This work presents a structural critique of calibration-based control frameworks for superconducting quantum computing systems, with particular focus on architectures relying on recursive calibration loops and dependency graph formalism. It is shown that the current paradigm does not resolve the fundamental problem of physical instability, but instead formalizes it as an operational requirement. Continuous recalibration, parameter drift, and dependency-driven control structures indicate the absence of stable, reproducible computational states. The analysis demonstrates that the system does not admit a stationary operational regime, and that control is effectively shifted from physical determinacy to procedural scheduling. Directed acyclic graphs and calibration routines are shown to reorganize instability rather than eliminate it. Furthermore, the framework lacks invariant quantities, external validation criteria, and any demonstrated convergence toward stable configurations. Validation remains internal and self-referential, preventing the establishment of physically meaningful computational states. Scalability is assumed through automation, but no structural argument is provided to ensure bounded error propagation or stability under system growth. As a result, increasing system size amplifies the instability it attempts to manage. The work concludes that the calibration-based paradigm represents a systematic redefinition of instability as workflow. The resulting architecture does not achieve control of a quantum system, but continuous management of its failure modes.
This work presents a structural critique of calibration-based control frameworks for superconducting quantum computing systems, with particular focus on architectures relying on recursive calibration loops and dependency graph formalism. It is shown that the current paradigm does not resolve the fundamental problem of physical instability, but instead formalizes it as an operational requirement. Continuous recalibration, parameter drift, and dependency-driven control structures indicate the absence of stable, reproducible computational states. The analysis demonstrates that the system does not admit a stationary operational regime, and that control is effectively shifted from physical determinacy to procedural scheduling. Directed acyclic graphs and calibration routines are shown to reorganize instability rather than eliminate it. Furthermore, the framework lacks invariant quantities, external validation criteria, and any demonstrated convergence toward stable configurations. Validation remains internal and self-referential, preventing the establishment of physically meaningful computational states. Scalability is assumed through automation, but no structural argument is provided to ensure bounded error propagation or stability under system growth. As a result, increasing system size amplifies the instability it attempts to manage. The work concludes that the calibration-based paradigm represents a systematic redefinition of instability as workflow. The resulting architecture does not achieve control of a quantum system, but continuous management of its failure modes.
Abstract Long-run quantum execution remains fundamentally constrained, not primarily by gate infidelity, but by cumulative instability of the rotating phase reference during runtime. While contemporary quantum control stacks rely on calibration, dynamical decoupling, and quantum error correction, these mechanisms operate reactively and assume that the underlying phase frame remains valid between interventions. This assumption breaks down as execution depth, runtime, and system size increase. This note reframes long-run execution failure as a phase-frame stability problem rather than a post-fault correction problem. Using empirical hardware-adjacent observations, it shows that longitudinal drift is structured, temporally correlated, and often collective across qubits, placing it outside the effective bandwidth of fast-noise suppression techniques. As a result, computation is frequently admitted under metastable conditions in which logical error amplification occurs despite unchanged physical gate metrics. Based on this empirical and structural analysis, the note identifies a missing architectural element: a preventive drift-bounding layer that constrains phase-frame deviation before execution proceeds. The argument is intentionally architectural rather than implementational. No hardware-specific parameters, algorithms, or corrective primitives are disclosed. The purpose of this document is to establish why scalable quantum execution requires preventive phase stabilization at the execution boundary, and why reactive correction alone cannot remove this limitation. Detailed theoretical foundations, validation pathways, and hardware-compatible realizations exist but are intentionally excluded from this public note.
As superconducting quantum processors scale toward hundreds of qubits, manual calibration becomes increasingly costly and difficult to sustain. Here we address two system-level factors governing automated calibration, namely, crosstalk induced by parallel operations and temporal drift of control parameters. On a 66-qubit superconducting processor, cross-entropy benchmarking shows that single-qubit calibration tolerates full-chip concurrency with minimal fidelity loss, whereas CZ calibration requires a minimum coupler-graph distance of four to avoid elevated control errors. Continuous monitoring of representative qubit and coupler parameters further yields quantitative refresh rules that assign refresh priority by error-budget consumption. These results turn two conventionally heuristic choices, the concurrency density of calibration tasks and the refresh priority of each control parameter, into measurable operating rules. Implemented within an automated calibration framework, the rules support a six-qubit Greenberger-Horne-Zeilinger state with a zero-noise-extrapolated fidelity of 89.64%, distance-dependent logical-error suppression in a single-cycle repetition-code benchmark, and a reduction of the mean single-qubit error from 0.023 to 0.011 on a 337-qubit processor, providing an experimentally grounded reference for the automated calibration and maintenance of current and future large-scale superconducting quantum systems.
Quantum error correction protects logical information only when every physical operation remains below the fault-tolerance threshold, a condition that must be maintained continuously rather than only at the initial calibration. In practice, however, analog control parameters inevitably drift because of environmental fluctuations. As future fault-tolerant quantum computations are expected to run for days or even months, interrupting computation for repeated recalibration becomes fundamentally impractical. A promising alternative is to integrate calibration directly into computation by repurposing syndrome measurements as a calibration signal (Sivak et al, Nature 2026), but whether such self-calibration can be achieved with provable efficiency remains an open question. Here we establish a theoretical framework for such self-calibrating quantum fault tolerance. We prove that, for a broad class of control-induced errors, the detection rate defines a locally strongly convex surrogate objective for analog calibration with high probability. This geometric property enables a simple and efficient online optimization algorithm using only syndrome measurements collected during normal error correction. We prove convergence to an ε detection rate within O(1/ε2) epochs for time-independent drifts and also establish guarantees for time-dependent drifts. We further show that the convergence rate is independent of the code distance for quantum low-density parity-check (LDPC) codes. Pulse-level simulations of neutral-atom arrays and large-scale circuit-level Clifford simulations confirm these theoretical predictions. Our results establish self-calibrating fault tolerance as a provably efficient paradigm in which the same syndrome measurements simultaneously protect logical information and stabilize the underlying hardware.
This paper reframes quantum scalability as a structural fragility problem: when correlated disturbance propagation exceeds corrective capacity, stability fails even if local error rates look small. ZLT yields a single canonical bifurcation—an index threshold at NFI_QC < 1—that separates regimes where quantum computation remains controllable from regimes where it is structurally non-scalable. Paper 50E integrates the measurement problem, decoherence, and quantum error correction (QEC) into a unified ZLT diagnostic: a Network Fragility Index for quantum systems (NFI_QC) defined from disturbance propagation and control capacity under memory and correlation. The core result is parameter-free in form: stability admits a canonical regime when NFI_QC < 1, and becomes structurally unstable when NFI_QC ≥ 1, regardless of local mitigation tactics. Engineering thresholds (e.g., safety margins such as 0.8 or scale-separation ratios such as 0.1) are explicitly treated as calibrable guardrails, not universal constants. The paper provides a Passive Alignment Protocol (Via Negativa) for reducing fragility by selectively disabling high-cascade pathways and correlation amplifiers rather than increasing intervention force. A falsification pack (EF/QF) is included: the framework is refuted if correlated-error scaling, cascade monotonicity, or predicted regime transitions fail under operational proxies. Supplementary code is provided as an illustrative operational witness for qualitative dependence (not a universal estimator of hardware-specific maxima).
The transition from classical to quantum computation marks a shift from deterministic binary logic to a probabilistic, entanglement‑driven framework able to address problems beyond classical reach. Today’s Noisy Intermediate ‑ Scale Quantum era features devices that lack full error correction yet already point toward larger, modular systems designed for fault‑tolerant operation. This paper examines the evolving paradigm shift from classical and NISQ ‑ era machines toward practical fault‑tolerant quantum computing, focusing on how advances in physical qubit technologies, control architectures, and error‑correction strategies are converging to bridge noisy prototypes and scalable, useful machines. We synthesize insights from historical semiconductor scaling trends, contemporary roadmaps from leading institutions and industry, and emerging modular designs with real‑time error decoding. Our analysis shows that while challenges around decoherence, connectivity, and classical co‑processing remain, coordinated progress in hardware, control, and software is laying a coherent foundation for future quantum platforms. The work concludes that quantum computing is maturing into a strategically significant paradigm, poised to redefine the limits of computation in simulation, optimization, and secure communication.
**Building on our earlier structural analysis of gate-based quantum computing,** recent advances in quantum technologies have further sharpened a long-standing tension between continuous quantum dynamics and discrete logical computation. Despite decades of progress in qubit coherence, fault-tolerant coding, and hybrid NISQ architectures, current quantum devices remain fundamentally constrained by a structural mismatch between fluctuating quantum states and the stability requirements of digital logic.This work extends and unifies that analysis by providing a geometry-based account of these limitations and situating quantum computing within a broader comparative framework of next-generation computation paradigms. The contributions of this work are threefold:• Historical and technical analysis: We review the evolution from Feynman’s proposal to Shor’s algorithm and modern fault-tolerance theory, highlighting how the community gradually shifted toward NISQ-based noisetolerant strategies.• Structural diagnosis of quantum limits: Building on the Protiformframework, we show that quantum systems inherently realize continuous fluctuation manifolds, whereas logical computation requires discrete convergencesurfaces. Measurement is therefore a forced collapse between incompatible geometries, making full fault-tolerant digital logic rendering practicalfault-tolerant scaling prohibitive—not merely technologically difficult.• Comparative evaluation of post-von Neumann architectures: Using a set of structural criteria (digital stability, noise resilience, scalability,native gate realizability, generality, and materials feasibility), we evaluatemajor candidates—quantum, photonic, neuromorphic, analog solvers, andtopological computing. The analysis shows that topological computing isthe only architecture satisfying all structural requirements, owingto its intrinsic protection of logical degrees of freedom by global invariants.Taken together, these results suggest that the fundamental limitation of quantum computing is not technological but structural. Protiform provides a unifiedexplanation for this boundary, while also identifying topological computing as thestructurally consistent path beyond the von Neumann paradigm.