Structured quantum circuits are often summarized by low-dimensional records. Records lose control-dependent information when they merge outcomes whose probabilities respond differently to circuit parameters. We assess this loss without a parametric hardware-noise model or low-dimensional statistical family. Quantum Fisher information bounds premeasurement sensitivity; Fisher metrics of measurements and records describe device-attainable sensitivity. A Hellinger residual measures the response removed by a record, while its local quadratic term is the conditional covariance of the full-outcome score. Simultaneous confidence bounds support approval, refusal, or deferral.
We prove a finite-library completion theorem: executable augmentations terminate with either a record preserving every declared response or proof that no library augmentation removes the loss. For an analytic control germ, integral closures characterize preservation along every analytic control arc, and finitely many Rees valuations detect failure. This state--measurement--record chain connects an all-arc criterion to executable completion or refusal, an attainable-Fisher local kernel criterion, and finite-sample decisions.
A three-qubit calculation separates measurement loss from record loss. IBM experiments on Kingston and Marrakesh test decisions in fixed-particle-number and GHZ families, including negative controls. An end-to-end Kingston experiment reduces calibration shots by 33.3% while meeting prespecified noninferiority criteria on two held-out objectives. In two-epoch IQM Garnet data, median record-level drift is 0.0797 times full-distribution drift, but a significant residual remains in 35 of 36 settings. These experiments validate failure detection on the tested circuits; they do not establish universal compression performance or device quantum Fisher information.
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24 pages, 4 figures; supplementary material included
Structured quantum circuits are often summarized by low-dimensional records. Records lose control-dependent information when they merge outcomes whose probabilities respond differently to circuit parameters. We assess this loss without a parametric hardware-noise model or low-dimensional statistical family. Quantum Fisher information bounds premeasurement sensitivity; Fisher metrics of measurements and records describe device-attainable sensitivity. A Hellinger residual measures the response removed by a record, while its local quadratic term is the conditional covariance of the full-outcome score. Simultaneous confidence bounds support approval, refusal, or deferral.
We prove a finite-library completion theorem: executable augmentations terminate with either a record preserving every declared response or proof that no library augmentation removes the loss. For an analytic control germ, integral closures characterize preservation along every analytic control arc, and finitely many Rees valuations detect failure. This state--measurement--record chain connects an all-arc criterion to executable completion or refusal, an attainable-Fisher local kernel criterion, and finite-sample decisions.
A three-qubit calculation separates measurement loss from record loss. IBM experiments on Kingston and Marrakesh test decisions in fixed-particle-number and GHZ families, including negative controls. An end-to-end Kingston experiment reduces calibration shots by 33.3% while meeting prespecified noninferiority criteria on two held-out objectives. In two-epoch IQM Garnet data, median record-level drift is 0.0797 times full-distribution drift, but a significant residual remains in 35 of 36 settings. These experiments validate failure detection on the tested circuits; they do not establish universal compression performance or device quantum Fisher information.
This manuscript presents a methods-forward, operational protocol for evaluating whether any structured dependence remains in quantum-computing measurement records after explicit modeling of standard quantum and device-level mechanisms. Classical definiteness is defined at the record layer, and pre-record states are treated as predictive descriptions rather than as classical outcome facts. Within this operational stance, the protocol converts questions about outcome status and record formation into a falsifiable test program grounded in preregistered analysis rules and standard measurement telemetry. A locked null-model family is specified in advance, incorporating standard quantum dynamics together with documented device-level mechanisms including drift, correlated and non-Markovian noise, crosstalk proxies, and leakage indicators. The framework provides operational definitions, a conservative postulate set, preregistered endpoints, residual-adjudication criteria, negative controls, a fixed windowing discipline, and a bound-first reporting standard designed to yield informative constraints under null results. Any candidate contribution beyond the declared null family must appear as structured, reproducible residual dependence that survives the locked null family and the full residual-filter sequence. Version 4.4 refines the protocol specification, clarifies evidentiary boundaries, and strengthens the integration of the synthetic demonstration. The manuscript includes a fully specified classical simulation that executes the decision pipeline under controlled conditions. The synthetic study illustrates how the protocol classifies a bounded-null case, a measured-artifact case, a partial-artifact/unresolved-covariate case, an injected structured-residual case, and a failed-topology case. This demonstration establishes computational executability of the protocol and clarifies the behavior of the decision tree, but it does not constitute empirical evidence for any physical mechanism. Because the protocol relies only on standard measurement telemetry and preregistered analysis rules, it is directly implementable across contemporary quantum-computing platforms and does not depend on any single dataset, backend, or hardware realization. The manuscript is a specification paper: it defines a reproducible evidentiary framework for record-level claims, while large-scale empirical implementation, hardware benchmarking, and cross-platform replication remain subsequent studies.
Calibrated support observations can constrain a complete quantum instrument without identifying its action by unrestricted tomography. We study what those observations guarantee when the noise law is not supplied. On a fixed four-dimensional incidence-record experiment, we define the set of all complete two-outcome completely positive instruments compatible with the exact raw rejection and outcome probabilities, retaining the classical flags. Exact ideal data identify the target, but an explicit family of complete instruments reproduces the nonzero-data category laws of a low-error contamination device while admitting coherent error of square-root order. A target-ray mass certificate and a common complete-dilation comparison give a universal upper, while an exactly feasible rational instrument supplies a stronger lower witness. At the diagnostic parameter r = 1/300000000, the unhalved target-relative worst-case radius lies between 0.000258065115532250 and 0.000951566242566. The result separates avoidable inequality conservatism from information absent from the measured data. Fixed-functional and fixed-map optimizations have separately certified scopes; they do not solve the global radius. The conclusions are conditional on the supplied carrier, calibration and common-device model. They do not establish an apparatus, device-independent certification, a finite-sample power guarantee or complete formal verification. Selected supporting declarations have one recorded successful Lean 4.19.0 macOS execution and declaration-specific source, type and axiom review; this is not an end-to-end formalization.
This work separates several physical and theoretical burdens that are often grouped together under “the quantum measurement problem” and develops an experimentally answerable test of one of them: outcome-conditioned continuation. The proposal does not treat measurement as one indivisible physical event. It distinguishes the admission of a measurement interaction and apparatus, durable record formation, later availability of that record, agreement among physical carriers, global outcome standing, quantum-probability weighting, and the rule governing what physical or predictive description continues after an outcome. These burdens can remain open or fail independently. The principal experimental proposal is the Quantum Continuation Closure Test (QCCT). QCCT-I asks whether two physically distinct proper-mixture preparation procedures that are represented by the same admitted standard quantum state can produce different later statistics after the same admitted first measurement. The canonical preparation pair consists of equal-weight Z-basis and X-basis proper mixtures that are represented by the same maximally mixed qubit density operator under standard quantum mechanics. A fixed standard quantum instrument cannot depend on which proper-mixture decomposition produced that state. Published generalized state-update rules provide explicit theory-side foils for which the preparation decomposition can instead remain relevant to the postmeasurement continuation. Ordinary quantum physics is given first refusal. Preparation mismatch, improper-mixture substitution, calibration failure, different first-measurement seats, preparation side channels, ordinary non-Lüders instruments, temporal process memory, and independently warranted expansion of the physical reference must be tested at their own declared scopes before a stronger preparation-indistinguishability violation can be inferred. QCCT therefore does not treat deviation from an ideal Lüders prediction, failure of one fitted instrument, or a preparation-dependent sequential signal as immediate evidence for new quantum dynamics. The comparison architecture escalates from fixed-instrument closure to finite-horizon process-tensor closure and only then to stronger bounded residual claims. The experiment is modular. Prospective QCCT-I execution, process-memory characterization, coarse-graining invariance, archival-data analysis, and later distributed partial closure may contribute distinct local results. A result transfers to a later experiment only through an explicit interface preserving the relevant physical carrier, reference, scope, calibration, provenance, and unresolved burdens. The deposit also contains a machine-auditable formal surface. One consolidated Lean file contains two scientifically distinct Quantum Measurement modules: Seam G, concerning Born weighting / quantum probability measure, and QCCT-I, concerning preparation-indistinguishability / outcome-conditioned continuation. Their shared file packaging does not merge their objects, burdens, evidence states, dispositions, or claims. Both generic machine dispositions remain Not Yet Adjudicable. Seam G retains open domain-owned probability-admission burdens. QCCT-I retains open empirical preparation, reference, measurement, side-channel, comparator, and adjudication burdens. The consolidated Quantum Measurement contracts-and-adapters file was appended directly beneath the unchanged Structural Flow Universal Kernel and elaborated cleanly twice during the release audit. Clean elaboration establishes only that the encoded contracts and adapters coexist coherently at their declared formal scopes. It does not derive the Born rule, establish the physical validity of the generalized continuation family, demonstrate preparation equivalence, close the ordinary quantum comparators, establish an anomaly, falsify standard quantum mechanics, or select an interpretation of quantum measurement. The physical answer remains the responsibility of experiment.
Abstract Decoherent-histories methods identify time-extended alternatives whose diagonal weights may support probabilistic interpretation, while environmental-record approaches ask which alternatives a specified observer can recover. We formulate their intersection as a finite branch-record packing problem generated from one cross-branch construction. A codebook is admissible only if its declared coarse-graining obeys a bounded probability-sum-rule error and its accessible states can be decoded under a specified observer policy with finite error. Uniform reweighting defines a geometric packing number; a communication interpretation additionally requires a preparation instrument. Retrospective resolution is stricter: the base history family is exhaustive, selected histories must cover sufficient physical diagonal weight and be individually recoverable, and the same declared quantum-to-classical measurement channel used for decoding must preserve approximate consistency after histories are refined by its registered outcomes. This measurement-refined condition quantitatively controls the difference between the actual outcome distribution and the normalized diagonal classical-quantum prediction. For uniform branch-record packing and its communication realizations, general converses follow from accessible dimension, fixed outcome count, Holevo-Fano information, and hypothesis testing. Exact models quantify record compression, access, memory, measurement policy, temporal dependence, and shared latent errors. In a jointly realized four-bit benchmark, scalar consistency and recovery admit six histories, whereas direct measurement-refined consistency under the declared local Helstrom instrument admits four at the same tolerances. Finite-sample procedures distinguish held-out recovery achievability, structure-conditional consistency certification, structural converses, independently constructed parameter intervals, and abstention.
Quantum processors are now used as feature generators for classical models on tabular data. A circuit encodes each record, the device returns expectation values, and a classical model learns from them. A recent report claimed large gains from such features, gains that appeared only on noisy hardware. These claims are hard to check, because a quantum device is not a static function. Its state changes from job to job and from one calibration to the next, and that drift can leak information about the outcome into the features. We propose a five-step protocol for testing claims of this kind. It runs a circuit that carries no data in the same jobs as the real one. It checks whether the hardware leaves a recognizable mark on each job. It compares random and natural assignments of records to jobs, replays the null results under other submission orders, and closes the leak with a job-purged backtest. We apply it, pre-registered, to the HSBC and IBM study of fill probabilities in bond trading, which reported a large hardware-only gain. We use a public analog task and run the study's circuit on a 129-qubit chain of an IBM Heron processor. Under controlled assignment the hardware features give no gain over classical features, and the device reproduces the ideal features about as well as shot noise allows. Yet every job carries a distinct fingerprint. A circuit with no data at all predicts fills well above chance when records are batched by outcome and the same job sits on both sides of the train/test split. Removing that overlap removes the effect. The protocol costs under an hour of processor time and is designed for any hardware feature or kernel pipeline on tabular data.
H. Billah and M.M.H. Sarker contributed equally to this work. Interpreting a fixed quantum circuit's output as evidence of a hardware effect requires ruling out two things usually conflated with it: finite-sample fluctuation, and structure already present in the circuit's own noiseless output. Less commonly checked is a third: whether the reference circuit compared against is the one actually executed, once compiler-level qubit routing is accounted for. We execute a fixed 35-qubit, 243-gate diagnostic circuit on IBM Heron-family hardware (three runs, two backends) and show this third check is essential: the routed circuit submitted to hardware has different noiseless predictions than the logical circuit intended, for several qubits. Against the correct, routed-circuit reference, the aggregate deviation is significant in two of three runs, and four registers (0, 9, 14, 27) show a significant output-probability deviation in every run — though we distinguish a high-confidence subset, {0, 9, 27}, with tightly time-matched calibration, from qubit 14, included only on an exploratory basis given its calibration was retrieved roughly two weeks post-execution. Same-backend replicates correlate more strongly by the Pearson measure, though a rank-based (Spearman) test shows this gap does not survive at the level of register ordering, indicating substantial leverage from a small number of registers rather than a broadly robust pattern; these three executions also share a byte-identical payload and are not independent replications in the strictest sense. The mechanism is only partially resolved: independent single-qubit readout error and raw gate count are ruled out as complete explanations for most of these registers, but the simplest version of the leading hypothesis for the single most-affected register does not reproduce the observed cross-backend pattern even with live, backend-specific timing data. A second, structurally different circuit validated only in simulation calibrates the statistical procedure's behavior under one synthetic noise model; it does not itself establish generality to real hardware, and the specific register set found here should not be expected to generalize beyond this study. Note on scope: this is a methodology and case-study contribution centered on executed-circuit references for fixed-circuit diagnostics, not a characterization of IBM Heron hardware in general or a randomized-benchmarking experiment in the formal sense. Supporting data, the routed OpenQASM circuits, raw measurement counts, and analysis code for this study are available on request from the corresponding author. Affiliation: Sonicium Quantum Lab Ltd., Dhaka, Bangladesh.