Preregistered Tests of Local-Noise Predictions for GHZ Coherence Under Matched Qubit Environments on IBM Kingston

Abstract

DOI: 10.5281/zenodo.22283967Record set: EC-MECH campaign (EC-MECH-001 pilot + EC-MECH-002)Related to: EC-STORAGE-001, DOI 10.5281/zenodo.21299091 Research question: Can the coherence lifetime of an entangled multi-qubit state be predicted from the measured coherence losses of its individual qubits? Plain language summary When several qubits are entangled together, how fast does the entangled state lose its coherence compared with the qubits measured one at a time? The textbook expectation, if each qubit's noise is its own private business, is that the losses simply add up. This record tests that expectation directly on IBM hardware, and reports two experiments: one that returned ABSTAIN under its own preregistered rules rather than supporting a scientific conclusion, and a redesigned successor that did produce one. The first experiment failed for an instructive reason. Its quality gate asked whether the measured decay curves looked like clean exponentials, when the question that actually mattered was whether the decay rate had been pinned down precisely. Those are different things, and for shallow decays they come apart badly. Five measurements whose rates were known to within 4–6% were discarded because their curves were too flat for the goodness-of-fit statistic to work with. Under the frozen rules that cascaded into an ABSTAIN on every downstream question. The verdict stands unamended. Diagnosing that failure exposed a second and more serious problem: the single-qubit reference measurements had been performed in a different noise environment from the entangled measurements they were being compared against. The redesigned experiment fixed both problems and added a dedicated probe of the environment mismatch itself. The result: once the environments were matched, the discrepancies during plain idling became substantially smaller — especially for the 4- and 6-qubit states — but the preregistered precision was still insufficient to establish additivity. Under a standard error-suppression pulse sequence, additivity was rejected at all three sizes. And the dedicated probe confirmed the environment mismatch was real, not merely a theoretical worry. Total hardware cost: 241 seconds across both experiments. Background: an unsupported claim, entered into the record EC-STORAGE-001 (DOI 10.5281/zenodo.21299091) recorded a pre-registration miss — a bare-arm coherence witness crossing at 9.0 µs against a registered 10–30 µs band — and explained it by asserting that the payload resided in weight-4 stabilizer correlations "whose coherences decay at the sum of constituent rates." That explanation does not close numerically against data in the same deposit. The selected qubits had reported T₂ of 178–368 µs. A sum-of-rates model over four such qubits predicts a joint coherence time of roughly 45–60 µs; the measured value was 8.81 ± 0.30 µs. The stated model over-predicts by a factor of roughly 5–7. The claim was therefore a hypothesis written in the grammar of a derivation. It is entered in the adjudication ledger as UNSUPPORTED, and the EC-MECH campaign was constructed to either repair it or retract it. This deposit does not resolve it in EC-STORAGE-001's favour, and readers of that record should treat the mechanism sentence as withdrawn pending a direct test on the encrypted-cloning encoding itself. What we did Both experiments ran on ibm_kingston (156-qubit IBM Heron processor) on a connected 6-qubit chain, physical qubits [14, 15, 19, 35, 34, 33], selected by a frozen policy from the same-day calibration snapshot with no manual override. Neither experiment uses, requires, or reproduces the encrypted-cloning protocol. They test the underlying physics assumption in isolation, using GHZ states and idle delays only. No proprietary components are involved, and the deposited code is fully self-contained. EC-MECH-001 (pilot) — rate additivity Nested GHZ states on the first k qubits (k = 2, 4, 6) were idled for τ ∈ [0, 45] µs and their weight-k coherence read out via parity oscillation. In parallel, all six qubits were prepared in |+⟩ and idled simultaneously to obtain per-qubit in-situ dephasing rates. The frozen predicate compared the fitted GHZ decay rate Γ_k against the sum Σ Γᵢ of the measured single-qubit rates. 320 circuits, 1024 shots each, one job, 93 s QPU. EC-MECH-002 — coherence-function additivity The successor abandons fitted rates entirely. For any family, define c(τ) = C(τ) / C(0) χ(τ) = −ln c(τ) Under independent local phase noise, the GHZ phase is the sum of the local phases, so the coherence factorises exactly: χ_S(τ) = Σ_{i∈S} χ_i(τ) This identity assumes nothing about decay shape — exponential, Gaussian, stretched, and non-Markovian decays all satisfy it. The scientific object is the residual Δ_S(τ) = χ_S(τ) − Σ χᵢ(τ), adjudicated through the scale-free ratio r_S(τ) = Δ_S(τ) / Σ χᵢ(τ) as a preregistered equivalence test with margin |r| ≤ 0.15, using simultaneous 95% confidence intervals (Bonferroni, n = 8, z = 2.734). CI wholly inside the margin → ACCEPT; wholly outside → REJECT; overlapping the boundary → ABSTAIN. Two design repairs distinguish it from the pilot: No R² gate, no fitted rate, no assumed decay law. Matched noise environments. Every non-target chain qubit is pinned in |0⟩ — including the GHZ spectators at k < 6 — rather than left in |+⟩. This matters because a GHZ block is immune to intra-block ZZ coupling: |0…0⟩ and |1…1⟩ are both +1 eigenstates of Z_iZ_j, so the relative phase carrying the coherence is untouched. In the pilot, the single-qubit reference was exposed to neighbour-state-dependent dephasing consistent with this mechanism, while GHZ symmetry cancels intra-block static ZZ — biasing the prediction high. Single-qubit controls use a two-colour scheme on the chain (targets {14, 19, 34}, then {15, 35, 33}) so every target has all chain neighbours pinned. τ = 0 is oversampled at 4096 shots because it is the shared normaliser and its uncertainty enters every χ, inducing covariance that is carried explicitly in the analysis. Design parameters (frozen). Normalisation point τ = 0 at 4096 shots, never adjudicated. Eight informative τ points at 1024 shots each: 12, 18, 20, 22, 25, 28, 35, 45 µs The grid is pilot-informed and deliberately non-uniform: the low end starts at 12 µs because the D_min = 0.10 denominator gate would exclude earlier times once neighbour pinning reduces the local χ, and five of the eight points are clustered in the 18–28 µs window to resolve structure in Δ(τ) there. See the evidence ceiling for what this costs. Arms: bare (plain delay) and dd (symmetric XY4, one cycle). Four phase points per sweep, spanning one full period of the weight-k oscillation. Runtime dynamical decoupling and twirling disabled, so the arms are defined solely by the circuits. Diagnostic family diagPlus on the bare arm at τ ∈ {12, 25, 45} µs — all three exact members of the primary grid, so no interpolation is performed. Circuit execution order randomised under frozen seed 20260902. 376 circuits, 520,192 shots, one job, 148 s QPU against a preregistered estimate of ~139 s (6.1% error). Driver provenance. The EC-MECH-002 driver was hardened after the EC-MECH-001 pilot and before the EC-MECH-002 freeze. The hardening bound submission to the freeze manifest and to the binding layout report (removing hand-entered qubit chains), replaced diagnostic interpolation with exact grid indexing, added randomised circuit execution order under a frozen seed, and added a drift-robustness case to the offline validator. All of it predates the freeze; the deposited digest covers the hardened files, and no change was made after data was seen. Results EC-MECH-001 — ABSTAIN (frozen, unamended) All six weight predicates returned ABSTAIN. Cause: five single-qubit component fits failed the frozen R² ≥ 0.90 gate (bare q15 = 0.883, q33 = 0.873; DD q15 = 0.893, q19 = 0.871, q33 = 0.859) despite relative rate uncertainties of 3.7–5.5%. Because q15 participates from k = 2 onward, the failure cascaded into every weight. All 18 fits in the run had σ(Γ)/Γ ≤ 0.064. R² measures the fraction of variance in log C explained by the line; when a decay is shallow the true variance is small and ordinary scatter consumes a large share of it. R² was the wrong gate. The pilot did establish, as observation rather than verdict, that in-situ dephasing under simultaneous idling ran ~2.4–4.3× faster than the reported T₂ on every qubit (e.g. q35: 67.4 µs in situ against 292.9 µs reported). EC-MECH-002 — primary adjudication Arm k usable τ median r χ²/dof p Verdict bare 2 7 −0.217 2.40 0.0185 ABSTAIN bare 4 8 −0.014 0.62 0.7625 ABSTAIN bare 6 8 −0.087 1.16 0.3166 ABSTAIN dd 2 7 −0.396 5.46 <0.0001 REJECT dd 4 8 −0.213 5.36 <0.0001 REJECT dd 6 8 −0.206 6.90 <0.0001 REJECT Negative r means the GHZ state retains coherence better than the independently measured single-qubit coherences predict. The bare ABSTAINs are not a proof of independence. The equivalence predicate was built precisely so that "we could not reject zero" cannot be reported as "we demonstrated independence." At k = 4 and k = 6 the residual is small (−0.014, −0.087) and the confidence intervals straddle the ±0.15 boundary; the correct statement is that a positive equivalence claim was not supported at the preregistered precision. k = 2 warrants extra caution in both arms. It is the only weight that lost a τ point to the denominator gate, and because r = χ_S/D − 1 with the smallest denominator, it amplifies any bias in D more than the other weights. Its values (−0.217 bare, −0.396 DD) are the most extreme on the board and the least reliable. ZZ diagnostic (preregistered as diagnostic, excluded from the predicate) A dedicated family reproduced the pilot's all-|+⟩ environment to test whether intra-chain ZZ coupling really was contaminating the reference. The preregistered qualitative prediction was excess χ > 0