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Substrate Independent Topology Framework (SITF) topological error protection in quantum computing systems

DAVID GOLD

Published Mar 24, 2026• 0 citations
OpenAlex

Abstract

Three predictions derived from the Substrate Independent Topology Framework (SITF) concerning topological error protection in quantum computing systems. The predictions are entered into the prior art record before examination of any experimental dataset against which they would be tested. The registration timestamp is the operative prior art date. The three predictions concern: (1) local noise suppression scaling in a superconducting qubit chain engineered to enforce Fibonacci state space structure; (3) the substrate-independent suppression ratio per encoding depth level in Fibonacci-structured quantum systems across hardware platforms; and (4) a hierarchy of topological protection quality indexed to the attractor value of the state space recursion, distinguishing Fibonacci-structured from Ising-structured quantum systems. Each prediction is specific enough to be falsified by existing or readily obtainable experimental data from current quantum hardware platforms. The generative architecture that produces these predictions is not disclosed in this document. This preregistration establishes priority for the phenomenological predictions — what the framework predicts, where, and at what numerical values — without revealing the structural logic that generates them. The two are legally distinct and maintained separately. Note on prediction numbering: This preregistration covers P-QC-01, P-QC-03, and P-QC-04. P QC-02 is held pending completion of the substrate translation derivation required to state it with the operational precision a preregistration demands. P-QC-05 is withheld per standing protocol.

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Abstract Current quantum computing architectures rely on probabilistic error correction codes that scale exponentially with the number of logical qubits. This work proposes a conceptual shift toward resonance-invariant structures, where protection against certain classes of noise arises from global topological properties of the multi-qubit Hamiltonian rather than from local redundancy alone. The central object is a dimensionless sensitivity parameter Ψ = ρ / A, where ρ is the effective growth rate of perturbations and A is a measure of the local stability basin in the many-body Hilbert space. When Ψ remains below a critical threshold, specific decoherence channels are topologically suppressed. The framework is purely theoretical and does not claim hardware feasibility at present. It is offered as a starting point for discussion within the quantum error-correction and topological quantum computing communities.

•Mar 6, 2026•0 citations
Three predictions derived from the Substrate Independent Topology Framework (SITF) concerning topological error protection in quantum computing systems. The predictions are entered into the prior art record before examination of any experimental dataset against which they would be tested. The registration timestamp is the operative prior art date. The three predictions concern: (1) local noise suppression scaling in a superconducting qubit chain engineered to enforce Fibonacci state space structure; (3) the substrate-independent suppression ratio per encoding depth level in Fibonacci-structured quantum systems across hardware platforms; and (4) a hierarchy of topological protection quality indexed to the attractor value of the state space recursion, distinguishing Fibonacci-structured from Ising-structured quantum systems. Each prediction is specific enough to be falsified by existing or readily obtainable experimental data from current quantum hardware platforms. The generative architecture that produces these predictions is not disclosed in this document. This preregistration establishes priority for the phenomenological predictions — what the framework predicts, where, and at what numerical values — without revealing the structural logic that generates them. The two are legally distinct and maintained separately. Note on prediction numbering: This preregistration covers P-QC-01, P-QC-03, and P-QC-04. P QC-02 is held pending completion of the substrate translation derivation required to state it with the operational precision a preregistration demands. P-QC-05 is withheld per standing protocol.
The Event Density (ED) framework provides a substrate-level account of quantum computation in which three substrate quantities—local multiplicity (the count of available participation pathways at the system’s endpoints), cross-endpoint connectivity (the substrate-mediated bandwidth that links them), and commitment-injection rate (the rate at which the environment forces individuation)—jointly determine whether quantum computation is possible. The Unresolved-Regime Characterization Theorem (UR-1) identifies three independently necessary conditions on these quantities, and the resulting QC operating window is given structurally by τ_QC = min(τ_(i), τ_(ii), τ_(iii)) over the three corresponding failure timescales. Each architectural platform binds on whichever timescale is shortest under its protection strategy. Three architectural classes—engineered-low-multiplicity (A) covering superconducting qubits, trapped ions, and gate-model photonics; global-geometric-rigidity (B) covering topological qubits and photonic Chern channels; and high-multiplicity-redundancy (C) covering bosonic codes and multi-timescale photonics—exhaust the substrate-allowed strategies for holding the operational regime. Error correction, dynamical decoupling, reservoir engineering, and hybrid architectures are derived as compositions or extensions of the three classes rather than new strategies. The multiplicity-cap function M unifies the classes as three projections of one substrate object, with platform-specific behavior obtained by specializing class-dependent parameters. The framework’s strongest output is cross-platform unification: the matter-wave quantum-classical boundary observed empirically at 140–250 kDa molecular mass and the multiplicity walls that limit qubit-system scaling are the same substrate-determined boundary projected onto two different platforms, evaluated at consistent values of one underlying substrate constant. Sharp predictions follow directly: superconducting platforms encounter a hard scaling ceiling unless they are composed with logical-qubit encoding; topological qubits can outrun this ceiling exponentially in the topological gap if topology engineering can deliver stable structures; redundancy-based architectures saturate at a substrate-determined correlation budget. Four classes of near-term experimental tests with explicit falsification conditions are specified. The structural form of the framework is derived from substrate primitives; specific numerical thresholds (the critical multiplicity, the correlation budget, the maximum stable topological gap, and the platform-specific wall locations) are downstream empirical calibrations rather than free parameters, with the empirical anchors that fix them identified explicitly. The verdict is architectural-level structural completeness with an explicit empirical-calibration roadmap: the substrate-level account of quantum computation is delivered, the predictions are sharp enough to be falsified by near-term measurements, and the calibration program that converts structural predictions into platform-specific numerical bounds is engineering-tractable rather than theoretically blocked.
In superconducting quantum circuits, decoherence improvements are frequently obtained through process interventions that simultaneously modify surface chemistry, microstructural topology, and device geometry, leaving mechanistic attribution structurally underdetermined. Predictive materials engineering requires measurable structural statistics to be separated from geometry-dependent coupling coefficients into independently testable factors. We introduce the concept of classical and quantum microstructure. In that context, we formulate a channel-wise separable framework for decoherence in superconducting transmon qubits in which each loss channel is described by a reduced prescriptor. Here, a channel-specific microstructural state variable is determined independently of device geometry, and a geometry-dependent coupling functional is computable from field solutions without reference to surface chemistry. We derive this product form from a spatially resolved kernel representation and establish a perturbative separability criterion that defines the regime where independent variation of the variables is valid. The framework specifies five prescriptor classes for dominant loss pathways in transmon-class devices. Falsifiability is operationalized through a pre-committed 2x2 experimental protocol in which the variables must satisfy independent ratio checks within propagated uncertainty. A Minimum-Dataset Specification standardizes reporting for cross-laboratory inference. Part I establishes the conceptual and mathematical architecture; coordinated experimental validation is reserved for Part II.
Abstract Current quantum computing architectures rely on probabilistic error correction codes that scale exponentially with the number of logical qubits. This work proposes a conceptual shift toward resonance-invariant structures, where protection against certain classes of noise arises from global topological properties of the multi-qubit Hamiltonian rather than from local redundancy alone. The central object is a dimensionless sensitivity parameter Ψ = ρ / A, where ρ is the effective growth rate of perturbations and A is a measure of the local stability basin in the many-body Hilbert space. When Ψ remains below a critical threshold, specific decoherence channels are topologically suppressed. The framework is purely theoretical and does not claim hardware feasibility at present. It is offered as a starting point for discussion within the quantum error-correction and topological quantum computing communities.