We consolidate a previously described IBM Quantum ibm_marrakesh compiled Shor-15 readout comparison (128 shots in a RAW configuration versus 8 shots in a preconfigured configuration) with three local, reproducible algorithmic analyses. First, an independent-binomial model quantifies the probability that a hypothetical 4-shot batch meets the original accepted-peak mass threshold of 0.60: at an assumed per-shot peak probability p=0.90 the pass probability is 0.947700, requiring p≈0.902389 for a 95% pass rate. Second, decision-preserving adaptive stopping of an eight-shot binary acceptance rule is proven pathwise by terminating at five accepted peaks or four failures. Under IID p=0.90 it requires 5.544908 shots on average, a 30.69% expected count reduction while preserving the fixed-eight-shot decision, conditional on per-shot feedback. Third, phase-denominator lifting tests a multiple of the measured phase denominator against modular order and factor constraints. For the period-informed compiled N=15, a=2 example this recovers factors from outcomes 0100, 1000 and 1100, versus two directly informative outcomes under the stricter denominator-only diagnostic. A five-shot intermediate candidate achieves a 0.988443 model probability for the joint peak-mass and lifted-evidence criterion at p=0.90, compared with 0.940581 for four and 0.994877 for eight. No new IBM QPU execution, hardware 32× speedup, independently measured throughput improvement or blind Shor period-finding result is claimed. We supply executable scripts, tests, archived local outputs, limitations, and a proposed matched-hardware validation protocol.
We consolidate a previously described IBM Quantum ibm_marrakesh compiled Shor-15 readout comparison (128 shots in a RAW configuration versus 8 shots in a preconfigured configuration) with three local, reproducible algorithmic analyses. First, an independent-binomial model quantifies the probability that a hypothetical 4-shot batch meets the original accepted-peak mass threshold of 0.60: at an assumed per-shot peak probability p=0.90 the pass probability is 0.947700, requiring p≈0.902389 for a 95% pass rate. Second, decision-preserving adaptive stopping of an eight-shot binary acceptance rule is proven pathwise by terminating at five accepted peaks or four failures. Under IID p=0.90 it requires 5.544908 shots on average, a 30.69% expected count reduction while preserving the fixed-eight-shot decision, conditional on per-shot feedback. Third, phase-denominator lifting tests a multiple of the measured phase denominator against modular order and factor constraints. For the period-informed compiled N=15, a=2 example this recovers factors from outcomes 0100, 1000 and 1100, versus two directly informative outcomes under the stricter denominator-only diagnostic. A five-shot intermediate candidate achieves a 0.988443 model probability for the joint peak-mass and lifted-evidence criterion at p=0.90, compared with 0.940581 for four and 0.994877 for eight. No new IBM QPU execution, hardware 32× speedup, independently measured throughput improvement or blind Shor period-finding result is claimed. We supply executable scripts, tests, archived local outputs, limitations, and a proposed matched-hardware validation protocol.
This publication freezes the first completed evidence block of a joint Adriano Ciardo Labs (ACL) - TERRA-OUX validation programme spanning quantum-hardware resource use, classical quantum-emulation/QEC kernels, real-QPU context, and high-throughput chemistry screening on Aurora. The purpose is not to combine heterogeneous performance numbers into a single universal acceleration claim. Instead, each result is preserved within the computational boundary in which it was measured, and ACL terminology distinguishes independent verification of supplied execution evidence from independent re-execution. For the IBM Quantum line, the archived matched A/B record on backend ibm_marrakesh compares a RAW compiled Shor-15 order-readout run using 128 shots with a TERRA-OUX preconfigured run using 8 shots. Both passed the same predefined peak-mass threshold; the TERRA-OUX run therefore records an exact 16.0x shot-count ratio for this component. The compiled ISA depth changed from 104 to 63 and CZ operations from 27 to 18. Client wall time was approximately 16.59 s versus 16.84 s, so the result is explicitly not a 16x wall-clock speedup. Classical closure recovered order r=4 and factors 3 and 5. For the standard-PC QCEA line, ACL protocol-locked the frozen dense-GF(2)-reference versus sparse/vectorized syndrome benchmark. The locked local measurement files record a dense median reference time of 0.190476750 s, a vector median display time of 0.000021000 s, 1000 timed repetitions, exact bit-for-bit syndrome equality and a recorded median acceleration factor of 9070.353x. The acceleration applies only to the defined GF(2) component kernel. A historical matched whole-emulator A/B measurement remains separately recorded at 2.538x. For the OUXCHEM line, ACL independently verified the consolidated execution evidence for predeclared staged-spectrum workflows. Aurora results were 12.313x, 23.749x and 52.812x when detailed surrogate spectra were retained for 10%, 5% and 2% of candidates respectively, with corresponding local reference values of 21.038x, 58.162x and 119.584x. These are staged screening/routing measurements under changed predeclared output contracts, not identical-output speedups over VASP, Quantum ESPRESSO, CP2K, PySCF or another high-fidelity electronic-structure package. A later corrected Aurora R4 run established 11.275x 12-tile kernel scaling with 93.9585% efficiency; the earlier malformed rank-mapping subtest is retained as invalid for distributed-scaling claims. The accompanying Zenodo deposit includes reader-executable IBM and QCEA source code without source-code comments, extensive README and user-manual files, machine/protocol evidence, SHA-256 manifests and a non-commercial research-use license. Readers are encouraged to rerun the packages and publish the results they actually obtain, whether favourable or unfavourable.
Order finding is the core subroutine of Shor's algorithm. On NISQ hardware, phase estimation output distributions are often distorted by noise, making correct order recovery difficult. We study recoverability in noisy order finding: given a measured precision-register distribution, when does standard classical post-processing still return the true order? We analyze 680 distributions from IBM quantum systems across problem instances and circuit settings. For each distribution, we apply continued-fraction post-processing with modular verification and define recoverability as whether the recovered order equals the true one. We characterize each distribution using four features: autocorrelation peak strength, normalized entropy, dominant verified mass fraction, and verified margin fraction. We evaluate these quantities using marginal feature comparisons, single-feature AUROC analysis, and multivariate tree-based classifiers. We use random-forest permutation importance to assess which quantities contribute distinct predictive information once the other features are known. To make classification behavior interpretable, we train a decision tree that exposes threshold rules for recoverable and non-recoverable distributions. We find that recoverability is strongly associated with residual comb-like structure in the measured distribution and the way verified probability mass is organized across candidate denominators. The dominant verified mass fraction is the strongest single-feature indicator of recoverability, and tree-based analysis shows it also provides the primary split in an interpretable threshold description. Some highly distorted distributions remain recoverable when one verified denominator dominates the post-processing mass, while some visibly structured distributions fail because classical post-processing favors an incorrect verified denominator.
Order finding is the core subroutine of Shor’s algorithm. On NISQ hardware, its phase estimation output distributions are often distorted by noise, making correct order recovery difficult. We study recoverability in noisy order finding: given a measured precision-register distribution, when does standard classical post-processing still return the true order? We analyze 680 distributions collected from IBM quantum systems across multiple problem instances and circuit settings. For each distribution, we apply continued-fraction post-processing with modular verification and define recoverability as a binary outcome according to whether the recovered order equals the true one. We then characterize each distribution using four features: autocorrelation peak strength, normalized entropy, dominant verified mass fraction, and verified margin fraction. We evaluate these quantities using marginal feature comparisons, single-feature AUROC analysis, and multivariate tree-based classifiers. We further use random-forest permutation importance to assess which quantities contribute distinct predictive information once the other features are known. To make the resulting classification behavior interpretable, we also train a decision tree that exposes threshold rules for recoverable and non-recoverable distributions. We find that recoverability is strongly associated with both residual comb-like structure in the measured distribution and the way verified probability mass is organized across candidate denominators. The dominant verified mass fraction is the strongest single-feature indicator of recoverability, and the tree-based analysis shows that it also provides the primary split in an interpretable threshold description. Some highly distorted distributions remain recoverable when one verified denominator dominates the post-processing mass, while some visibly structured distributions fail because classical post-processing favors an incorrect verified denominator.
Quantum circuit execution estimates output distributions by repeated measurements, yet developers commonly choose a fixed shot budget before execution. This static choice is brittle: low budgets can under-sample the distribution, while high budgets waste measurements. In this paper, we present StableShots, a black-box online stopping rule for static quantum circuits. The method executes a fixed circuit in small batches, monitors the total-variation distance between cumulative empirical distributions, and stops after repeated evidence of local stability. We evaluate StableShots on 180 QSimBench traces spanning six circuit families, six sizes from 4 to 14 qubits, and five noisy IBM simulated backends. With validation-only calibration and 100 repeated backend-holdout splits, the selected configuration reaches TVD <= 0.05 on all held-out test evaluations with median 7,650 shots, whereas fixed-shot baselines either fail more often or spend substantially more shots.
This paper takes the first step towards hardware evidence for The Quantum Pi Benchmark (QPB) under its provenance (P) and blindness (B) axes and non-total capability grid (R). Using IBM Heron r2 Quantum Processing Units (QPUs), this paper reports findings to support P0/B0/R2 compiled-address amplification and P1/B0/R3 only for the loaded-content equality-predicate family, spanning 220 logical results and 324 job records. In the compiled-address family, single-iteration efficiency is approximately 66% through 110 routed CZ gates and falls to roughly 15% at the traceable larger instances. The two recoverable N = 512, k = 1 executions used 270 CZ gates and returned 84 marked outcomes in 32,768 shots, or 0.256% (95% Wilson interval 0.207%–0.317%), 1.31 times the uniform expectation. Matched true, scrambled, and zero controls show that this signal amplifies a compiled mark rather than evaluating Pi content. A content-addressed Quantum Read Only Memory (QROM) bridge and a coherent block-equality negative result are retained as P1/B0 diagnostics. Loaded-content equality separates supplied Pi blocks from corrupted controls: the monolithic discrimination gap decreases from 0.780 at six bits to 0.132 at 24 bits. Across three matched transpiler placements, tiled equality gives gaps of 0.761 ± 0.004, 0.404 ± 0.153, 0.344 ± 0.037, and 0.128 ± 0.034 at 6, 12, 18, and 24 bits, respectively, where uncertainties are descriptive sample standard deviations. The replicated mean routed-cost reduction is 29%–41%. Phase-pair circuits are classified as P1/B0 diagnostics rather than R3: five non-overlapping spans per control, ten circuits total, were submitted in one quantum hardware job. They recover 106/106 expected signs in each control with mean edge magnitudes 0.964 and 0.951. These are bounded results that do not establish direct digit access, controller-blind search, collision finding, frontier performance, or end-to-end advantage.
This paper evaluates quantum recovery of minimal cut set (MCS) structure across eight IBM hardware runs spanning four runtime arms (A1–A4) and two backends (ibm_torino and ibm_marrakesh), using an independent raw-counts recomputation as the authoritative analysis layer. Each arm combines a resilience level (RL0, RL1, or RL2) with a dynamical decoupling (DD) setting (on or off), applied to CL-QUBO fault tree circuits encoding 8 reactor-scale pilot subtrees from a prior hardware study. Each run submitted 8 primitive unified blocs (pubs), one per subtree, at 8,192 shots each with bind parameters [0.2, 0.2]. The canonical analysis spans 64 pubs and 12,800 top-200 rows with zero unresolved issues. The principal finding is that the IBM hardware runs produced nonzero exact and nonzero superset MCS recovery. Across the study, mean top-200 exact hits were 16.6 per pub (range 10.4–22.6 across runs), mean exact MCS mass was 0.074, mean exact-or-superset mass was 0.820, and mean superset-nonexact mass was 0.746. Recovery is present but is not dominated by exact MCS outcomes: approximately 91% of the recovered exact-or-superset probability mass lies in superset-nonexact structure. ibm_torino showed descriptively stronger exact recovery (mean exact hits 20.8 versus 12.5 for ibm_marrakesh), while ibm_marrakesh showed descriptively stronger broad superset-heavy recovery (mean superset hits 146.4 versus 134.3 for ibm_torino). An earlier scorer-layer analysis yielded a zero-recovery interpretation; the independent raw-counts recomputation showed that this was an artifact of a contract mismatch and supersedes the earlier result. This paper does not claim quantum advantage.