling (RCS) on noisy quantum hardware is widely modeled as exhibiting exponential decay of fidelity metrics (e.g., XEB, HOG) with circuit depth, converging toward Haar-random statistics beyond a characteristic noise-limited scale. This work introduces a minimal phenomenological recurrence for a coarse-grained local coherence observable defined on the qubit connectivity graph. The recurrence reproduces standard exponential decay in unstructured (fully scrambled) circuits but predicts delayed thermalization and a nonzero plateau when repeated local motifs are engineered into circuit compilation. The model introduces a single topology-dependent memory parameter α(µ), where µ denotes motif density. A transcritical bifurcation occurs when α(µ) exceeds the effective per-layer decoherence rate γ, producing a calculable plateau height and build-up depth scale. A matched-pair experimental protocol—holding qubit count, two-qubit gate count per layer, and reported hardware error rates fixed while varying only motif density—provides a direct falsification criterion. Absence of statistically significant topology dependence would rule out the model in its minimal form. The recurrence is an effective coarse-grained description at the metric level and does not modify underlying quantum channel structure or violate complete positivity.
Random circuit sampling (RCS) on noisy quantum hardware is widely modeled as exhibiting exponential decay of fidelity metrics (e.g., XEB, HOG) with circuit depth, converging toward Haar-random statistics beyond a characteristic noise-limited scale. This work introduces a minimal phenomenological recurrence for a coarse-grained local coherence observable defined on the qubit connectivity graph. The recurrence reproduces standard exponential decay in unstructured (fully scrambled) circuits but predicts delayed thermalization and a nonzero plateau when repeated local motifs are engineered into circuit compilation. The model introduces a single topology-dependent memory parameter α(µ), where µ denotes motif density. A transcritical bifurcation occurs when α(µ) exceeds the effective per-layer decoherence rate γ, producing a calculable plateau height and build-up depth scale. A matched-pair experimental protocol—holding qubit count, two-qubit gate count per layer, and reported hardware error rates fixed while varying only motif density—provides a direct falsification criterion. Absence of statistically significant topology dependence would rule out the model in its minimal form. The recurrence is an effective coarse-grained description at the metric level and does not modify underlying quantum channel structure or violate complete positivity.
This paper presents the application of Relational Field Theory (RFT) to random circuit sampling (RCS), a standard benchmark in quantum computing. Building on the reduced relational law: {\dot{R}}_c=-\lambda R_c+F_{int},\bigm and the operational coherence functional: R_c=\alpha\cdot\beta\cdot\gamma,\bigm the framework is applied to reported RCS data from superconducting qubit experiments. Within this setting: α corresponds to distribution sharpness (e.g., cross-entropy benchmark or peak statistics) β reflects circuit connectivity and gate structure γ captures persistence across circuit depth and repeated runs Using published results, the relational coherence functional is evaluated against observed behaviors in RCS systems, including: Persistence of structured output distributions beyond expected circuit depth Formation of coherence wells, where structure remains stable under noise Attractor-like clustering of high-probability output states Suppression of entropy relative to fully randomized expectations These observations are consistent with the four falsifiable predictions introduced in RFT v2.0: critical slowing near coherence thresholds hysteresis-like behavior under parameter variation persistence in coherence wells emergence of structural anchors This work does not modify quantum mechanics or attempt to reproduce standard RCS results. Instead, it provides a structural interpretation of observed behavior using a coherence-based framework applied to existing experimental data. The results extend Relational Field Theory from classical and toy-model systems into the quantum domain, supporting its potential as a cross-domain framework for understanding persistence, structure, and transition dynamics.
Standard Random Circuit Sampling (RCS) predicts full thermalization at sufficient depth, with output distributions converging rapidly toward uniform noise under realistic hardware conditions. Yet several recent experimental results have displayed unexpected persistence of structured output distributions far beyond the expected decoherence horizon. This paper presents a vendor-agnostic benchmark demonstrating that such persistence is not an architectural anomaly, but a direct signature of a deep Rc coherence well as defined in Relational Field Theory (RFT). Rc wells arise when curvature-stiffened regions of the universal scalar field resist chaotic dispersion, enabling stable probability attractors even in circuits where standard quantum dynamics predict complete entropy saturation. We provide a minimal, architecture-independent circuit that any quantum hardware vendor can execute to detect Rc well behavior. The benchmark uses symmetric entanglers, global phase rotation, chaotic scrambling, and convergence layers to probe curvature-stiffened regimes. Four measurable signatures—XEB decay behavior, entropy suppression, HOG persistence, and inverse participation ratio (IPR)—constitute a clear, falsifiable Rc-well fingerprint. This work generalizes beyond any specific architecture and requires no specialized routing, collapse engineering, or deterministic control systems. It offers the first universal test for detecting Rc-governed coherence persistence and forms a reproducible foundation for cross-vendor validation of RFT predictions
Present-day quantum processors are open systems in which dissipation and decoherence degrade the information carried by a quantum state as it propagates through a circuit. We study this degradation in dissipative random quantum circuits, modeling each two-qubit gate as a diluted unitary that interpolates between the intended unitary operation and a random dissipative quantum channel. Using the fidelity between the ideal and noisy output states as a diagnostic, we show that sufficiently random unitary gates or dissipative Kraus operators lead to a universal decay of the average fidelity. This decay is determined only by the dissipation strength, system size, and circuit depth, while microscopic details of the gates and noise, including the Kraus rank, appear only in subleading corrections to higher moments. We derive a closed-form expression for the average fidelity in terms of three physically meaningful error parameters, dissipation strength, coherent two-qubit gate-error strength, and connectivity-error probability. Finally, we identify the cases when dissipative effects can be reproduced by an unitary-noise model and when dissipation-induced decoherence remains distinguishable from coherent noise at the level of the average fidelity.
This note presents an RFT interpretation of an anomalous coherence persistence effect reported publicly in 2025 RCS benchmark data. Standard quantum-circuit expectations predict full thermalisation on noisy 16-qubit superconducting hardware by depth ~30, driving XEB toward zero and eliminating internal structure. Instead, the publicly reported metrics indicated XEB > 4, HOG > 0.8, and a measurable entropy deficit, revealing structured attractors in a regime where standard models predict complete chaotic dispersion. Relational Field Theory (RFT) provides a natural theoretical explanation for this behavior: the reported anomaly matches the expected signatures of a system entering a deep curvature-stiffened coherence well in the universal scalar field 𝑅 𝑐 R c , allowing attractor structure and causal memory to persist far beyond the expected decoherence horizon. This analysis presents a minimal RFT interpretation based solely on publicly released benchmark metrics. Note: This analysis uses only publicly released circuit metrics. It makes no claims about proprietary architectures, internal mechanisms, trade secrets, or patented methods. No inference is made about the mechanisms or design intentions of QSCE or any other proprietary system.
Unrecorded or ``forgetful'' measurements -- physically, a local dephasing channel -- can arise naturally as syndrome-measurement errors in fault-tolerant protocols and as uncontrolled decoherence in open systems. We numerically study random Clifford circuits in which recorded projective Z measurements compete with unrecorded (forgotten) Z measurements, focusing on the dynamical, finite-depth regime relevant to decoding and quantum memory. In the forget-only limit the global entropy density thermalizes at a rate independent of system size, and the forgetting rate at which thermalization sets in decays with circuit depth as a power law pf∗∼dv, consistent with the critical-depth scaling inversely with the noise rate found for related noisy-circuit quantities. With recorded measurements present, the mutual information I(A:B) -- which quantifies the recoverable correlation between the two halves -- develops a finite-depth peak whose height grows sub-extensively with N: its effective scaling exponent α(pf) decreases monotonically, so that forgetting drives the recoverable correlation from near-volume-law toward area-law scaling. We map the recoverability landscape in the (pm,pf) plane and show that forgetting destroys the measurement-induced purification transition. These results complement earlier stat-mech analyses of noisy monitored circuits and quantify the competition between measurement and forgetting relevant to quantum error correction.
Quantum circuits with a constant rate of depolarizing noise per qubit per time step are known to converge to the uniform distribution at depth ω(p−1logn), and hence become trivially classically simulable by uniform sampling. We show that under the physically natural constraint of geometric locality, noisy circuits become classically simulable at shallower depths by substantially more structured classical algorithms. We consider arbitrary geometrically local quantum circuits on n qubits, initialized in an arbitrary product state, with nearest-neighbor gates in O(1) spatial dimensions and interspersed depolarizing noise of any constant strength p. Our first result is that when the depth exceeds a threshold d∗=Θ(p−1logn), the output distribution can be approximately sampled in quasipolynomial time. This gives a worst-case simulability result for noisy geometrically local circuits, and matches in its n-dependence the best previously known results for noisy random circuits. The proof is based on new information-theoretic bounds showing that in geometrically local noisy circuits, local regions lose correlations and independently converge to maximally mixed strictly before the entire system converges to the uniform distribution. We further prove structural results suggesting a sharper transition at depth Θ~(p−1): after coarse-graining the lattice, Pauli weight supported on long connected paths can be truncated with exponentially small error. These results provide evidence for a percolation-like mechanism behind classical simulability at constant depth, and motivate our conjecture that all noisy geometrically local circuits admit quasipolynomial-time approximate sampling once circuit depth exceeds Θ~(p−1).